Network partitioning is a popular research topic. Not all available partitioning methods are equally suitable for power grids. Community detection is a critical issue in complex network theory, and power grid is a typical type of complex network. This paper proposes a functional community structure based on an extended weighted network model. An extended adjacency matrix is used to represent an extended weighted complex network model based on coupling strength rather than the conventional adjacency matrix. Meanwhile, we upgraded the Newman fast algorithm of community detection for establishing a novel power grid partitioning algorithm. The electrical coupling strength (ECS) is defined to better reflect electrical characteristics between any two nodes in power grid. Modularity is also redefined as electrical modularity based on ECS. The Newman fast algorithm is upgraded with electrical modularity maximization as the objective to detect functional communities in power grids. A case study on IEEE test systems with 30, 39, 118, 300 buses and one Italian power network demonstrates the rationality of the extended weighted network model and partitioning algorithm.

In addition to active energy management, this article proposes active planning as another critical feature of active distribution networks (ADNs). To develop this set of tasks, this article introduces a three-layer active planning framework consisting of a physical layer, cyber layer, and socioeconomic layer. Furthermore, a three-step developing strategy for ADNs based on a virtual microgrid (VM) is put forward. Then, according to this framework, this article focuses on a specific and fundamental issue that often arises: the optimal allocation of distributed generation (DG). A two-stage scheme based on VMs is a proposed solution. In the first stage, VM boundaries are determined based on the characteristics of a network structure. Using the identified VM boundaries as constraints, a bilevel hierarchical optimization method is applied to determine the optimal DG allocation in the second stage. The proposed method is verified in the popular PG&E 69-bus distribution network.

The contributions of this article include a new concept, a new question, and a new method. This article proposes the concept of functional community, which is different from conventional topological community. Functional community is defined with two meanings: (1) tighter internal coupling for better efficiency within the same community; (2) more internal transmission from source to sink nodes within the same community. Then a new question about how to detect functional communities in power grids is analyzed, and most existing algorithms are not applicable. Therefore, a new method is put forward. Corresponding to meaning 1, electrical coupling strength (ECS) is defined to replace conventional adjacency matrix; corresponding to meaning 2, power supply strength is defined and integrated with ECS to form the newly defined electrical functional strength. Based on these two changes, we apply the proposed power supply modularity as a benchmark to evaluate any partitioning of power grids. Moreover, the Newman fast algorithm is modified with power supply modularity maximization to detect functional communities in power grids. The capability of the proposed partitioning method is demonstrated via the IEEE-118, IEEE-300 bus systems, and an Italian power grid. We argue that the conventional topological modularity may exaggerate the community characteristics of power grids and is inferior to the power supply modularity in detecting some functional features in communities. The work can also give inspiration to other engineering networks for functional communities.

Recently, the development of the Internet of Things (IoT) enables more comprehensive and intelligent analysis and defense for cascading failures in power grids. This paper summarizes power grids as Temporal Weighted Networks (TWN) which are different from conventional temporal networks. For TWN, the topological structure is fixed but weight distribution is time-varying. Then it is noted that for different operating states represented by different weight (power flow) distribution at different time sections, the risks of cascading failures would be completely different. Inspired by analysis of inter-subnetworks power shifts in cascading failures, Inverse-Community (IC) structure is proposed in TWN to intuitively identify the risk of cascading failures. IC describes a structure in weighted networks with several communities in which the weighted interaction between communities is significantly stronger than that within the same community. Furthermore, the conventional modularity is upgraded as Inverse Modularity (IM) to quantify the characteristic of IC structure in power networks. Subsequently, considers the risk of cascading failures represented by IM and the cost of power network operation, a security/economic dispatch (SED) method is designed to handle the optimal power dispatch issues. Simulation results prove a positive correlation between IM of power flow distribution and risk of cascading failures. Furthermore, the results on the IEEE 118-bus system demonstrate the effectiveness of the proposed SED method in mitigating cascading failure risks.

The theory of complex networks has been studied extensively since its inception. However, until now, the impact of the node-type distributions is related to network topology and cannot be evaluated independently. In this paper, a network structure is modeled via an adjacency matrix (network topology) and a set of node type distribution vectors. Three specific issues that need to be considered for node type distributions in smart grid testing and planning are summarized in this paper. First, a set of metrics are proposed and defined to evaluate the impact of node-type distributions on network performance independently. Second, another metric named the generation distribution factor is proposed to evaluate the distribution of generation buses resulting from the specific function and purpose of power grids and by considering the distribution of load buses as given conditions. Third, another metric, i.e., the power supply redundancy metric based on entropy, is proposed to evaluate the inequality of load in power supply. Finally, a discrimination factor is defined to ensure the overall evaluation and comparison of different networks is made for this inequality. All proposed metrics can be applied to the IEEE-30, IEEE-118, IEEE-300 bus systems, as well as Italian power grid components. The simulation results indicate that the IEEE-118 system has the best node type distribution and minimum discrimination; the Italian system has the worst node-type distribution and most serious discrimination of load power supply.