Enhancing Smart Grid Data Utilization within the Internet of Things Paradigm: A Cyber-Physical Security Framework

Abstract

The integration of Internet of Things (IoT) technologies transforms traditional power systems into smart grids with more opportunities for optimizing power generation and consumption. However, this integration incurs significant cyber-physical security challenges that must be addressed to ensure the authenticity of critical data. This chapter explores the intersection of smart grid data utilization and cyber-physical security within the IoT paradigm. We first introduce the key components of IoT systems and their communication in smart grids, highlighting the interdependencies and vulnerabilities. Then, we discuss the potential risks associated with the collection, transmission, and utilization of data in smart grid environments, emphasizing the importance of cyber-physical security countermeasures in mitigating these risks. Finally, we propose a cyber-physical security framework equipped with dual risk-mitigation layers, including offline parameter configuration and online intrusion detection, to safeguard smart grid data against cyber-physical threats. By adopting this security framework, stakeholders can leverage the full potential of IoT technologies in smart grids while ensuring the security of the critical infrastructure. This chapter contributes to the ongoing discourse on cyber-physical security in smart grids and provides practical insights for policymakers, industry practitioners, and researchers seeking to address the evolving challenges in this domain.

1. Introduction

In recent decades, the Internet of Things (IoT) technologies have assumed a pivotal role in the evolution of modern smart grids, significantly enhancing data collection and utilization processes [1]. The integration of IoT technologies provides substantial benefits to smart grids, including advanced smart sensing capabilities and intelligent monitoring systems [2]. However, despite these advantages, the IoT framework presents significant challenges to the secure operation of smart grids. These challenges arise from both cyber and physical perspectives, particularly in environments characterized by uncertainty. Consequently, addressing these security concerns is crucial to ensuring the reliability and stability of smart grid operations.

The uncertainties originating from the IoT system in smart grids can be broadly categorized into two main aspects: data collection from power infrastructures and devices, and data exchange within IoT communication networks. The first aspect pertains to data collection, which typically involves heterogeneous sensors such as phasor measurement units (PMUs) and remote telemetry units (RTUs). These sensors, often installed in outdoor environments, are composed of numerous intelligent units designed for specific purposes such as data measuring, processing, and broadcasting [3, 4, 5]. Due to prolonged exposure to outdoor environments, these sensors face various uncertain factors, including limited processing capacities, functional disorders, sensor aging, and potential physical attacks from adversaries. These limitations can result in temporary sensor failures, leading to the degradation of the authenticity and reliability of the collected data. The second aspect involves data exchange within the IoT communication network. Modern smart grids often span distinct geographical landscapes, including multiple cities and remote communities. These areas share local data with their neighbors in real time, facilitated by wireless sensor networks (WSNs) due to their advantages in flexible deployment, adaptable relocation, and cost-effective installation and maintenance. However, the inherent openness of wireless transmission makes WSNs vulnerable to cyber attacks [6, 7]. Adversaries can exploit these vulnerabilities by injecting false data into the communication links of WSNs, thereby altering data values and potentially destroying the power equipment. These two primary concerns, encompassing both cyber and physical dimensions, form the core topics to be addressed in this chapter.

To address the vulnerabilities inherent in the data collection of smart grids, significant efforts have been undertaken, yielding several promising solutions in recent years [8, 9, 10, 11, 12, 13, 14, 15]. For instance, Ref. [8] examined PMU faults from a hardware-software interaction perspective, developing a comprehensive reliability model for PMUs based on Markov models. This model facilitates the estimation of PMU false data using Monte Carlo simulation techniques. Ref. [10] introduced a hybrid algorithm designed for fast path recovery in wide-area measurement systems to mitigate the effects of intermittent PMU outputs. Ref. [11] identified that intermittent PMU measurements are caused by both natural factors and physical attacks. It employed a Bernoulli process with a specified probability to model these intermittent measurements and the degrees of PMU failure. From the perspective of data utilization, various stability criteria have been employed to ensure the efficient operation of smart grids, despite the imperfections in PMU models, such as mean-square asymptotic stability [11] and stochastic stability [13], both of which are essential for guaranteeing the stability and robustness of smart grids amidst imperfect data collection. These methodologies and criteria serve as valuable tools in enhancing the security of smart grids from cyber-physical perspectives, addressing both hardware-software interactions and external threats to data integrity.

In response to cyber attacks targeting data exchange within IoT communication networks, extensive research has been conducted on cyber attack detection methodologies [7, 16]. Prominent methods include intrusion-detector-dependent attack detection [17, 18], credibility-based attack detection [19, 20], observer/filter-based detection [21], and learning-based detection [22]. For instance, Ref. [17] developed a ${\chi }^2$-detector-dependent approach to identify false data injection (FDI) attacks in distributed frequency regulation, leveraging the decentralized model of each area to provide the frequency reference signal. Ref. [20] incorporated credibility evaluation into frequency regulation within smart grids, effectively mitigating the impact of FDI attacks on frequency dynamics. Ref. [21] proposed a reduced-order observer-based approach for monitoring FDI attacks in large-scale smart grids, utilizing a reduced-order observer to generate residual signals and embedding an adaptive detection threshold to minimize conservativeness. Ref. [7] introduced a data-driven framework encompassing detection, classification, and control signal retrieval to mitigate the impacts of unobservable FDI attacks on smart grids. This framework includes a classifier designed to dynamically learn from historical data and accurately classify FDI attacks under challenging conditions. These advanced methodologies collectively enhance the robustness and security of smart grids against cyber threats, ensuring more reliable operation in the face of unexpected cyber attacks.

Based on the preceding discussion, we acknowledge that these results have contributed to the effective utilization of smart grid data within the IoT architecture. However, these findings are dispersed and lack a unified framework. This chapter aims to establish a comprehensive and systematic framework to enhance smart grid data utilization from both cyber and physical security perspectives, incorporating a wide range of potential uncertainties inherent in the IoT architecture. The proposed framework is designed to be general and represents a significant advancement toward providing a scientific foundation for smart grids in the context of IoT with inherent uncertainties. This framework is inspired from a macro perspective, focusing on system-level data utilization enhancement rather than merely local operations. It is structured into two risk-mitigation layers from cyber-physical perspectives. The first risk-mitigation (physical) layer involves offline control parameter configuration, which aims to integrate easily modeled uncertainties, such as intermittent sensor measurements, into system modeling and control design. This configuration is conducted prior to the deployment of smart grids, thereby contributing to offline security enhancement. To address the inaccurate or incomplete modeling issues that the first layer may not fully resolve, the second risk-mitigation layer is implemented. This layer focuses on online intrusion detection to counter potential cyber attacks within IoT communication networks. The dual-layer framework allows for both independent application and practical integration, providing a high degree of flexibility and universality. This approach offers valuable guidance for both academic researchers and industry practitioners, facilitating effective risk-mitigation and enhancing the reliability of smart grid operations in the face of diverse uncertainties.

The remainder of this chapter is structured as follows. Section 2 introduces the data collection and exchange within IoT in smart grids. Section 3 models the smart grids and potential risks. Section 4 designs the dual-layer security framework for enhancing smart grid data utilization. Section 5 validates the effectiveness of the dual-layer secure framework. Section 6 concludes this chapter.

2. Data collection and exchange within IoT in smart grids

As a representative example of cyber-physical systems, the smart grid exemplifies the intricate interaction between the physical and cyber layers during its operation. The physical layer is primarily responsible for data acquisition, encompassing the measurement and processing of essential signals through various sensor devices, such as PMUs and RTUs. In contrast, the cyber layer focuses on data communication, including the transmission, reception, and exchange of the collected data. Together, these layers form an IoT system, a pivotal concept in the context of smart grids. The IoT system encompasses devices equipped with sensors, computational capabilities, software, and auxiliary technologies, enabling their interconnectivity and data exchange with other devices and systems via the Internet or other communication networks. This interconnectivity is crucial for the implementation of supervisory control and data acquisition (SCADA) systems, which monitor the operational states of smart grids. The IoT system’s applications span various stages of smart grid operation, including power generation, transmission, distribution, and consumption, thereby enhancing efficiency and reliability [23].

The ways of data exchange within IoT are realized by the communication topology, which is commonly determined by the physical connection. Take a typical application scenario of smart grids, the communication topology of a power generation system is determined by the amount of areas and performance requirements. To better describe the characteristics of the communication topology of smart grids, we here introduce the concept of a directed graph.

In graph theory, $\mathbb{G}=\left(\mathbb{V},\mathbb{E},\mathbb{L}\right)$ represents the mathematical formulation of a directed graph, which is employed to describe the communication topology in this chapter. Here, $\mathbb{V}=\left\{1,2,\dots ,n\right\}$ denotes the set of labels corresponding to different areas. The set $\mathbb{E}\subseteq \mathbb{V}\times \mathbb{V}$ characterizes the communication links between these areas. The adjacency matrix $\mathbb{L}={\left(l_{\mathit{ij}}\right)}_{n\times n}$ encodes the presence and weights of these communication links, where $l_{\mathit{ij}}>0$ indicates that data transmission occurs from the $i$-th PMU to the $j$-th PMU. An area $j$ is defined as a neighbor of an area $i$ if $l_{\mathit{ij}}=1$. Consequently, the set ${\mathbb{N}}_i\triangleq \left\{j\in \mathbb{V}|\left(i,j\right)\in \mathbb{E}\right\}$ specifies the neighbors of the $i$-th PMU, indicating that the $i$-th PMU can receive state measurements from its neighboring PMUs $j\in {\mathbb{N}}_i$ according to the defined communication topology.

3. Modeling of smart grids and potential risks

3.1 Modeling of smart grids

This chapter takes the load frequency control (LFC), also named automatic generation control, a typical application in smart grids, as an example. The LFC dynamics of each area contain the following five parts, i.e., generator, governor, power system, tie-line power, and area control error. The dynamics of these five parts are

$$\mathrm{\Delta }{\dot{P}}_{m_i}=-\frac{1}{T_{d_i}}\mathrm{\Delta }{P}_{m_i}+\frac{1}{T_{d_i}}\mathrm{\Delta }{P}_{v_i},$$E1

$$\mathrm{\Delta }{\dot{P}}_{v_i}=-\frac{1}{R_i{T}_{g_i}}\mathrm{\Delta }{f}_i-\frac{1}{T_{g_i}}\mathrm{\Delta }{P}_{v_i}+\frac{1}{T_{g_i}}\mathrm{\Delta }{P}_{c_i},$$E2

$$\mathrm{\Delta }{\dot{f}}_i=-\frac{D_i}{T_{m_i}}\mathrm{\Delta }{f}_i+\frac{1}{T_{m_i}}\mathrm{\Delta }{P}_{m_i}-\frac{1}{T_{m_i}}\mathrm{\Delta }{P}_{\mathrm{tie}}^i-\frac{1}{T_{m_i}}\mathrm{\Delta }{P}_{L_i},$$E3

$$\mathrm{\Delta }{\dot{P}}_{\mathrm{tie}}^i=\sum _{j=1,j\ne i}^{\mathbb{N}}2\pi T_{\mathit{ij}}\left(\mathrm{\Delta }{f}_i-\mathrm{\Delta }{f}_j\right),$$E4

$${\mathit{ACE}}_i={\mu }_i\mathrm{\Delta }{f}_i+\mathrm{\Delta }{P}_{\mathrm{tie}}^i,$$E5

where the physical meanings of the system parameters are shown in Table 1 [11].

Symbol	Physical meaning
$\mathrm{\Delta }{f}_i$	deviation of frequency
$\mathrm{\Delta }{P}_{W_i}$	the wind power deviation
$\mathrm{\Delta }{P}_{m_i}$	deviation of generator mechanical power
$\mathrm{\Delta }{P}_{v_i}$	deviation of turbine value position
$\mathrm{\Delta }{P}_{\mathrm{tie}}^i$	net tie-line active power flow
$\mathrm{\Delta }{P}_{L_i}$	load disturbance
$\mathbb{N}$	the number of areas
$T_{d_i}$	time constant of the generator
$T_{g_i}$	time constant of the governor
$T_{m_i}$	time constant of the power system
$R_i$	speed drop
$D_i$	equivalent damping coefficient of the generator
$T_{\mathit{ij}}$	tie-line synchronizing coefficient between the area $i$ and $j$
${\mu }_i$	frequency bias constant ${\mu }_i=1/R_i+D_i$

Table 1.

Parameters of area $i$.

The compact form of (1)–(5) can be described as

$$\left\{\begin{array}{l}{\dot{x}}_i={\mathcal{A}}_i{x}_i+\sum _{j=1,j\ne i}^{\mathbb{N}}{\mathcal{A}}_{\mathit{ij}}{x}_j+{\mathcal{B}}_i{u}_i+{\mathcal{F}}_i{\omega }_i,\\ y_i={\mathcal{C}}_i{x}_i,\end{array}\right.$$E6

where $x_i={\left[\mathrm{\Delta }{f}_i\mathrm{\Delta }{P}_{m_i}\mathrm{\Delta }{P}_{v_i}\mathrm{\Delta }{P}_{\mathrm{tie}}^i\int {\mathit{ACE}}_i\right]}^T$ denotes the state vector; $y_i$ denotes the measured output; $u_i$ denotes the control input; ${\omega }_i$ denotes the load disturbance;

$$\begin{array}{lll}{\mathcal{A}}_i& =& \left[\begin{array}{ccccc}\frac{-D_i}{T_{m_i}}& \frac{1}{T_{m_i}}& 0& \frac{-1}{T_{m_i}}& 0\\ 0& \frac{-1}{T_{d_i}}& \frac{1}{T_{d_i}}& 0& 0\\ \frac{-1}{R_i{T}_{g_i}}& 0& \frac{-1}{T_{g_i}}& 0& 0\\ \sum _{j=1,j\ne i}^{\mathbb{N}}2\pi T_{\mathit{ij}}& 0& 0& 0& 0\\ {\mu }_i& 0& 0& 1& 0\end{array}\right],\end{array}$$

$$\begin{array}{lll}{\mathcal{A}}_{\mathit{ij}}& =& \left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ -2\pi T_{\mathit{ij}}& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\end{array}\right],{\mathcal{C}}_i^T=\left[\begin{array}{cc}{\mu }_i& 0\\ 0& 0\\ 0& 0\\ 1& 0\\ 0& 1\end{array}\right],\\ {\mathcal{B}}_i& =& {\left[00\frac{1}{T_{g_i}}00\right]}^T,{\omega }_i=\mathrm{\Delta }{P}_{L_i},u_i=\mathrm{\Delta }{P}_{c_i},\\ {\mathcal{F}}_i& =& {\left[\frac{1}{T_{m_i}}0000\right]}^T.\end{array}$$E7

Given that state measurement and feedback control in smart grids are implemented through digital devices like PMUs and RTUs, a discrete-time state-space model is derived to facilitate the subsequent analysis. The discrete-time representation of the continuous-time system model (6) is formulated as

$$\left\{\begin{array}{l}{x}_i\left(k+1\right)=A_i{x}_i\left(k\right)+B_i{u}_i\left(k\right)+\sum _{j=1,j\ne i}^{\mathbb{N}}{A}_{\mathit{ij}}{x}_j\left(k\right)+F_i{\omega }_i\left(k\right),\\ y_i\left(k\right)=C_i{x}_i\left(k\right),\end{array}\right.$$E8

where $A_i=e^{{\mathcal{A}}_{i}h}$, $B_i={\int }_0^h{e}^{{\mathcal{A}}_{i}s}{\mathcal{B}}_i\mathit{ds}$, $A_{\mathit{ij}}=e^{{\mathcal{A}}_{\mathit{ij}}h}$, $F_i={\int }_0^h{e}^{{\mathcal{A}}_{i}s}{\mathcal{F}}_i\mathit{ds}$, and $C_i={\mathcal{C}}_i$; $h$ denotes the sampling period.

3.2 Potential risks and descriptions

This chapter examines the potential risks to smart grids from both physical and cyber perspectives. Physical risks arise from sensor faults, which can be caused by limited processing capacities, functional impairments, sensor aging, and physical attacks from adversaries. Such sensor faults compromise the authenticity and reliability of the collected data. To model the impact of these physical risks, this chapter utilizes Bernoulli variables to capture the intermittent nature of measurements affected by sensor faults. Consequently, the actual measured output from the sensor $i$ is represented as

$${\overline{y}}_i\left(k\right)={\theta }_i\left(k\right)y_i\left(k\right),$$E9

where ${\theta }_i\left(k\right)=0$ means that the sensor $i$ suffers faults at the time $k$, while ${\theta }_i\left(k\right)=1$ means the sensor $i$ is healthy. The probability distribution of ${\theta }_i\left(k\right)$ satisfies

$$\text{Prob}\left\{{\theta }_i\left(k\right)=1\right\}={\overline{\theta }}_i,\text{Prob}\left\{{\theta }_i\left(k\right)=0\right\}=1-{\overline{\theta }}_i,$$E10

where Prob$\left\{\cdot \right\}$ denotes the probability operator, ${\theta }_i\left(k\right)$ at different times are assumed to be independent and identically distributed.

Note that ${\theta }_i\left(k\right)$ serves as a comprehensive representation of various factors, including limited processing capacities, functional impairments, sensor aging, and physical attacks from adversaries. Specifically, ${\theta }_i\left(k\right)$ can be expressed as ${\theta }_i\left(k\right)={\theta }_i^1\left(k\right){\theta }_i^2\left(k\right){\theta }_i^3\left(k\right)\cdots {\theta }_i^M\left(k\right)$, where denotes the total number of potential factors contributing to sensor faults.

From the cyber perspective, potential risks arise in the data exchange within the IoT communication network. Modern smart grids typically encompass multiple control areas, which share local data with neighboring areas in real time. However, the inherent openness of these communication networks renders them vulnerable to cyber attacks. Adversaries can inject false data into the communication links based on malicious intent, thereby compromising the data integrity of the national power grid and endangering public safety. In the context of false data injection (FDI) attacks on the communication network, the received data in the control area $i$, transmitted from neighboring area $j$, can be modeled as:

$${\tilde{y}}_j\left(k\right)={\overline{y}}_j\left(k\right)+G_j{g}_j\left(k\right)$$E11

where ${\overline{y}}_j\left(k\right)$ denotes the measured output at area $j$; $g_j\left(k\right)$ denotes a column vector implying the false data deliberately injected into the communication link from area $j$ to area $i$ by adversaries; and $G_j$ defines the attack selection matrix. For the purposes of the ensuing sensitivity analysis, $G_j$ is assumed to be a diagonal matrix with entries of 0 or 1, where 0 implies a real measurement and one implies a compromised measurement.

4. Dual-layer security framework for enhancing smart grid data utilization

This chapter endeavors to propose a dual-layer security framework for enhancing smart grid data utilization. Section 4.1 focuses on the first risk-mitigation layer, offline control parameter configuration, while Section 4.2 addresses the second risk-mitigation layer, online intrusion detection. In the following, we will discuss these two layers in detail.

4.1 Offline control parameter configuration: First risk-mitigation layer

Since we focus on multi-area smart grids, the distributed output feedback controller is designed considering the sensor faults, whose mathematical formulation is

$$u_i\left(k\right)={\theta }_i\left(k\right)K_i{y}_i\left(k\right)+\sum _{j=1,j\ne i}^{\mathbb{N}}{\theta }_j\left(k\right)K_{\mathit{ij}}{y}_j\left(k\right),$$E12

where $K_i$ and $K_{\mathit{ij}}$ are local and neighboring control gains to be determined.

Then, the closed-loop system model (8) becomes

$$\left\{\begin{array}{l}{x}_i\left(k+1\right)=\left(A_i+{\theta }_i\left(k\right)B_i{K}_i{C}_i\right)x_i\left(k\right)+\sum _{j=1,j\ne i}^{\mathbb{N}}\left(A_{\mathit{ij}}+{\theta }_j\left(k\right)B_i{K}_{\mathit{ij}}{C}_j\right)x_j\left(k\right)+F_i{\omega }_i\left(k\right),\\ {\overline{y}}_i\left(k\right)={\theta }_i\left(k\right)C_i{x}_i\left(k\right).\end{array}\right.$$E13

Based on the closed-loop system (13), we will propose Theorem 1 and Theorem 2 to facilitate the control parameter configuration.

Theorem 1.1 Considering the sensor fault probability ${\overline{\theta }}_i$, the closed-loop system (13) is mean-square asymptotically stable with $\mathrm{\Delta }{f}_i$ satisfying the prescribed ${\mathcal{H}}_{\infty }$ performance indicator ${\gamma }_i$ if there exist matrices $P_i\succ 0$ such that, for $i=1,2,\cdots ,\mathbb{N}$,

$$\left[\begin{array}{cc}\mathrm{\Xi }+D^{T}D& {\overline{A}}^T\mathit{PF}\\ \ast & F^T\mathit{PF}-{\gamma }^{2}I\end{array}\right]\prec 0$$E14

where $P_i$ is the Lyapunov matrix; “$\succ$” and “$\prec$” define “positive definite” and “negative definite” of a matrix, respectively; “$\ast$” denotes the symmetric item of a sophisticated matrix; ${\text{Diag}}_{\mathbb{N}}^i\left\{C_i\right\}$ indicates that only the $i$-th diagonal block owns a nonzero value $C_i$ while other diagonal blocks are all zero; and $\mathrm{\Xi }={\overline{A}}^{T}P\overline{A}+{\sum }_{i=1}^{\mathbb{N}}{\rho }_i^2{L}_i^T{\mathit{PL}}_i-P$, $\overline{A}=A+\mathit{BK}\overline{\theta }C$, $B=\text{Diag}\left\{B_1,B_2,\cdots ,B_{\mathbb{N}}\right\}$, $C=\text{Diag}\left\{C_1,C_2,\cdots ,C_{\mathbb{N}}\right\}$, $D=\text{Diag}\left\{D_1,D_2,\cdots ,D_{\mathbb{N}}\right\}$, $F=\text{Diag}\left\{F_1,F_2,\cdots ,F_{\mathbb{N}}\right\}$, $P=\text{Diag}\left\{P_1,P_2,\cdots ,P_{\mathbb{N}}\right\}$, $\theta =\text{Diag}\left\{{\theta }_1,{\theta }_2,\cdots ,{\theta }_{\mathbb{N}}\right\}$, $\gamma =\text{Diag}\left\{{\gamma }_1,{\gamma }_2,\cdots ,{\gamma }_{\mathbb{N}}\right\}$, $\overline{\theta }=\text{Diag}\left\{{\overline{\theta }}_1,{\overline{\theta }}_2,\cdots ,{\overline{\theta }}_{\mathbb{N}}\right\}$, ${\rho }_i=\sqrt{{\overline{\theta }}_i\left(1-{\overline{\theta }}_i\right)}$, $D_i=\left[10000\right]$, $L_i={\mathit{BKE}}_i$, $E_i={\text{Diag}}_{\mathbb{N}}^i\left\{C_i\right\}$, $A$ has the identical form with $K$,

$$K=\left[\begin{array}{cccc}{K}_1& K_{12}& \cdots & K_{1\mathbb{N}}\\ K_{21}& K_2& \cdots & K_{2\mathbb{N}}\\ ⋮& ⋮& \ddots & ⋮\\ K_{\mathbb{N}1}& K_{\mathbb{N}2}& \cdots & K_{\mathbb{N}}\end{array}\right].$$E15

Proof: A similar proof procedure can be found in Ref. [24].

Careful readers may observe that condition (14) is not a strict linear matrix inequality (LMI) due to the coupling between the distributed controller gain $K$ and the Lyapunov matrix $P$. Consequently, to determine the value of $K$, we further propose Theorem 2.

Theorem 1.2 Considering the sensor fault probability ${\overline{\theta }}_i$, the closed-loop system (13) is mean-square asymptotically stable with $\mathrm{\Delta }{f}_i$ satisfying the prescribed ${\mathcal{H}}_{\infty }$ performance indicator ${\gamma }_i$ if there exist matrices $P_i\succ 0$ and $Q_i\succ 0$ such that, for $i=1,2,\cdots ,\mathbb{N}$,

$$\left[\begin{array}{ccccc}-\tilde{Q}& 0& \overline{L}& 0& \\ \ast & -Q& \tilde{A}& F& \\ \ast & \ast & \tilde{D}& 0& \\ \ast & \ast & \ast & -{\gamma }^{2}I& \\ & & & & \end{array}\right]\prec 0,$$E16

$$P_i{Q}_i=I,$$E17

where $\tilde{A}=A+\mathit{BK}\overline{\theta }C$, $\tilde{D}=D^{T}D-P$, $\overline{L}={\left[{\rho }_1{L}_1^T\left(k\right),{\rho }_2{L}_2^T\left(k\right),\cdots ,{\rho }_{\mathbb{N}}{L}_{\mathbb{N}}^T\left(k\right)\right]}^T$, $\tilde{Q}={\text{Diag}}_{\mathbb{N}}\left\{Q,Q,\cdots ,Q\right\}$, and $Q=\text{Diag}\left\{Q_1,Q_2,\cdots ,Q_{\mathbb{N}}\right\}$.

Proof: A similar proof procedure can be found in Ref. [24].

From Theorem 2, the distributed controller gain $K$ can be determined automatically using the mincx solver in the LMI toolbox. Subsequently, the quantity of the control action can be calculated via(12) and applied to update the system (13). The obtained distributed controller gain $K$ has a certain resiliency to different sensor fault probabilities.

4.2 Online intrusion detection: second risk-mitigation layer

The first risk-mitigation layer aims to tolerate certain categories of easily modeled uncertainties, such as temporary sensor faults, which are modeled offline prior to calculating the controller gains. However, in real-world applications, pre-modeling may be inaccurate or incomplete. Additionally, smart grids may encounter other hard-to-predict uncertainties, such as cyber attacks on communication networks. Consequently, the proposed security framework includes a second risk-mitigation layer to address the deficiencies of the first layer.

To mitigate the impacts of hard-to-predict uncertainties, such as potential false data injection (FDI) attacks on communication networks, on the stable operation of smart grids, an online intrusion detection unit is established at the control center of each area. Given that load disturbances typically follow a normal distribution, this section presents a decentralized model-based ${\chi }^2$ detection mechanism to evaluate the authenticity of data transmitted from neighboring areas in the presence of potential FDI attacks. This detection unit, installed at the local controller, is responsible for verifying the integrity of received data prior to executing control actions.

The fundamental logic behind ${\chi }^2$ detection is to identify abnormal signals by comparing the accumulated error between measured values and their estimates against a predefined alarm threshold. The accumulated error is calculated by

$${\xi }_j\left(k\right)=\sum _{l=k-\Gamma +1}^k{\left[{\widehat{y}}_j\left(l\right)-{\tilde{y}}_j\left(l\right)\right]}^T\left[{\widehat{y}}_j\left(l\right)-{\tilde{y}}_j\left(l\right)\right],k\ge \Gamma ,$$E18

where ${\xi }_j\left(k\right)$ follows a ${\chi }^2$ distribution with $5\times \left(\Gamma -1\right)$ degrees of freedom, ${\widehat{y}}_j\left(l\right)$ represents the estimates of neighboring measurements, and $\Gamma$ denotes the time window used to determine the number of signals considered.

The ${\chi }^2$ detector at time $k$ is defined as

$${\xi }_j\left(k\right)\underset{H_1}{\overset{H_0}{\lessgtr }}{\delta }_j$$E19

where the threshold ${\delta }_j$ is chosen with precision according to the desired security level, Hypothesis $H_0$ assumes that the received signals are identical to the actual measurements, while the hypothesis $H_1$ posits that there are significant discrepancies. When hypothesis $H_0$ is rejected, the hypothesis $H_1$ is accepted, triggering an alarm. Consequently, the smart grid operators will isolate the compromised communication link.

Note that the precision of the ${\chi }^2$ detection is tightly related to the selected alarming threshold ${\delta }_j$. Determining the optimal alarming threshold remains an open challenge in the field. A trade-off is necessary to balance the false isolation rate (FIR), false connection rate (FCR), and average detection time (ADT). The impacts of ${\delta }_j$ on FIR, FCR, and ADT are thoroughly examined through simulations, aiming to provide valuable insights for researchers and practitioners.

In (18), the estimates of neighboring measurements are calculated based on their respective decentralized models, as follows

$$\left\{\begin{array}{l}{\widehat{x}}_j\left(k+1\right)=A_j{\widehat{x}}_j\left(k\right)+B_j{u}_j\left(k\right),\\ {\widehat{y}}_j\left(k\right)={\widehat{x}}_j\left(k\right),\\ {\widehat{x}}_j\left(0\right)={\widehat{x}}_{j0}.\end{array}\right.$$E20

where the tie-line related signals in (13) are set as zero in (20), to facilitate the calculation of (18).

4.3 Scalability analysis

Careful readers may observe that the mathematical formulation of each layer in the proposed security framework involves numerous parameters. These parameters significantly influence the framework’s implementation efficiency. A particularly important parameter is the subscript $i$, which appears in almost all mathematical formulas and denotes the number of areas within a large-scale power grid. Theoretically, the number of areas can impact the scalability of the proposed security framework. However, it is advantageous that each area of the large-scale power grid can be represented by an equivalent single-machine-single-load system, ensuring that the number of areas remains manageable. Consequently, each generator within an area will receive a power generation reference based on the reference obtained from the equivalent model and predetermined participation factors. Therefore, scalability is not a concern. The computational complexity and integration cost of the proposed framework with existing systems and control strategies are closely tied to the scale of the smart grid. Given that the number of areas is limited, both computational complexity and integration costs remain reasonable. As a result, the proposed security framework exhibits broad applicability.

5. Validation results

5.1 Structure and parameters of the smart grid

To verify the efficacy of the proposed dual-layer security framework, a four-area fully-connected smart grid is utilized for demonstration. In this configuration, each area is physically interconnected with the other three via tie-lines, facilitating mutual communication. The parameters of the smart grid are detailed in Table 2.

Area 1	Area 2	Area 3	Area 4	Unit
$D_1=5$	$D_2=1$	$D_3=3$	$D_4=4$	$\mathit{pu}/\mathit{Hz}$
$2H_1=20$	$2H_2=14$	$2H_3=11$	$2H_4=9$	$\mathit{pu}\cdot s$
$T_{{\mathit{ch}}_1}=1.2$	$T_{{\mathit{ch}}_2}=1.0$	$T_{{\mathit{ch}}_3}=0.7$	$T_{{\mathit{ch}}_4}=0.5$	$s$
$T_{g_1}=1.2$	$T_{g_2}=0.6$	$T_{g_3}=1.4$	$T_{g_4}=0.8$	$s$
$R_1=0.016$	$R_2=0.03$	$R_3=0.05$	$R_4=0.08$	$\mathit{Hz}/\mathit{pu}$
$T_{12}=0.1$	$T_{21}=0.1$	$T_{31}=0.1$	$T_{41}=0.1$	$\mathit{pu}/\mathit{rad}$
$T_{13}=0.1$	$T_{23}=0.1$	$T_{32}=0.1$	$T_{42}=0.1$	$\mathit{pu}/\mathit{rad}$
$T_{14}=0.1$	$T_{24}=0.1$	$T_{34}=0.1$	$T_{43}=0.1$	$\mathit{pu}/\mathit{rad}$

Table 2.

Parameters of the four-area smart grid.

5.2 First risk-mitigation layer validation

To validate the effectiveness of the first risk-mitigation layer, which involves offline control parameter configuration, a traditional PI controller is used as a benchmark. The traditional controller gains are automatically determined using the LMI toolbox in MATLAB, without accounting for PMU faults. Conversely, the risk-mitigation controller gains are automatically selected using the LMI toolbox, considering various PMU fault probabilities. The parameters are set as $h_i=1$, ${\Gamma }_i=0.12$, and $\mathrm{\Delta }{P}_{L_i}\left(k\right)=0.06e^{-0.05k}\left(rand\left(1\right)-0.5\right)$.

Figures 1 and 2 compare the dynamics of $\mathrm{\Delta }{f}_i$ between the traditional controller and the proposed risk-mitigation controller against PMU fault probabilities of $1-{\overline{\theta }}_i=0.1$ and $0.3$. The results indicate that the proposed risk-mitigation controller consistently outperforms the traditional controller, although the extent of improvement varies across scenarios. The incorporation of the first risk-mitigation layer significantly reduces the settling time for each area. In summary, by considering different PMU fault probabilities during the offline control parameter configuration, the controller’s resilience to PMU faults is enhanced. This validates the feasibility and effectiveness of the first risk-mitigation layer.

Figure 1.

Dynamics of $\mathrm{\Delta }{f}_i$ under traditional controller (solid lines) and under risk-mitigation controller (dotted lines) against PMU fault probability $\mathit{1}-{\overline{\theta }}_i=\mathit{0.1}$.

Figure 2.

Dynamics of $\mathrm{\Delta }{f}_i$ under traditional controller (solid lines) and under risk-mitigation controller (dotted lines) against PMU fault probability $\mathit{1}-{\overline{\theta }}_i=\mathit{0.3}$.

5.3 Second risk-mitigation layer validation

To validate the effectiveness of the second risk-mitigation layer, which focuses on online cyber attack detection within the communication network, the parameters for the decentralized model-based ${\chi }^2$ detection mechanism is specified as follows: ${\Gamma }_j=20$, ${\mathrm{\Phi }}_j=\text{Diag}\left\{1,1\right\}$, $G_j=\text{Diag}\left\{1,0\right\}$, and ${\delta }_j=10$. For demonstration purposes, we assume that the communication link from Area 3 to Area 2 is subjected to the FDI attacks characterized by $g_2\left(k\right)={\left[0.5+0.015k0\right]}^T$ starting from $k=50$.

Figure 3 compares the dynamics of $\mathrm{\Delta }{f}_i$ with and without the proposed intrusion detection unit. Without the online cyber attack detection unit, all four areas become unstable under FDI attacks, with Area 2 showing the most significant divergence due to cyber attacks on the communication link from Area 3 to Area 2. The other areas exhibit slower divergence influenced by the state updates from Area 2. With the deployment of the model-based ${\chi }^2$ intrusion detection unit, the FDI attacks are promptly identified at $t=57$s. Subsequently, implementing an attacked data compensation scheme based on the decentralized state estimation model (20), all four areas swiftly return to stable states after a brief period of divergence. The extent of divergence and the detection time are closely related to the false alarm threshold ${\delta }_2$. A larger ${\delta }_2$ requires a longer detection time and results in greater divergence, and vice versa.

Figure 3.

Solid lines imply $\mathrm{\Delta }{f}_i$ without ${\chi }^2$ detection unit while dotted lines imply $\mathrm{\Delta }{f}_i$ with ${\chi }^2$ detection unit.

We also investigate the impacts of various ${\delta }_2$ values (6, 15, 30, 45, 60) on $\mathrm{\Delta }{f}_2$ under the given FDI attacks, and similar conclusions are drawn. We conduct 100 independent tests to obtain statistical results between a wider range of alarming thresholds ${\delta }_2$ and the Key Performance Indicator (KPIs), as shown in Table 3. Observant readers may note that the FCR remains zero even when ${\delta }_2$ values as large as 90 are used. This occurs because the time-varying FDI attack, characterized by $g_2\left(k\right)=0.5+0.015k$, continually increases in amplitude over time. Consequently, the proposed ${\chi }^2$ detection mechanism can identify such FDI attacks. However, a significant drawback is the extended detection duration, resulting in a more pronounced divergence in frequency deviation dynamics. Table 3 aims to serve as a guide for researchers and practitioners, providing references for balancing the FIR, FCR, and ADT.

${\delta }_2$	FIR	FCR	ADT
90	0	0	88.60
75	0	0	69.11
60	0	0	48.86
30	0	0	28.24
15	0	0	8.15
10	0	0	5.54
6	2%	0	3.03
5	8%	0	2.79
3	14%	0	1.29
1	27%	0	1.00

Table 3.

KPIs under different ${\delta }_2$.

6. Conclusions

This chapter proposes a dual-layer security framework addressing cyber-physical aspects within the context of IoT systems in smart grids. This framework enhances data utilization in smart grids under conditions of cyber-physical generalized uncertainties, such as sensor faults and cyber attacks. It introduces a novel approach to facilitate data collection and utilization under imperfect conditions and offers a valuable reference for researchers and practitioners in the fields of smart grids. Validation results confirm the feasibility and effectiveness of the proposed cyber-physical security framework for smart grids.

Acknowledgments

This work is supported in part by the A*STAR under its IAF-ICP Programme I2001E0067 and the Schaeffler Hub for Advanced Research at NTU, in part by National Research Foundation of Singapore under its Medium-Sized Center for Advanced Robotics Technology Innovation and by Naval Group Far East Pte Ltd via an RCA with NTU.