Radiality constraints are involved in both distribution system restoration and reconfiguration problems. However, a set of widely used radiality constraints, i.e., the spanning tree (ST) constraints, has its limitations which have not been well recognized. In this letter, the limitation of the ST constraints is analyzed and an effective set of constraints, referred to as the single-commodity flow constraints, is presented. Furthermore, a combined set of constraints is proposed and case studies indicate that the combined constraints can gain computational efficiency in the reconfiguration problem. Recommendations on the use of radiality constraints are also provided.

In recent decades, the rapid rise in electricity demand has compelled transmission and distribution systems to operate at almost their maximum capacity. This can pose numerous technical challenges such as excessive power losses, voltage and transient instabilities, as well as reduced power quality and reliability. Employment of Flexible Alternating Current Transmission System (FACTS) devices can be an effective approach to obviate such challenges and reinforce the power system functionality. Nevertheless, FACTS devices require a high initial investment, and hence their optimal allocation in terms of various aspects such as type, size and location is of utmost importance. This cannot be achieved without the deployment of optimization techniques. The aim of this paper is to provide a comprehensive review of the existing proposals for the enhancement of power system performance adopting FACTS devices. Adhering to that, an in-depth analysis is carried out, in which the most pertinent options are classified into specific groups based on their optimization objectives. Finally, a comparative analysis is accomplished in which the main attributes and drawbacks of each optimization technique are presented.

Distribution networks have complex topologies and limited number of monitoring devices. Because quick and accurate fault location is critical for the operation quality and reliability of distribution systems, a lot of methods have been proposed, including installation of additional monitoring equipment. Although accurate fault location is possible by dividing the complex topologies into simple ones with fewer branches, the cost of installing additional devices is uneconomic, which makes it hard to be widely applied in practical systems. Based on the theoretical analysis of the relationship between electrical measurements and fault points, an intelligent location method with limited measurement information for multi-branch distribution networks is proposed. Logical reasoning and machine learning are combined to locate fault points with limited measurement information. The relationship between the fault point and unknown distribution of uncontrollable factors in fault equivalents are fitted by machine learning model which can preserve time-related features of electrical waveforms. An adaptive migration strategy by transfer learning is proposed to deal with the problem of small samples in practical application. The proposed method is tested in different topologies. Simulation results prove the effectiveness and generalization capability of the proposed method under complex operating conditions.

With the increasing frequency of extreme weather events such as heavy rainstorm disasters, the stable operation of power systems is facing significant challenges. This paper proposes a two-stage restoration strategy for the distribution networks (DNs). First, a grid-based modeling approach is developed for urban DNs and transportation networks (TNs), capturing the dynamic evolution of heavy rainstorm disasters and more accurately modeling the impact on TNs and DNs. Then, a two-stage restoration strategy is designed for the DN by coordinating soft open points (SOPs) and mobile energy storage systems (MESSs). In the disaster progression stage, SOPs are utilized to enable the flexible reconfiguration and islanding of the DN, minimizing load loss. In the post-disaster recovery stage, the MESS and repair crew are optimally dispatched, taking into account the state of the TN to expedite power restoration. Finally, the experimental results demonstrate that the proposed method reduces load loss during restoration by 8.09% compared to approaches without precise TN and DN modeling.

The proliferation of distributed renewable resources increases the uncertainty in distribution systems. Coupling the distribution system and district heating system helps leverage the flexibility of thermal storage and thus supports the operation of the electrical grid. This paper proposes a method to characterize flexibility from district heating system via polyhedral sets. First, a recursive robust feasibility condition that ensures heat supply adequacy under uncertain demand is established. Then, stagewise robust feasible sets of thermal storage levels are calculated using a customized projection algorithm. Finally, dynamic bounds of electric heaters are computed by a further projection step. With those dynamic bounds, the electric heaters behave like reducible loads, and the demands in each period are decoupled over time, although the dispatch of thermal storage units must comply with inter-temporal constraints. The proposed method allows the two coupled systems to be operated in a distributed way without forecasts and extensive communications. Numerical simulations on small and practically sized testing systems validate the advantage of the proposed method. On average, the set calculation takes about 8 minutes for the day-ahead problem and 11 seconds for real-time dispatch on a portable laptop, and the prediction-free operation policy has an average optimality gap of $3.6\%$ compared to the hindsight optimum.

In optimal dispatch (OD) of multiple integrated energy systems (MIES), Purely data-driven reinforcement learning (RL) methods often encounter challenges such as transient data boundaries, robustness, and interpretability. For this problem, this paper proposes a multi-agent physics-informed reinforcement learning (MAPIRL) method for MIES optimal dispatch. MAPIRL analytically integrates safety constraints using hyperbolic tangent functions, implementing a physics-informed learning process that enforce these constraints within the actor networks. The well-trained MAPIRL can achieve highly generalized real-time decision making. The MAPIRL method is compared with none-physics-based classical RL in a MIES market. The results demonstrate that MAPIRL not only facilitates highly safe and reliable dispatch decisions but also surpasses other methods in convergence efficiency. Additionally, embedding physics knowledge enhances the interpretability for the intelligent OD process.