Search Results (23)

Under the “Dual Carbon” strategy, high-penetration integration of distributed generators (DG) into distribution networks has triggered bidirectional power flow and reactive power-voltage violations. This phenomenon undermines the accuracy guarantee of conventional relaxation models (represented by second-order cone programming, SOCP), causing solutions to deviate from the AC power flow feasible region. Notably, ensuring solution feasibility becomes particularly crucial in engineering practice. To address this problem, this paper proposes a collaborative optimization framework integrating convex inner approximation (CIA) theory and a solution recovery algorithm. First, a system relaxation model is constructed using CIA, which strictly enforces ACPF constraints while preserving the computational efficiency of convex optimization. Second, aiming at the conservatism drawback introduced by the CIA method, an admissible region correction strategy based on Stochastic Gradient Descent is designed to narrow the dual gap of the solution. Furthermore, a multi-objective optimization framework is established, incorporating voltage security, operational economy, and renewable energy accommodation rate. Finally, simulations on the IEEE 33/69/118-bus systems demonstrate that the proposed method outperforms the traditional SOCP approach in the 24 h sequential optimization, reducing voltage deviation by 22.6%, power loss by 24.7%, and solution time by 45.4%. Compared with the CIA method, it improves the DG utilization rate by 30.5%. The proposed method exhibits superior generality compared to conventional approaches. Within the upper limit range of network penetration (approximately 60%), it addresses the issue of conservative power output of DG, thereby effectively promoting the utilization of renewable energy. Full article

To handle the uncertainties brought by the increasing penetration of renewable energy sources and random loads, we design a stochastic multi-timescale distribution network reconfiguration (SMTDNR) framework to coordinate diverse scheduling resources across different timescales and develop an efficient heuristic algorithm to solve this complex NP-hard combinatorial optimization problem with high efficiency for medium- and high-voltage distribution networks. First, the SMTDNR problem, incorporating distributed renewable generators, fuel generators, energy storage systems, and controllable loads, is simplified through circular constraint linearization, Jabr relaxation, and second-order cone (SOC) relaxation techniques. Then, a one-stage multi-timescale successive branch reduction (MTSBR) algorithm is developed for distribution networks with one redundant branch, which transforms the SMTDNR problem into a stochastic multi-timescale optimal power flow (SMTOPF) problem. This is extended to a two-stage MTSBR algorithm for general networks with multiple redundant branches, which iteratively runs the proposed one-stage MTSBR algorithm. Numerical results on modified IEEE 33-bus and 123-bus distribution networks validate the superior optimality, feasibility, and computational efficiency of the proposed algorithms, particularly in scenarios of high renewable penetration and increased uncertainty, offering robust and feasible solutions where traditional methods may fail. Full article

To address the challenges of strong nonlinearity, stringent terminal constraints, and the trade-off between computational efficiency and accuracy in the midcourse guidance trajectory optimization problem of aerodynamically controlled interceptors, this paper proposes a variable-discrete-scale sequential convex programming (SCP) method. Firstly, a dynamic model is established by introducing the range domain to replace the traditional time domain, thereby reducing the approximation error of the planned trajectory. Second, to overcome the critical issues of solution space restriction and trajectory divergence caused by terminal equality constraints, a terminal error-proportional relaxation approach is proposed. Subsequently, an improved second-order cone programming (SOCP) formulation is developed through systematic integration of three key techniques: terminal error-proportional relaxation, variable trust region, and path normalization. Finally, an initial trajectory generation algorithm is proposed, upon which a variable-discrete-scale optimization framework is constructed. This framework incorporates a residual-driven discrete-scale adaptation mechanism, which balances discretization errors and computational load. Numerical simulation results indicate that under large discretization scales, the computation time required by the improved SOCP is only about 5.4% of that of GPOPS-II. For small-discretization-scale optimization, the SCP method with the variable discretization framework demonstrates high efficiency, achieving comparable accuracy to GPOPS-II while reducing the computation time to approximately 7.4% of that required by GPOPS-II. Full article

The high-proportion integration of renewable energy sources, represented by wind power and photovoltaics, into active distribution networks (ADNs) can effectively alleviate the pressure associated with advancing China’s dual-carbon goals. However, the high uncertainty in renewable energy output leads to increased system voltage fluctuations and localized voltage violations, posing safety challenges. Consequently, research on optimal dispatch for ADNs with a high penetration of renewable energy has become a current focal point. This paper provides a comprehensive review of research in this domain over the past decade. Initially, it analyzes the voltage impact patterns and control principles in distribution networks under varying levels of renewable energy penetration. Subsequently, it introduces optimization dispatch models for ADNs that focus on three key objectives: safety, economy, and low carbon emissions. Furthermore, addressing the challenge of solving non-convex and nonlinear models, the paper highlights model reformulation strategies such as semidefinite relaxation, second-order cone relaxation, and convex inner approximation methods, along with summarizing relevant intelligent solution algorithms. Additionally, in response to the high uncertainty of renewable energy output, it reviews stochastic optimization dispatch strategies for ADNs, encompassing single-stage, two-stage, and multi-stage approaches. Meanwhile, given the promising prospects of large-scale deep reinforcement learning models in the power sector, their applications in ADN optimization dispatch are also reviewed. Finally, the paper outlines potential future research directions for ADN optimization dispatch. Full article

In midcourse guidance, strong constraints and dual-channel control coupling pose major challenges for trajectory optimization. To address this, this paper proposes an optimal guidance method based on terminal relaxation and range convex programming. The study first derived a range-domain dynamics model with the angle of attack and bank angle as dual control inputs, augmented with path constraints including heat flux limitations, to formulate the midcourse guidance optimization problem. A terminal relaxation strategy was then proposed to mitigate numerical infeasibility induced by rigid terminal constraints, thereby guaranteeing the solvability of successive subproblems. Through the integration of affine variable transformations and successive linearization techniques, the original nonconvex problem was systematically converted into a second-order cone programming (SOCP) formulation, with theoretical equivalence between the relaxed and original problems established under well-justified assumptions. Furthermore, a heuristic initial trajectory generation scheme was devised, and the solution was obtained via a sequential convex programming (SCP) algorithm. Numerical simulation results demonstrated that the proposed method effectively satisfies strict path constraints, successfully generates feasible midcourse guidance trajectories, and exhibits strong computational efficiency and robustness. Additionally, a systematic comparison was conducted to evaluate the impact of different interpolation methods and discretization point quantities on algorithm performance. Full article

Aiming to solve optimization scheduling difficulties caused by the double uncertainty of source-side photovoltaic (PV) output and load-side demand response in active distribution networks, this paper proposes a two-stage distribution robust optimization method. First, the first-stage model with the objective of minimizing power purchase cost and the second-stage model with the co-optimization of active loss, distributed power generation cost, PV abandonment penalty, and load compensation cost under the worst probability distribution are constructed, and multiple constraints such as distribution network currents, node voltages, equipment outputs, and demand responses are comprehensively considered. Secondly, the second-order cone relaxation and linearization technique is adopted to deal with the nonlinear constraints, and the inexact column and constraint generation (iCCG) algorithm is designed to accelerate the solution process. The solution efficiency and accuracy are balanced by dynamically adjusting the convergence gap of the main problem. The simulation results based on the improved IEEE33 bus system show that the proposed method reduces the operation cost by 5.7% compared with the traditional robust optimization, and the cut-load capacity is significantly reduced at a confidence level of 0.95. The iCCG algorithm improves the computational efficiency by 35.2% compared with the traditional CCG algorithm, which verifies the effectiveness of the model in coping with the uncertainties and improving the economy and robustness. Full article

The high proportion of distributed photovoltaic (DPV) access has changed the traditional distribution network structure and operation mode, posing a huge threat to the stable operation and economy of the distribution network. Aiming at a reasonable access capacity of DPV in the distribution network, this paper proposes an economic access capacity evaluation method for DPV in the distribution network considering proper PV power curtailment. Firstly, a method for generating typical joint light intensity and load power operation scenarios based on an improved K-means clustering algorithm is proposed, which provides comprehensive scenario support for the evaluation. Secondly, based on active and reactive power regulation, this paper proposes a DPV access capacity enhancement method to improve the DPV access capacity. Thirdly, considering proper PV power curtailment, an evaluation model of DPV economic access capacity in the distribution network is established to solve the maximum DPV economic access capacity in the distribution network. And aiming at the nonlinear problem in the model, the second-order cone relaxation method is employed to transform the model into the second-order cone programming model, so as to solve the objective function conveniently and efficiently. Finally, based on the improved IEEE 33-node distribution network analysis, the results show that the proposed method can be more comprehensive and effective in evaluating the DPV economic access capacity in the distribution network, and proper PV power curtailment can significantly increase the DPV economic access capacity in the distribution network. Full article

Smart Transformer (ST)-based Meshed Hybrid AC/DC Microgrids (MHMs) present a promising solution to enhance the efficiency of conventional microgrids (MGs) and facilitate higher integration of Distributed Energy Resources (DERs), simultaneously managing active and reactive power dispatch. However, MHMs face challenges in resource management under uncertainty and control of electronic converters linked to the ST and DERs, complicating the pursuit of optimal system performance. This paper introduces a Data-Driven Distributionally Robust Optimization (DDDRO) approach for day-ahead operation planning in ST-based MHMs, focusing on minimizing network losses, voltage deviations, and operational costs by optimizing the reactive power dispatch of DERs. The approach accounts for uncertainties in photovoltaic generator (PVG) output and demand. The Column-and-Constraint Generation (C&CG) algorithm and the Duality-Free Decomposition (DFD) method are employed. The initial mixed-integer non-linear planning problem is also reformulated into a mixed-integer (MI) Second-Order Cone Programming (SOCP) problem using second-order cone relaxation and a positive octagonal constraint method. Simulation results on a connected MHM system validate the model’s efficacy and performance. The study also highlights the advantages of the meshed MG structure and the positive impact of integrating the ST into MHMs, leveraging the multi-stage converter’s flexibility for optimal energy management under uncertain conditions. Full article

To address the challenges associated with wind power integration, this paper analyzes the impact of distributed renewable energy on the voltage of the distribution network. Taking into account the fast control of photovoltaic inverters and the unique characteristics of photovoltaic arrays, we establish an active distribution network voltage reactive power-optimization model for planning the active distribution network. The model involves solving the original non-convex and non-linear power-flow-optimization problem. By introducing the second-order cone relaxation algorithm, we transform the model into a second-order cone programming model, making it easier to solve and yielding good results. The optimized parameters are then applied to the IEEE 33-node distribution system, where the phase angle of the node voltage is adjusted to optimize the reactive power of the entire power system, thereby demonstrating the effectiveness of utilizing a second-order cone programming algorithm for reactive power optimization in a comprehensive manner. Subsequently, active distribution network power quality control is implemented, resulting in a reduction in network loss from 0.41 MW to 0.02 MW. This reduces power loss rates, increases utilization efficiency by approximately 94%, optimizes power quality management, and ensures that users receive high-quality electrical energy. Full article

In response to challenges in constructing charging and hydrogen refueling facilities during the transition from conventional fuel vehicles to electric and hydrogen fuel cell vehicles, this paper introduces an innovative method for siting and capacity determination of Electric Hydrogen Charging Integrated Stations (EHCIS). In emphasizing the calculation of vehicle charging and hydrogen refueling demands, the proposed approach employs the Voronoi diagram and the particle swarm algorithm. Initially, Origin–Destination (OD) pairs represent car starting and endpoints, portraying travel demands. Utilizing the traffic network model, Dijkstra’s algorithm determines the shortest path for new energy vehicles, with the Monte Carlo simulation obtaining electric hydrogen energy demands. Subsequently, the Voronoi diagram categorizes the service scope of EHCIS, determining the equipment capacity while considering charging and refueling capabilities. Furthermore, the Voronoi diagram is employed to delineate the EHCIS service scope, determine the equipment capacity, and consider distance constraints, enhancing the rationality of site and service scope divisions. Finally, a dynamic optimal current model framework based on second-order cone relaxation is established for distribution networks. This framework plans each element of the active distribution network, ensuring safe and stable operation upon connection to EHCIS. To minimize the total social cost of EHCIS and address the constraints related to charging equipment and hydrogen production, a siting and capacity model is developed and solved using a particle swarm algorithm. Simulation planning in Sioux Falls city and the IEEE33 network validates the effectiveness and feasibility of the proposed method, ensuring stable power grid operation while meeting automotive energy demands. Full article

The problem regarding the optimal siting and sizing of photovoltaic (PV) generation units in electrical distribution networks with monopolar direct current (DC) operation technology was addressed in this research by proposing a two-stage convex optimization (TSCO) approach. In the first stage, the exact mixed-integer nonlinear programming (MINLP) formulation was relaxed via mixed-integer linear programming, defining the nodes where the PV generation units must be placed. In the second stage, the optimal power flow problem associated with PV sizing was solved by approximating the exact nonlinear component of the MINLP model into a second-order cone programming equivalent. The main contribution of this research is the use of two approximations to efficiently solve the studied problem, by taking advantage of convex optimization models. The numerical results in the monopolar DC version of the IEEE 33-bus grid demonstrate the effectiveness of the proposed approach when compared to multiple combinatorial optimization methods. Two evaluations were conducted, to confirm the efficiency of the proposed optimization model. The first evaluation considered the IEEE 33-bus grid without current limitations in all distribution branches, to later compare it to different metaheuristic approaches (discrete versions of the Chu and Beasley genetic algorithm, the vortex search algorithm, and the generalized normal distribution optimizer); the second simulation included the thermal current limits in the model’s optimization. The numerical results showed that when the maximum point power tracking was not regarded as a decision-making criterion, the expected annual investment and operating costs exhibited better performances, i.e., additional reductions of about USD 100,000 in the simulation cases compared to the scenarios involving maximum power point tracking. Full article

Optimal power flow (OPF) is a crucial aspect of distribution network planning and operation. Conventional heuristic algorithms fail to meet the system requirements for speed and accuracy, while linearized OPF approaches are inadequate for distribution networks with high R/X ratios. To address these issues and cater to multi-period scenarios, this study proposes a dynamic linearized second-order cone programming-based (SOCP) OPF model. The model is built by first establishing a dynamic OPF model based on linearized second-order conic relaxation (LSOCR-DOPF). The components of the active distribution network, such as renewable energy power generation units, energy storage units, on-load-tap-changers, static var compensators, and capacitor banks, are then separately modeled. The model is implemented in MATLAB and solved by YALMIP and GUROBI. Finally, three representative scenarios are used to evaluate the model accuracy and effectiveness. The results show that the proposed LSOCR-DOPF model can ensure calculation time within 3 min, voltage stability, and error control within 10⁻⁶ for all three applications. This method has strong practical value in the fields of active distribution network day-ahead dispatch, accurate modeling of ZIP load, and real-time operation. Full article

In order to cope with the efficient consumption and flexible regulation of resource scarcity due to grid integration of renewable energy sources, a scheduling strategy that takes into account the coordinated interaction of source, grid, load, and storage is proposed. In order to improve the accuracy of the dispatch, a BP neural network approach modified by a genetic algorithm is used to predict renewable energy sources and loads. The non-convex, non-linear optimal dispatch model of the distribution grid is transformed into a mixed integer programming model with optimal tides based on the second-order cone relaxation, variable substitution, and segmental linearization of the Big M method. In addition, the uncertainty of distributed renewable energy output and the flexibility of load demand re-response limit optimal dispatch on a single time scale, so the frequency of renewable energy and load forecasting is increased, and an optimal dispatch model with complementary time scales is developed. Finally, the IEEE 33-node distribution system was tested to verify the effectiveness of the proposed optimal dispatching strategy. The simulation results show an 18.28% improvement in the economy of the system and a 24.39% increase in the capacity to consume renewable energy. Full article

In order to adjust to the change of the large-scale deployment of photovoltaic (PV) power generation and fully exploit the potentialities of an integrated energy distribution system (IEDS) in solar energy accommodation, an evaluation method on maximum hosting capacity of solar energy in IEDS based on convex relaxation optimization algorithm is proposed in this paper. Firstly, an evaluation model of maximum hosting capacity of solar energy for IEDS considering the electrical-thermal comprehensive utilization of solar energy is proposed, in which the maximization of PV capacity and solar collector (SC) capacity are fully considered. Secondly, IEDS’s potential in electricity, heat, and gas energy coordinated optimization is fully exploited to enhance the hosting capacity of solar energy in which the electric distribution network, heating network, and natural gas network constraints are fully modeled. Then, an enhanced second-order cone programming (SOCP)-based method is employed to solve the proposed maximum hosting capacity model. Through SOCP relaxation and linearization, the original nonconvex nonlinear programming model is converted into the mixed-integer second-order cone programming model. Meanwhile, to ensure the exactness of SOCP relaxation and improve the computation efficiency, increasingly tight linear cuts of distribution system and natural gas system are added to the SOCP relaxation. Finally, an example is given to verify the effectiveness of the proposed method. The analysis results show that the maximum hosting capacity of solar energy can be improved significantly by realizing the coordination of an integrated multi-energy system and the optimal utilization of electricity, heat, and gas energy. By applying SOCP relaxation, linearization, and adding increasingly tight linear cuts of distribution system and natural gas system to the SOCP relaxation, the proposed model can be solved accurately and efficiently. Full article

Traditional reactive power optimization mainly considers the constraints of active management elements and ignores the randomness and volatility of distributed energy sources, which cannot meet the actual demand. Therefore, this paper establishes a reactive power optimization model for active distribution networks, which is solved by a second-order cone relaxation method and interval optimization theory. On the one hand, the second-order cone relaxation technique transforms the non-convex optimal dynamic problem into a convex optimization model to improve the solving efficiency. On the other hand, the interval optimization strategy can solve the source–load uncertainty problem in the distribution network and obtain the interval solution of the optimization problem. Specially, we use confidence interval estimation to shorten the interval range, thereby improving the accuracy of the interval solution. The model takes the minimum economy as the objective function and considers a variety of active management elements. Finally, the modified IEEE 33 node arithmetic example verifies the feasibility and superiority of the interval optimization algorithm. Full article