This article studies enhanced droop-free control strategies with sparse neighboring communication for achieving effective active power sharing of distributed energy resources (DERs) while maintaining the frequency stability of islanded microgrids. The normalized active power consensus (NAPC) based droop-free control can share the load among controllable DERs in proportion to their available capacities. However, existing literature exclusively takes the asymptotic stability of the NAPC-based droop-free control for granted, lacking a comprehensive theoretical proof that is critical for ensuring its effective design and practical implementation. This article, for the first time, provides a thorough theoretical proof of the asymptotic stability of two NAPC-based droop-free control schemes: ordinary NAPC (O-NAPC) and amplifier-equipped NAPC (A-NAPC), by testifying that all effective eigenvalues have negative real parts. The effect of various system settings on the stability margins is further analyzed with respect to the average admittance of the electrical network, the sparseness of the communication network, and the average available capacity of controllable DERs. Based on the sensitivity of eigenvalues with respect to perturbations, a vulnerability analysis is conducted to identify the weaknesses in the microgrids. Case studies demonstrate that the available capacity of controllable DERs has the most decisive influence on the stability margin of NAPC-based droop-free control, while O-NAPC/A-NAPC control scheme is more suitable for microgrids with DERs of larger/ smaller available capacities.

As data sharing is essential in applications such as distributed state estimation of cyber-physical power systems (CPPSs), the issue of data privacy leakage among individual regional system operators is increasingly concerned. To solve the issue, this paper proposes a new distributed security state estimation (DSSE) method based on homomorphic encryption for privacy-preserving consensus. First, considering that regional measurement data managed by individual regional system operators could be attacked by false data injection attacks (FDIAs), a new active attack detection method based on the statistical characteristics of the watermarking signal before and after FDIAs is proposed to improve detection proactivity and accuracy, and it is found that the detection accuracy is positively correlated with the watermarking intensity when the signal to interference plus noise ratio (SINR) is greater than 10db. Second, considering that each regional system operator needs to exchang intermediate data under the premise of protecting data privacy to guarantee the consistency process of distributed state estimation, a homomorphic encryption (HE)-based privacy-preserving consensus method is proposed, where a hash function-based dual verification mechanism is presented to prevent ciphertext data from being tampered by FDIAs. Third, according to the detection results and data compensation mechanism, a local secure state estimation model is proposed, and it is proved that the upper and lower bounds of the reconstructed estimation error covariance are not only related to system parameters and external noise but also negatively related to the compensation error. Furthermore, according to a Lyapunov function including privacy-preserving consensus, sufficient condition for consistency is proven, which depends on Laplacian matrix of the system and the iteration step size. Finally, experimental results demonstrate the feasibility and effectiveness of the proposed dynamic watermarking-based active attack detector and distributed secure state estimation method for CPPSs. Moreover, the computational overhead of incorporating advanced IND-CPA countermeasures (i.e., ciphertext re-randomization and branchless arithmetic) is quantified, which confirms the feasibility of practical deployment.

Secure information exchange of the devices among different domains for cyber-physical power systems (CPPSs) is important yet challenging. Conventional blockchain-based authentication schemes generally adopt single blockchain and signature algorithm, only achieving intradomain or interdomain authentication with lower efficiency, and always failing to meet the confidentiality requirement during information interaction in CPPSs. To address these issues, this paper proposes a cross-domain authentication scheme based on distributed two-layer collaborative blockchains for CPPSs. First, a two-layer-blockchain collaborative authentication architecture is designed, deploying edge servers and taking into account the distributed characteristic of CPPSs. Second, a signcryption algorithm is developed by combining elliptic curve cryptography (ECC) with certificateless cryptography (CLC), which guarantees both the confidentiality and non-repudiation of the block information simultaneously. Furthermore, upper-layer alliance blockchain and lower-layer private blockchain are formed and interact collaboratively via index and Merkle proof, achieving intradomain and interdomain authentication with higher efficiency. Finally, a security analysis and experimental results are presented to superiorly demonstrate the security features and performance in comparison to other schemes in literature.

This paper presents a distributed energy resource and energy storage investment method under a coordination framework between transmission system operators (TSOs) and distribution system operators (DSOs), which simultaneously addresses two main aspects of the flexibility aggregation of DSOs, i.e., flexibility enhancement and dynamic flexibility provision. First, to characterize the key flexibility features of power distribution networks, a multi-port multi-period feasible region formulation is designed using the robust optimization conception while avoiding over-parameterized formulations that require extensive information exchange. Second, a two-stage robust planning model is built to enhance distribution system flexibility by maximizing the volume of feasible regions, in which the uncertainty of dispatch instructions is modeled as a decision-dependent uncertainty (DDU) set and the worst realization is identified for the operational security evaluation. The proposed two-stage robust planning model is solved via a customized column-and-constraint generation algorithm. Finally, a distributed framework for TSO-DSO coordination is proposed to enable the dynamic adjustment of feasible region provision of DSO, given the TSO’s preference, which is then solved by a DDU-based two-stage robust extension of the alternating direction method of multipliers algorithm. Numerical results verify the effectiveness of our proposed models and the scalability of the associated algorithm.Note to Practitioners—The increasing integration of renewable energy resources has stimulated the need for aggregated flexibility provided by power distribution networks (PDNs). However, there are three challenges: i) using the currently feasible region formulation of PDN requires extensive information exchange with the transmission system operator (TSO), thus not compatible with the current structure. ii) the optimal investment of various assets to leverage their cost-effectiveness in feasible region enhancement needs to be addressed. iii) lack of a proper coordination mechanism between TSO and distribution system operators (DSOs) to facilitate the optimal feasible region provision and leverage the spatiotemporal flexibility. To address the above challenges, we design an easy-to-implement feasible region formulation to characterize the key flexibility features of PDNs. Upon this, we propose a feasible region enhancement planning method based on an extended two-stage robust model to address the decision-dependent uncertainty. Furthermore, we facilitate the optimal feasible region provision through the TSO-DSO coordination process in a distributed manner. The numerical results show that the proposed planning method and coordination mechanism could effectively achieve optimal flexibility enhancement and dynamic flexibility provision. In practical application, our proposed planning method can be readily implemented with advanced analytical tools. The coordination mechanism is also compatible with the current TSO-DSO structure and can be easily integrated into it.

Most of the existing signcryption schemes utilize a key generation center to generate pseudonyms without updating, and usually opt for bilinear pairing to design authentication schemes. The disadvantage is that these schemes not only incur heavy computation and communication overheads during information interaction, but also can not eliminate security risks arising from not updating pseudonyms. These limitations render them less effective for smart terminals (STs) with limited computation and communication resources in cyber-physical power systems. The main purpose of this article is to explore a streamlined signcryption scheme tailored for resource-limited STs. To achieve this, a dynamical pseudonym self-generation mechanism (DPSGM) is first introduced to prevent the source from being linked and protect privacy. In addition, a streamlined signcryption scheme is designed based on elliptic curve cryptography and certificateless cryptography, integrating seamlessly with DPSGM. This design significantly reduces computation and communication burdens during information interaction. Finally, a real experimental platform is established to demonstrate the feasibility and effectiveness of the proposed scheme. Visual interfaces show the entire secure interaction process and the resistance to attacks.

The existing identity security schemes (e.g., based on bilinear pairing) have high computational complexity and large bytes of variables, which results in high computation and communication costs. It is difficult to apply the schemes to resource-constrained (i.e., computation and communication) devices. Moreover, most of these schemes adopt a fixed cycle key update strategy compromising the security of authentication schemes or dynamic (real-time) key update strategy with high computational cost. To solve these issues, this article explores a novel revocable lightweight authentication scheme for resource-constrained devices in cyber–physical power systems (CPPSs). First, a lightweight authentication scheme combined elliptic-curve cryptography (ECC) and certificateless cryptography (CLC) is proposed to negotiate a secure session key, which can achieve mutual authentication with low computation and communication costs. Second, aiming at security problem caused by key leakage, a real-time key update strategy with low computational cost is designed to improve the security of identity authentication. Third, according to a hardness assumption of the elliptic-curve discrete logarithm problem (ECDLP), theoretical analysis rigorously proves that the proposed authentication scheme ensures the security with respect to existential unforgeability against adaptively chosen message attacks (EUF-CMAs). Finally, experimental results confirm the feasibility and effectiveness of the proposed authentication scheme.

Under the background of the rapid change of energy technology and the deep integration of artificial intelligence into the power system, it is of great significance to study the intelligent decision-making method of security-constrained unit commitment (SCUC) with high adaptability and high accuracy. Thus, in this article, an expanded sequence-to-sequence (E-Seq2Seq)-based data-driven SCUC expert system for dynamic multiple-sequence mapping samples is proposed. First, dynamic multiple-sequence mapping samples of SCUC are reconstructed by analyzing the input–output sequence characteristics. Then, an E-Seq2Seq approach with a multiple-encoder–decoder architecture and a fully connected extension layer is proposed. On this basis, the simple recurrent unit is introduced as a neuron of the E-Seq2Seq approach to construct deep learning models, and an intelligent data-driven expert system for SCUC is further developed. The proposed approach has been simulated on a typical IEEE 118-bus system and a practical system in Hunan province in China. The results indicate that the proposed approach could possess strong generality, high solution accuracy, and efficiency over traditional methods.

This paper first presents a comprehensive model of the gas system with detailed formulations on pipelines, short pipes, resistors, valves, compressors, and compressor stations. Furthermore, an optimal energy flow model is proposed for integrated power-gas generation and transmission systems. Specifically, on the generation side, gas-fired units couple the two energy systems as the power generation and gas sink; on the transmission side, gas compressor stations link the two energy systems as the power demand and gas transportation. However, gas flow equations are nonlinear and gas flow directions also need to be optimized. Logical programming and tailored piecewise linearization techniques are performed, leading to a mixed-integer linear program (MILP). Only a logarithmic number of binary variables are introduced to represent the nonlinear quadratic function, and thus, the MILP model can be solved very efficiently. Numerical results on four power-gas test systems demonstrate the effectiveness of the proposed approach.

Smart grids require high reliability and sufficient bandwidth from wireless networks to support critical real-time applications and massive smart microgrid data. In general, smart microgrids need to guarantee delays at the order of a few μs for highly delay-sensitive data delivery; as well as delays within few seconds for regular data delivery. This paper presents a framework and its performance analysis for microgrid data aggregation where the microgrid is served by a wireless heterogeneous network. Using unsupervised machine learning, the framework introduces a multi-class and delay sensitivity-aware aggregation of microgrid data within the small cells of the heterogeneous network to ensure that clustering reduces the processing time for highly delay-sensitive messages. Thus, at each Transmission Time Interval (TTI), if there is queued delay-sensitive data, they are dequeued ahead of the delay-tolerant data at the scheduler. Through simulations, we show that the proposed approach successfully reduces the queuing delay by 93% for the packets of delay-sensitive (urgent) messages and the Packet Loss Rate (PLR) by 7% when compared to the benchmark where no aggregation mechanism exists prior to the small cell base stations.

Uncertainties practically arise from numerous factors, such as ambiguous information, inaccurate model, and environment disturbance. Interval arithmetic has emerged to solve problems with uncertain parameters, especially in the computational process where only the upper and lower bounds of parameters can be ascertained. In rectangular coordinate systems, the basic interval operations and improved interval algorithms have been developed in the numerical analysis. However, in polar coordinate systems, interval arithmetic still suffers from issues of complex computation and overestimation. This article defines a polar affine variable and develops a polar affine arithmetic (PAA) that extends affine arithmetic to the polar coordinate systems, which performs better in many aspects than the corresponding polar interval arithmetic (PIA). Basic arithmetic operations are developed based on the complex affine arithmetic. The Chebyshev approximation theory and the min-range approximation theory are used to identify the best affine approximation. PAA can accurately keep track of the interdependency among multiple variables throughout the calculation procedure, which prominently reduces the solution conservativeness. Numerical examples implemented in MATLAB programs show that, compared with benchmark results from the Monte Carlo method, the proposed PAA ensures completeness of the exact solution and presents a more compact solution region than PIA when dependency exists in the calculation process. Meanwhile, a comparison of affine arithmetic in polar and rectangular coordinates is presented. An application of PAA in circuit analysis is quantitatively presented and potential applications in other research fields involving complex variables in polar form will be gradually developed.

Smart grid (SG) represents a large-scale network system with the tight integration of a physical power network and an information network, which makes it more vulnerable to hybrid cyber attacks against different regional subsystems. First, an alternating direction method of multipliers-based distributed state estimation method is developed to overcome the limitation of conventional state estimation and performance analysis of SG against a single type of cyber attacks. Regional subsystems are partitioned via the K-means method. Second, a novel distributed state estimation method integrated with the characteristics of data deception attacks and denial of service (DoS) attacks is proposed to account for the simultaneous presence of different cyber attacks on individual regional subsystems. Third, the convergence of a distributed state estimation algorithm under hybrid cyber attacks is proved theoretically. Furthermore, the relationships between the convergence and algorithm parameters as well as the occurring probability of DoS attacks are established. Finally, the simulations on a modified IEEE 118-bus system are given to demonstrate the feasibility and effectiveness of the proposed method.

Microgrid (MG) represents one of the major drives of adopting Internet of Things for smart cities, as it effectively integrates various distributed energy resources. Indeed, MGs can be connected with each other and presented as a system of multimicrogrid (MMG). This paper proposes the optimal operation of MMGs by a cooperative energy and reserve scheduling model, in which energy and reserve can be cooperatively utilized among MMGs. In addition, values of Shapely are introduced to allocate economic benefits of the cooperative operation. Finally, a case study based on a system of MMGs is conducted, and simulation results verify the effectiveness of the proposed cooperative scheduling model.