Adaptive Edge–Cloud Framework for Real-Time Smart Grid Optimization with IIoT Analytics

Abstract

The large-scale integration of Distributed Energy Resources (DERs) in smart grids creates challenges related to real-time optimization, system scalability, and operational security. This paper presents GridOpt, a hybrid edge–cloud framework designed to address these challenges through distributed intelligence and coordinated control. In GridOpt, edge nodes handle latency-sensitive tasks, while cloud resources support the processing of large-scale grid data. Security is addressed through the integration of homomorphic encryption and blockchain-based consensus, together with an interoperability layer that enables coordination among heterogeneous grid components. Simulation results show that GridOpt achieves an average latency of 76 ms and an energy consumption of 25 Joules under high-throughput conditions. The framework further maintains scalability beyond 10 requests per second with a resource utilization of 54% in dense deployment scenarios. Comparative analysis indicates that GridOpt outperforms ECCGrid, JOintCS, and EdgeApp across key performance metrics.

1. Introduction

Including DERs in the smart grid system changes the whole process of energy generation, transmission, and consumption [1]. The increase in the use of renewable energy sources such as solar panels and wind turbines, as well as the development of energy storage solutions, has led to a shift from the conventional central power grid system to a decentralized system [2]. The concept of IIoT has made it easy for data to flow from one component to another. The aspect of edge computing and cloud services has become vital in dealing with the data generated by the system [3].

The traditional smart grid infrastructure, which relies on smarter infrastructure, has come with a number of challenges that are not ideal for perfect functionality. Scalability is one of the challenges that come with the integration of IIoT technology and DERs. There is a high level of data that this system is not capable of handling [4]. The reliance on cloud computing incurs latency that makes this system not ideal for addressing problems that need quick solutions [5]. The system has security risks that can easily fall through its edges since they are not capable of handling security issues [6].

We aim to design a comprehensive solution that is capable of handling the existing problems associated with the infrastructure of a smart grid. The key question that is essentially being sought through this research work is as follows: How can a hybrid edge–cloud solution be designed in a manner that ensures it is capable of offering optimal functionality in real time as well as scalability and enhanced security for a smarter grid infrastructure that is connected to energy resources through IIoT analysis technology?

The proposed solution involves the development of a hybrid computational model that integrates resources from edge and cloud computation. Data processing and analysis from the IIoT, as well as the use of edge computational devices, initiate immediate decision-making related to the critical activities in the power grid. Cloud computing provides comprehensive storage of information and complex analysis involving resource-intensive computations and machine learning techniques required for prediction and maintenance. Dynamic security systems that can develop improved designs and implementations of blockchain technology can enhance security against the flow of information related to the use of edge devices and cloud computing. The operational scenario of the proposed system is illustrated in Figure 1.

The significant contributions related to the proposed solution can be identified as follows:

• Develop a scalable and efficient architecture that balances computational loads between edge and cloud resources to optimize real-time operations in smart grids.
• Create advanced machine learning models to enhance predictive maintenance capabilities, improving grid reliability and reducing operational costs.
• Introduce adaptive security measures and establish interoperability frameworks to secure communications and device integration within the grid.

The structure of this paper is outlined as follows: Section 2 reviews the relevant literature. Section 3 details the proposed hybrid edge–cloud framework. Section 4 discusses the findings. Finally, Section 6 summarizes the conclusion.

2. Literature Review

The integration of DER devices in the smart power grid has been thoroughly analyzed in previous studies, and the latest development focuses on the implementation of edge computation and the IIoT solution to increase the efficiency of the power grid. The design of the edge computation system has been proven to significantly eliminate the delay and improve the real-time decision-making process [7]. In the proposed system architecture, the principle of distributed analysis has been employed to support the real-time monitoring and control of the DER devices but sometimes faces the challenge of scalability when more devices are connected through the implementation of the IIoT solution [8].

Cloud infrastructure has been used to implement the integration of machine learning techniques that support the prediction maintenance function and the smart power grid [9]. On the other hand, fog computing has been considered as a solution to bridge the remaining gap between the cloud and the edge. Fog computing has been recognized to aim at delegating some computation workload from both the cloud and the edge to the fog node [10]. However, the availability of the fog node tends to limit the efficiency of the fog computation.

For the security-related issues, the incorporation of blockchain-based security systems has been included to ensure the safety of communication among the components [11]. The computational complexity involved in the use of the blockchain system, particularly the PoW or PBFT algorithm-based systems used during the consensus phase, can hamper the system performance, especially when used in resource-limited devices at the edge of the network [12]. Although the challenge of computational complexity has been addressed through the introduction of less complex consensus algorithms like the Directed Acyclic Graphs (DAGs), the lack of scalability and standardization has limited their integration in the smart grid network [13].

Interoperability challenges were overcome by the design of the internet communication protocol used for devices employed in the smart grid infrastructure to improve the IIoT [14]. The implementation of the new norms brings about drastic changes to the already existing infrastructure. The ontology framework has been studied for enhancing semantic interoperability. This assists devices in exchanging significant information across diverse systems [15].

Hybrid edge–cloud architecture has been used to divide the workload of the edge–cloud based on the type of the involved data [16]. Artificial intelligence techniques involving LSTM and CNN models have been employed to improve the prediction analysis during maintenance and anomaly occurrences [17]. Another area of interest has been energy efficiency for the optimization of the smart grid [18]. Energy-efficient techniques involving hardware acceleration through the use of FPGAs and ASICs have been proposed to reduce the consumption of electricity during periods of high processing capacity [18].

Recent advances in IoT-enabled smart grid intelligence include frameworks that integrate advanced machine learning and privacy techniques to improve real-time prediction and energy optimization. A federated learning and homomorphic encryption-based IoT smart grid framework was proposed for secure energy consumption prediction [19]. Privacy-preserving machine learning applications in IoT-integrated smart grids, highlighting challenges and opportunities in deploying ML models under resource constraints, are surveyed by [20]. Earlier, a distributed edge computing-based green smart grid architecture was developed to demonstrate efficiency and reliability improvements [21]. The comparison of related approaches and the proposed framework is presented in

Table 1. Comparison of existing approaches and the proposed GridOpt framework.

Ref.	Previous Work	Proposed Work (GridOpt)
[7]	Edge systems reduce latency but lack scalability for large DER networks.	Scalable edge–cloud coordination suitable for expanding DER environments.
[9]	Cloud-based ML improves prediction but delays real-time responses.	Real-time tasks handled at the edge; cloud reserved for large data processing.
[11]	Blockchain secures communication but traditional consensus is computationally heavy.	Lightweight consensus and encryption to reduce processing cost at devices.
[14]	IoT improves connectivity but lacks unified interoperability across device types.	Interoperability layer to coordinate heterogeneous device environments.
[17]	ML enhances prediction but becomes resource-intensive for continuous workloads.	TDNN/HTM design lowers processing overhead during streaming operation.
[19]	Privacy models exist but lack unified optimization across system layers.	Integrated optimization with privacy and coordination in one operational framework.

.

3. Proposed Framework

This proposed framework provides a novel hybrid edge–cloud system design. The proposed system enhanced the real-time computation process of the smart grid environment, incorporating the integrated DER. In the case of the hybrid edge–cloud system design, the structure consists of the following: the industrial internet of things, involving sensors and actuators, edge computers used for computation at the edge of the network, and cloud servers. The edge devices continuously send data on grid parameters such as voltage, current flow, and power flow from the smart grid at a very high speed. The devices send data to the computers for initial processing. The processed data is then uploaded to the cloud servers, where intensive operations such as data analysis and model training take place. The cloud servers also facilitate coordination across different grid segments by aggregating data from multiple edge units, illustrated in Figure 2.

3.1. Real-Time Edge Analytics

At the edge layer, real-time analytics are essential for processing incoming data from IIoT sensors and making instantaneous decisions to optimize grid operations. Let $\mathbf{x}\left(t\right)\in {\mathbb{R}}^n$ be the measurement vector from IIoT devices at time t, and let $\mathbf{s}\left(t\right)\in {\mathbb{R}}^m$ represent the system state vector; their relationship is described in Equation (1):

$$\mathbf{x}\left(t\right)=\mathbf{H}\mathbf{s}\left(t\right)+\mathbf{v}\left(t\right),$$

(1)

where $\mathbf{H}\in {\mathbb{R}}^{n\times m}$ is the observation matrix and $\mathbf{v}\left(t\right)$ is the measurement noise assumed to be Gaussian with zero mean and $\mathbf{R}$-covariance. The optimal estimate of the system state $\widehat{\mathbf{s}}\left(t\right)$ minimizes the following cost function:

$$\widehat{\mathbf{s}}\left(t\right)=arg\underset{\mathbf{s}}{min}\left\{{∥\mathbf{x}\left(t\right)-\mathbf{H}\mathbf{s}∥}_{{\mathbf{R}}^{-1}}^2+{∥\mathbf{s}-\widehat{\mathbf{s}}(t-1)∥}_{{\mathbf{Q}}^{-1}}^2\right\},$$

(2)

where ${∥\mathbf{a}∥}_{\mathbf{M}}^2={\mathbf{a}}^{\top }\mathbf{M}\mathbf{a}$ and $\mathbf{Q}$ is the state covariance matrix. Anomaly detection is performed by evaluating the innovation vector:

$$\mathbf{e}\left(t\right)=\mathbf{x}\left(t\right)-\mathbf{H}\widehat{\mathbf{s}}\left(t\right).$$

(3)

The normalized residual is calculated as follows:

$$\mathbf{r}\left(t\right)={\mathbf{R}}^{-1/2}\mathbf{e}\left(t\right).$$

(4)

An anomaly is declared if the following condition is met:

$${∥\mathbf{r}\left(t\right)∥}_2>\delta ,$$

(5)

where $\delta$ is a predefined threshold based on the desired false alarm rate. For predictive maintenance, a Time-Delayed Neural Network (TDNN) is utilized to forecast future states. The TDNN model is defined as follows:

$$\widehat{\mathbf{s}}(t+\tau )=\varphi \left(\sum _{k=0}^K{\mathbf{W}}_k\mathbf{x}(t-k)+\mathbf{b}\right),$$

(6)

where $\tau$ is the prediction horizon, K is the number of delays, ${\mathbf{W}}_k$ are the weight matrices, $\mathbf{b}$ is the bias vector, and $\varphi (·)$ is the activation function applied element-wise. The training objective is to minimize the prediction error:

$$\mathcal{L}={\displaystyle \frac{1}{T}}\sum _{t=1}^T{∥\mathbf{s}(t+\tau )-\widehat{\mathbf{s}}(t+\tau )∥}_2^2.$$

(7)

Control is determined by addressing a constrained optimization problem in real time. The goal is to minimize the following objective function:

$$J=\sum _{i=0}^N\left(\mathbf{s}{(t+i)}^{\top }{\mathbf{Q}}_c\mathbf{s}(t+i)+\mathbf{u}{(t+i)}^{\top }{\mathbf{R}}_c\mathbf{u}(t+i)\right),$$

(8)

subject to the system dynamics

$$\mathbf{s}(t+1)=\mathbf{A}\mathbf{s}\left(t\right)+\mathbf{B}\mathbf{u}\left(t\right),$$

(9)

and constraints

$$\begin{array}{c}\hfill {\mathbf{u}}_{min}\le \mathbf{u}\left(t\right)\le {\mathbf{u}}_{max},\\ \hfill {\mathbf{s}}_{min}\le \mathbf{s}\left(t\right)\le {\mathbf{s}}_{max},\end{array}$$

(10)

where $\mathbf{u}\left(t\right)$ is the control input vector, $\mathbf{A}$ and $\mathbf{B}$ are system matrices, ${\mathbf{Q}}_c$ and ${\mathbf{R}}_c$ are weighting matrices, and N is the control horizon. To efficiently address the optimization problem at the edge, the ADMM is utilized. The augmented Lagrangian is formulated as follows:

$${\mathcal{L}}_a=J+{\mathit{\lambda }}^{\top }(\mathbf{G}\mathbf{z}-\mathbf{c})+{\displaystyle \frac{\rho }{2}}{∥\mathbf{G}\mathbf{z}-\mathbf{c}∥}_2^2,$$

(11)

where $\mathit{\lambda }$ is the Lagrange multiplier, $\rho$ is a penalty parameter, $\mathbf{G}$ and $\mathbf{c}$ represent the constraints in matrix form, and $\mathbf{z}$ is the vector of optimization variables. The optimization variables are updated iteratively:

$${\mathbf{z}}^{k+1}=arg\underset{\mathbf{z}}{min}{\mathcal{L}}_a(\mathbf{z},{\mathit{\lambda }}^k),$$

(12)

$${\mathit{\lambda }}^{k+1}={\mathit{\lambda }}^k+\rho (\mathbf{G}{\mathbf{z}}^{k+1}-\mathbf{c}).$$

(13)

To implement the real-time edge analytics, Algorithm 1 is presented, which outlines the step-by-step procedure executed at the edge computing units.

Algorithm 1: Real-time edge analytics procedure.

3.2. AI-Driven Predictive Maintenance

The proposed framework enhances advanced machine learning models to predict potential failures in grid components and optimize maintenance schedules. An HTM model is implemented to capture spatiotemporal patterns in the sensor data. Let $\mathbf{X}=\{{\mathbf{x}}_1,{\mathbf{x}}_2,\dots ,{\mathbf{x}}_T\}$ be a sequence of multidimensional sensor readings over time, where ${\mathbf{x}}_t\in {\mathbb{R}}^n$ represents the sensor vector at time t.

The HTM model has multiple levels of processing units. In each level l, the spatial pooling operation combines the inputs to generate sparse codes as follows:

$${\mathbf{S}}_t^{\left(l\right)}=\sigma \left({\mathbf{W}}^{\left(l\right)}{\mathbf{S}}_t^{(l-1)}+{\mathbf{b}}^{\left(l\right)}\right),$$

(14)

where ${\mathbf{S}}_t^{\left(0\right)}={\mathbf{x}}_t$, ${\mathbf{W}}^{\left(l\right)}$ and ${\mathbf{b}}^{\left(l\right)}$ are the weight matrix and bias vector at level l, and $\sigma (·)$ is a sparsity-inducing activation function, such as the ReLU (Rectified Linear Unit). Temporal pooling captures the temporal dependencies by updating the cell states:

$${\mathbf{h}}_t^{\left(l\right)}=f\left({\mathbf{S}}_t^{\left(l\right)},{\mathbf{h}}_{t-1}^{\left(l\right)}\right),$$

(15)

here, - ${\mathbf{h}}_t^{\left(l\right)}$ refers to the hidden states at time t and at level l and - $f(·)$ denotes the function used that combines the present input and previous hidden states. An anomaly score measures the difference between the present input and the patterns learned:

$$A_t=1-{\displaystyle \frac{\left|{\mathbf{S}}_t^{\left(L\right)}\cap {\widehat{\mathbf{S}}}_t^{\left(L\right)}\right|}{\left|{\mathbf{S}}_t^{\left(L\right)}\cup {\widehat{\mathbf{S}}}_t^{\left(L\right)}\right|}},$$

(16)

where ${\mathbf{S}}_t^{\left(L\right)}$ represents the sparse representation at the highest level L and $|·|$ indicates the cardinality of the set. The anomaly score $A_t$ has a minimum of 0 (normal) and a maximum of 1 (abnormal). The model makes predictions for future sensor values:

$${\widehat{\mathbf{x}}}_{t+1}=g\left({\mathbf{h}}_t^{\left(L\right)}\right),$$

(17)

where $g(·)$ is a decoding function that maps the hidden state to the original sensor space. The probability of a fault occurring is estimated using a logistic function:

$$P_{\mathrm{fault}}\left(t\right)={\displaystyle \frac{1}{1+exp\left(-\alpha A_t+\beta \right)}},$$

(18)

$\alpha$ and $\beta$ are parameters adjusted based on the actual fault history. Formulation of the maintenance plan can now be described as the optimization problem below, aimed at minimizing the cost of downtime. The optimization function is as follows:

$$\underset{\mathbf{m}}{min}\sum _{t=1}^T\left(C_{\mathrm{maint}}{m}_t+C_{\mathrm{downtime}}{P}_{\mathrm{fault}}\left(t\right)(1-m_t)\right),$$

(19)

subject to

$$\begin{array}{cc}\hfill & m_t\in \{0,1\},\forall t,\hfill \\ \hfill & \sum _{t=1}^T{m}_t\le M_{\max },\hfill \end{array}$$

(20)

where $m_t$ is a binary variable representing whether maintenance at time t is performed or not, $C_{\mathrm{maint}}$ represents the cost of performing the maintenance, $C_{\mathrm{downtime}}$ represents the cost due to downtime based on component failure, and $M_{\max }$ represents the maximum maintenance actions allowed during the planning horizon. The optimization technique used to solve the optimization problem is based on the use of the dynamic programming approach. The definition of the cost function $V_t\left(s_t\right)$ can now be given as follows:

$$V_t\left(s_t\right)=\underset{m_t}{min}\left\{C_{\mathrm{maint}}{m}_t+C_{\mathrm{downtime}}{P}_{\mathrm{fault}}\left(t\right)(1-m_t)+V_{t+1}\left(s_{t+1}\right)\right\},$$

(21)

with the boundary condition $V_{T+1}\left(s_{T+1}\right)=0$. The optimal policy is obtained by selecting $m_t$ that minimizes $V_t\left(s_t\right)$ at each time step.

3.3. Enhanced Security Protocols

The combination of advanced cryptographic techniques with adaptive security measures enables secure processing of encrypted data without decryption through a homomorphic encryption scheme. Let $m\in {\mathbb{Z}}_q$ represent the plaintext data collected by an IIoT device, where q is a large prime. The data is encrypted with a public key $pk$, resulting in the ciphertext c:

$$c=E_{pk}\left(m\right)=m·h^{r}modq,$$

(22)

where h is a generator of a multiplicative group modulo q and $r\in {\mathbb{Z}}_q$ is a random nonce. The homomorphic property allows for certain algebraic operations to be performed on ciphertexts. For addition, the operation is as follows:

$$E_{pk}\left(m_1\right)·E_{pk}\left(m_2\right)=E_{pk}(m_1+m_2),$$

(23)

and for scalar multiplication it is as follows:

$$E_{pk}{\left(m\right)}^k=E_{pk}(k·m),$$

(24)

where $k\in \mathbb{Z}$. These properties enable the edge devices to perform computations on encrypted data before transmitting results to the cloud, preserving data privacy. To authenticate devices without revealing sensitive information, ZKPs are employed. Let the prover (edge device) prove knowledge of a secret s such that

$$y=g^{s}modp,$$

(25)

where g serves as a generator for a cyclic group with prime order p, and y represents the public key. The protocol proceeds as follows:

• The prover selects a random $w\in {\mathbb{Z}}_p$ and computes the commitment:

  $$t=g^{w}modp.$$

  (26)
• The verifier sends a random challenge $c\in {\mathbb{Z}}_p$.
• The prover calculates the response:

  $$r=w+c·smodp.$$

  (27)
• The verifier checks the equality:

  $$g^r\stackrel{?}{=}t·y^{c}modp.$$

  (28)

If the equality holds, the prover is authenticated without revealing s. A private blockchain is implemented to maintain an immutable ledger of transactions and events within the grid. In each block, several details are stored: a set of transactions. In our formal description we continue the notation used above. The i-th block $B_i$ can therefore be expressed as follows:

$$B_i=\left(H\left(B_{i-1}\right),{\mathrm{MerkleRoot}}_i,T_i,{\sigma }_i\right),$$

(29)

here, $H\left(B_{i-1}\right)$ refers to the hash of the previous block $B_{i-1}$, ${\mathrm{MerkleRoot}}_i$ denotes the Merkle root of the transactions occurring in the $i^{th}$ block, $T_i$ denotes the timestamp, and ${\sigma }_i$ denotes the digital signature of the block creator.

This concurrent consensus protocol relies on the PBFT algorithm. Now, define the total number of nodes as n and the maximum faulty node as f for $n\ge 3f+1$, as given in Algorithm  2.

Computational Complexity Analysis

Let N denote the number of DER units and IIoT devices handled at the edge and E denote the number of edge nodes participating in coordination.

Algorithm 1 performs per-device state update and scheduling over all N units in each control interval. The dominant steps are linear scans and simple update operations, which yield a time complexity of $\mathcal{O}\left(N\right)$ per interval, with memory complexity proportional to the number of maintained device states, i.e., $\mathcal{O}\left(N\right)$.

Algorithm 2 coordinates the edge nodes and aggregates their local decisions. For each coordination round, it iterates over all E edge nodes and exchanges a bounded amount of state information. The resulting time complexity is $\mathcal{O}\left(E\right)$ per round, while the memory requirement is $\mathcal{O}\left(E\right)$ for storing edge-level summaries. Since $E\ll N$ in typical deployments, the overall computational cost remains manageable for large-scale smart grid scenarios.

Algorithm 2: PPBFT consensus mechanism.

An adaptive intrusion detection system (IDS) is incorporated within the edge devices. This IDS has the capability to analyze the network traffic. The IDS uses a statistical anomaly detection model. Let ${\mathbf{z}}_t\in {\mathbb{R}}^d$ denote the feature vector obtained from the network traffic at time t. The IDS models the normal behavior using a multivariate Gaussian distribution:

$$p\left({\mathbf{z}}_t\right)={\displaystyle \frac{1}{{\left(2\pi \right)}^{d/2}{|\Sigma |}^{1/2}}}exp\left(-{\displaystyle \frac{1}{2}}{({\mathbf{z}}_t-\mathit{\mu })}^{\top }{\Sigma }^{-1}({\mathbf{z}}_t-\mathit{\mu })\right),$$

(30)

where $\mathit{\mu }$ is the mean vector and $\Sigma$ is the estimated covariance matrix from the normal traffic. An anomaly score can now be written as follows:

$$S_t=-logp\left({\mathbf{z}}_t\right).$$

(31)

An intrusion is indicated when $S_t$ goes above a predefined threshold $\theta$, adapted over time based on the false positive rate through

$${\theta }_{t+1}={\theta }_t+\eta (\alpha -\mathbb{I}\{S_t>{\theta }_t\}),$$

(32)

where $\eta$ is the learning rate, $\alpha$ is the target false positive rate, and $\mathbb{I}\{·\}$ represents the indicator function. For efficient key management, Elliptic Curve Diffie–Hellman (ECDH) is employed for secure key exchange. Consider E as an elliptic curve over the finite field ${\mathbb{F}}_q$, specified by the equation

$$E:y^2=x^3+ax+bmodq,$$

(33)

where $a,b\in {\mathbb{F}}_q$ satisfy $4a^3+27b^2\ne 0$. Each device computes a private key $d\in {\mathbb{Z}}_q$ and a public key $Q=d·G$, with G being a base point on E. Two devices, A and B, compute the shared secret:

$$S_{AB}=d_A·Q_B=d_B·Q_A,$$

(34)

which is used to derive symmetric encryption keys. The security of the proposed protocols is analyzed using formal methods. The adversary’s advantage in breaking the encryption scheme is defined as follows:

$${\mathcal{A}}_{\mathrm{adv}}=\left|Pr[\mathcal{A}\left(E_{pk}\left(m\right)\right)=m]-{\displaystyle \frac{1}{|{\mathbb{Z}}_q|}}\right|,$$

(35)

which is negligible under the hardness assumption of the underlying cryptographic problem (e.g., Discrete Logarithm Problem). The resilience of the blockchain consensus mechanism against Byzantine faults is guaranteed as long as $f<{\displaystyle \frac{n}{3}}$, ensuring security and activity properties as per the PBFT protocol specifications.

3.4. Interoperability Framework

It is a standardized communication protocol built upon a layered architecture, inspired by the Open Systems Interconnection (OSI) model but tailored for smart grid applications. At the Physical Layer, devices utilize a common transmission medium with modulation schemes optimized for grid environments. Let the transmitted signal $s\left(t\right)$ be defined as follows:

$$s\left(t\right)=\sqrt{2P}·cos(2\pi f_{c}t+\varphi \left(t\right))·m\left(t\right),$$

(36)

where P denotes the transmission power, $f_c$ represents the carrier frequency, $\varphi \left(t\right)$ is the phase modulation, and $m\left(t\right)$ is the message signal.

In the Data Link Layer, a collision-free multiple access scheme based on TDMA communication is used. The time interval T is divided into N time slots. These time slots are represented as $\Delta t_1,\Delta t_2,\dots ,\Delta t_N$ and allocated based on the priority $\{p_1,p_2,\dots ,p_N\}$ for deterministic communication:

$$\Delta t_i={\displaystyle \frac{T·p_i}{{\sum }_{k=1}^N{p}_k}},\forall i\in \{1,2,\dots ,N\}.$$

(37)

In the Network Layer, the routing of the data packets is optimized using a QoS-aware routing algorithm. The cost function for routing from node i to node j is defined as follows:

$$C_{ij}=\alpha ·D_{ij}+\beta ·L_{ij}+\gamma ·E_{ij},$$

(38)

where $D_{ij}$ represents the delay, $L_{ij}$ denotes the packet loss rate, $E_{ij}$ denotes the energy consumption, and $\alpha$, $\beta$, and $\gamma$ are the weights that add up to 1.

To ensure consistent interpretation of data across devices, a standardized data model is defined using a hierarchical schema. Each data element is represented as an object with attributes and relationships. Let $\mathcal{D}$ denote the set of all data objects, where each object $d\in \mathcal{D}$ is defined as follows:

$$d=\left\{{\mathrm{ID}}_d,{\mathrm{Type}}_d,{\mathrm{Value}}_d,{\mathrm{Timestamp}}_d,{\mathrm{Meta}}_d\right\},$$

(39)

where

-

${\mathrm{ID}}_d$ is a unique identifier;

-

${\mathrm{Type}}_d$ specifies the data type (e.g., voltage, current, and power);

-

${\mathrm{Value}}_d$ contains the measurement value;

-

${\mathrm{Timestamp}}_d$ records the time of data acquisition;

-

${\mathrm{Meta}}_d$ includes metadata such as units and quality indicators.

Data relationships are defined using an adjacency matrix $\mathbf{A}\in {\mathbb{R}}^{\left|\mathcal{D}\right|\times \left|\mathcal{D}\right|}$, where

$$A_{ij}=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}{d}_i\mathrm{is}\mathrm{related}\mathrm{to}{d}_j,\hfill \\ 0,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(40)

Ontologies are used for semantic interoperability. This enables devices to interpret the semantics of the information. Let $\mathcal{O}$ represent the ontology, defined as a tuple:

$$\mathcal{O}=\left(\mathcal{C},\mathcal{R},\mathcal{I}\right),$$

(41)

where

-

$\mathcal{C}$ denotes the collection of concepts;

-

$\mathcal{R}$ represents the network of relationships among concepts;

-

$\mathcal{I}$ includes the set of instances. Concepts are structured in a taxonomy using a partial order relation ≤:

$$c_i\le c_j\Rightarrow c_i\mathrm{is}\mathrm{a}\mathrm{subtype}\mathrm{of}{c}_j,\forall c_i,c_j\in \mathcal{C}.$$

(42)

Semantic similarity between concepts is quantified using an information-theoretic measure:

$$\mathrm{Sim}(c_i,c_j)={\displaystyle \frac{2·logp\left(\mathrm{LCA}(c_i,c_j)\right)}{logp\left(c_i\right)+logp\left(c_j\right)}},$$

(43)

where $\mathrm{LCA}(c_i,c_j)$ is the least common ancestor of $c_i$ and $c_j$ in the taxonomy and $p\left(c\right)$ is the probability of concept c occurring.

To enable dynamic discovery of devices, a protocol based on service advertisements and queries is introduced. Each device broadcasts a service description $S_d$:

$$S_d=\left\{{\mathrm{ID}}_d,{\mathcal{F}}_d,{\mathcal{C}}_d\right\},$$

(44)

where ${\mathcal{F}}_d$ is the set of functionalities offered by device d and ${\mathcal{C}}_d$ represents the context information (e.g., location and capabilities). Devices seeking services perform queries Q defined as follows:

$$Q=\left\{{\mathcal{F}}_q,{\mathcal{C}}_q\right\},$$

(45)

and matching is performed using a compatibility function $\kappa (S_d,Q)$:

$$\kappa (S_d,Q)=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}{\mathcal{F}}_q\subseteq {\mathcal{F}}_d\wedge {\mathcal{C}}_d\sim {\mathcal{C}}_q,\hfill \\ 0,\hfill & \mathrm{otherwise},\hfill \end{array}\right.$$

(46)

where ${\mathcal{C}}_d\sim {\mathcal{C}}_q$ indicates context compatibility. An interoperability middleware is proposed that resides between the application layer and the network layer, providing translation and mediation services. The middleware includes the following:

• A Protocol Adapterthat translates proprietary device protocols into the unified communication protocol.
• A Semantic Mapper that aligns data elements to the standardized data model using mapping functions ${\mu }_d$:

  $${\mu }_d:{\mathcal{D}}_d\to \mathcal{D},$$

  (47)

  where ${\mathcal{D}}_d$ is the device-specific data set.
• A Service Registry that maintains information about available services and devices.

Theorem 1. 

Consider the finite-horizon control problem in (8)–(10) and write its condensed quadratic form

$$\underset{\mathbf{z}\in {\mathbb{R}}^p}{min}\frac{1}{2}{\mathbf{z}}^{\top }\mathbf{H}\mathbf{z}+{\mathbf{h}}^{\top }\mathbf{z}\mathrm{s}.\mathrm{t}.\mathbf{G}\mathbf{z}=\mathbf{c},$$

where $\mathbf{z}$ stacks the predicted states/inputs over the horizon, $\mathbf{H}\succ 0$ collects the stage weights ${\mathbf{Q}}_c\succ 0$ and ${\mathbf{R}}_c\succ 0$, and $\mathbf{G}$ encodes the lifted dynamics (9) and any linear equalities (slack variables can absorb box constraints). Assume the following: (i) the feasible set is nonempty; (ii) $\mathbf{G}$ has full row rank; and (iii) the ADMM penalty $\rho >0$. Let $\left\{({\mathbf{z}}^k,{\mathit{\lambda }}^k)\right\}$ be the sequence produced by the ADMM iterations (12) and (13) for the augmented Lagrangian (11).

Then, the following hold:

1. 

The problem admits a unique primal minimizer ${\mathbf{z}}^{★}$ and a dual solution ${\mathit{\lambda }}^{★}$ (KKT pair).

2. 

The ADMM iterates converge to the KKT point:

$${\mathbf{z}}^k\to {\mathbf{z}}^{★},{\mathit{\lambda }}^k\to {\mathit{\lambda }}^{★}.$$

3. 

Moreover, convergence is linear. There exists $q\in (0,1)$ and $C>0$ such that for all k,

$${\parallel {\mathbf{z}}^k-{\mathbf{z}}^{★}\parallel }_{\mathbf{H}}^2+\frac{1}{{\rho }^2}{\parallel {\mathit{\lambda }}^k-{\mathit{\lambda }}^{★}\parallel }_2^2\le C{q}^k.$$

A valid factor is

$$q={\displaystyle \frac{\kappa -1}{\kappa +1}}\mathrm{with}\kappa =\sqrt{\kappa \left({\mathbf{H}}^{-1/2}{\mathbf{G}}^{\top }\mathbf{G}{\mathbf{H}}^{-1/2}\right)},$$

and $\kappa (·)$ is the spectral condition number.

Proof of Theorem 1. 

Since $\mathbf{H}\succ 0$, the objective is strongly convex and coercive. The affine set $\{\mathbf{z}:\mathbf{G}\mathbf{z}=\mathbf{c}\}$ is closed and nonempty by assumption. A strongly convex objective over a nonempty affine set admits a unique minimizer ${\mathbf{z}}^{★}$. By convexity and constraint qualification (full row rank of $\mathbf{G}$), KKT conditions are necessary and sufficient, yielding a dual solution ${\mathit{\lambda }}^{★}$.

(Convergence). The augmented Lagrangian

$${\mathcal{L}}_a(\mathbf{z},\mathit{\lambda })=\frac{1}{2}{\mathbf{z}}^{\top }\mathbf{H}\mathbf{z}+{\mathbf{h}}^{\top }\mathbf{z}+{\mathit{\lambda }}^{\top }(\mathbf{G}\mathbf{z}-\mathbf{c})+\frac{\rho }{2}{\parallel \mathbf{G}\mathbf{z}-\mathbf{c}\parallel }_2^2$$

is $\mu$-strongly convex in $\mathbf{z}$, with $\mu ={\lambda }_{min}\left(\mathbf{H}\right)>0$. The ADMM $\mathbf{z}$-update computes the unique minimizer of a strongly convex quadratic; the dual update is a gradient step on the dual of the augmented problem with step size $1/\rho$. Because $\mathbf{G}$ has full row rank, the dual function is smooth and strongly concave with curvature constants determined by the spectrum of $\mathbf{G}{\mathbf{H}}^{-1}{\mathbf{G}}^{\top }$. This renders the primal–dual operator firmly nonexpansive in a weighted norm, yielding global convergence of $({\mathbf{z}}^k,{\mathit{\lambda }}^k)$ to $({\mathbf{z}}^{★},{\mathit{\lambda }}^{★})$.

(Linear rate.) Strong convexity of the primal quadratic and full row rank of $\mathbf{G}$ imply strong monotonicity and Lipschitz continuity of the KKT map. The ADMM iteration is equivalent to a preconditioned Douglas–Rachford splitting on two maximal monotone operators with a cocoercive component. Standard spectral arguments then give the linear contraction bound

$${\parallel {\mathbf{e}}^{k+1}\parallel }_{\mathbf{M}}\le q{\parallel {\mathbf{e}}^k\parallel }_{\mathbf{M}},$$

for a suitable metric $\mathbf{M}\succ 0$, where $q=(\kappa -1)/(\kappa +1)\in (0,1)$ and $\kappa$ is the condition number of ${\mathbf{H}}^{-1/2}{\mathbf{G}}^{\top }\mathbf{G}{\mathbf{H}}^{-1/2}$. Rewriting this in the stated energy norm yields the claimed inequality. □

4. Simulation Outcomes

A comprehensive simulation environment was created using MATLAB/Simulink R2023b to model a smart grid with integrated Distributed Energy Resources (DERs) and IIoT devices. The simulation involves extensive models of generation units, transmission lines, loads, and control systems. The dataset employed for simulations is the NREL SMART-DS (Synthetic Models for Advanced, Realistic Testing) distribution system dataset, which offers OpenDSS feeder models with attached time-series loads for SFO, GSO, and AUS [22]. GridOpt integrates a TDNN for short-term temporal prediction and an HTM model for real-time pattern learning and anomaly detection. The performance of the presented framework was tested against primary metrics such as latency, scalability, security, and reliability. The suggested method, GridOpt, is compared to ECCGrid [23], EdgeApp [24], and JOintCS [25]. The detailed simulation and experimental parameter settings are summarized in

Table 2. Simulation and experimental parameter settings.

Parameter	Setting
Simulation platform	MATLAB/Simulink R2023b
Dataset	NREL SMART-DS (SFO, GSO, AUS feeders)
Grid components	DERs, transmission lines, controllable loads, IIoT sensors
TDNN architecture	Three-layer network
TDNN temporal window	5 time steps
TDNN optimizer	Adam
TDNN learning rate	0.001
HTM columns	2048
HTM sparsity level	2%
HTM permanence threshold	0.21
Data split ratio	70% training, 15% validation, 15% testing
Evaluation metrics	Accuracy, Precision, Recall, F1-score, RMSE
Comparative methods	ECCGrid, EdgeApp, JOintCS

.

4.1. Latency Reduction

The latency comparison of GridOpt, ECCGrid, EdgeApp, and JOintCS among the six edge–cloud scenarios is depicted in the graph below. From Figure 3, it can be observed that when the devices were deployed at varied density levels (low, medium, and high), GridOpt had the lowest average latency of around 70 ms at medium density, followed by JOintCS at 80 ms at high density, while EdgeApp had the highest latency of around 95 ms at high density. In high data processing and high data transmission scenarios, GridOpt had an average latency of around 76 ms and outperformed others, like the 86 ms of average latency of ECCGrid and 83 ms of JOintCS. EdgeApp had an average latency of 93 ms.

4.2. Scalability Evaluation

In Figure 4, the comparative analysis of the average throughput of the six scalability scenarios shows that GridOpt always had the largest average throughput of 11.5 in Scenario 1 (low device density) and above 10 request/s in Scenario 6 (High Throughput Requirement), followed by a moderate decrease of an average of 10.2 request/s in medium- and high-density scenarios for both ECCGrid and JOintCS. The average throughput of EdgeApp had the steepest fall from 9.8 request/s in Scenario 1 to below 8 request/s in Scenario 6.

4.3. Resource Utilization

Figure 5 synthesizes the resource utilization efficiency of six scenarios to highlight the scalability qualities of the strategies based on the load perspective. The resource utilization of GridOpt remains constant at the lowest levels, commencing from around 28% in low-device-density settings to around 54% for high throughput. The moderate resource utilization levels of ECCGrid and JOintCS remain comparable to GridOpt but tend to slowly separate as the total count of devices within the IIoT setup escalates. The resource utilization levels of EdgeApp begin from higher base thresholds of around 34% in low-device-density settings and accelerate dramatically to above 62% for high-throughput settings.

4.4. Energy Consumption

Figure 6 shows the energy consumption comparison of GridOpt with respect to ECCGrid, EdgeApp, and JOintCS. In “Low Device Density (Low)”, GridOpt showed the least energy consumption of 15 Joules, followed by 18 Joules in ECCGrid, 17 Joules in JOintCS, and 22 Joules in EdgeApp. As the device density increased in “Medium Device Density (Medium)” devices, the energy intake of GridOpt increased marginally to 18 Joules. Additionally, the energy increased to 22 Joules in ECCGrid, 21 Joules in JOintCS, and 28 Joules in EdgeApp. In “High Device Density (High)”, GridOpt continued to function with 22 Joules of efficiency. The energy intake of ECCGrid increased to 28 Joules, JOintCS increased to 27 Joules, and EdgeApp increased to 35 Joules. In “Increased Data Load (Data Load)”, GridOpt showed a 24 Joule energy intake. The energy intake of ECCGrid increased to 30 Joules. EdgeApp showed 38 Joules. In “Edge–Cloud Integration (Integration)”, the energy intake of GridOpt marginally reduced to 20 Joules. The energy intake of both ECCGrid and EdgeApp increased to 26 Joules and 34 Joules. In “High Throughput Requirement (Throughput)”, GridOpt continued to work with the least energy of 25 Joules. The energy intake of ECCGrid increased by 32 Joules. JOintCS increased by 31 Joules. EdgeApp showed increased energy of 40 Joules.

5. Defense Applications and Future Research Directions

The proposed GridOpt framework can be expanded to apply to operations in the defense and critical infrastructure sectors where there is a need for secure, autonomous, and uninterrupted energy management. Through the integration of edge computing and blockchain authentication mechanisms for validated users, GridOpt provides secure power management within critical settings, such as military stations, naval stations, and off-shore stations. The capacity of the framework to function regardless of communication interruptions and through localized intelligent control mechanisms increases the resilience of the system against both cyber and physical attacks. The same framework can be applied to marine and underwater systems by incorporating Internet of Underwater Things devices.

The future research work should concentrate on improving the flexibility and security of GridOpt when it comes to large-scale and cross-domain applications. The work should include the integration of 6G communication systems and IoT frameworks that can facilitate low-latency and high-reliability data transfer. The integration of federated learning and Reinforcement Learning algorithms may also enhance the efficiency of decentralized control. The most important aspect may include quantum-resistant cryptography algorithms as well as bio-inspired intrusion detection algorithms. The digital twin platform can also aid in testing control and security strategies without requiring actual execution. This may help in the efficient modernization of the energy infrastructure.

6. Conclusions

The paper proposes GridOpt, a hybrid framework for edge–cloud optimization, enhancing runtime processing, improving scalability, and increasing security in smart power management with integrated DERs. This paper employed edge computation for processing real-time data and utilized cloud computation for handling large datasets, enabling predictive and long-term analysis. The proposed framework was simulated comprehensively. Simulation outcomes have confirmed that the proposed framework of GridOpt had the lowest latency of 76 ms in high-throughput processing and outshone ECCGrid at 86 ms, JOintCS at 83 ms, and EdgeApp at 93 ms. The proposed framework had high scalability of above 10 req/s at high density and the lowest resource use of 54%, which surpassed 62% of competitors. In addition, it had a high energy efficiency of 25 Joules at high throughputs and outshone ECCGrid at 32 Joules. The proposed framework had better efficiency than JOintCS at 31 Joules and EdgeApp at 40 Joules. GridOpt is currently constrained to simulation-based validation, where the framework assumes stable edge–cloud connectivity and controlled communication overhead; real-world deployment with variable network conditions and hardware constraints remains for future work.