Research on Dynamic Reactive Power Optimization of Distribution Network Based on Modern Mathematical Algorithms

To solve the problem of mixed integer nonlinear programming in dynamic reactive power optimization of distribution networks, a two-stage dynamic reactive power optimization model is used to reduce the size of the reactive power optimization calculation.The first stage is nonlinear planning, with the objective of minimizing the combined system network loss and node voltage offset. The second stage is a mixed-integer planning, with the objective of minimizing the incremental power system network loss on the basis of satisfying the constraints such as the number of equipment regulation throughout the day. In view of the fact that the conventional penalty function method to deal with the constraints will result in improper selection of penalty factors, an improved quantum state transfer algorithm with mixed filter technique is proposed. The algorithm adopts a two-population parallel search approach, and the individual adaptation degree and constraint violation degree are constituted as filter pairs as evaluation metrics to replace the penalty functions. Finally, the proposed algorithm, the traditional state transfer algorithm and Colony Algorithm are solved separately for the model using the IEEE 14 system as examples, and the correctness of the proposed model and algorithm is verified by comparing and analyzing the simulation results.

Reactive power optimization considering the load changing of the node in the system is also called as dynamic reactive power optimization. The paper presents a practical algorithm to solve the dynamic reactive power optimization based on the time-interval control, using the improved GA to optimize the discrete control variable and the predictor-corrector interior point method to the smooth control variable on the basis of traditional genetic algorithm. The IEEE-30 node system based on the forecasted load curve of some place is built to simulate the dynamic reactive power optimization. It is concluded that a greater loss reduction can be achieved by the proposed method and the optimal schedule is simple.

Reactive power optimization of distribution network is an effective means to ensure the safe and economic operation of distribution network, and it is an important measure to improve the voltage quality of distribution network. The reactive power optimization of distribution network can improve the voltage distribution of distribution network system, improve the voltage quality of users, reduce the power loss of power transmission, reduce the power cost, and improve the power transmission and distribution capacity and stable operation level of distribution network. This paper studies the optimality of ant colony algorithm and artificial bee colony algorithm for distribution network reactive power optimization. Taking the minimum system active power loss as the objective function, the mathematical model of distribution network reactive power optimization is established. Based on IEEE33 node system, the simulation experiments of distribution network reactive power optimization based on ant colony algorithm and artificial bee colony algorithm are carried out respectively, and the experimental results are compared and analyzed. The experimental results show that both algorithms can improve the system node voltage, the artificial bee colony algorithm has better performance in reducing the efficiency of system active power loss, and the ant colony algorithm runs faster.

In order to solve the practical problem of 24-hours dynamic reactive power optimization in power system dispatching, according to the limit output range of generator’s operation, this paper divides generator’s operation into three regions in PQ mathematical model and takes the action times of discrete control equipment as global inequality constraints, finally establishes a complete 24-hours non-linear mixed integer dynamic reactive power optimization mathematical model. The simulation results show that the mathematical model in this paper can adjust the output of the generators according to the actual situation effectively when the generators are in phase-leading operation. In addition, dynamic reactive power optimization reduces the number of control equipment’s action at the cost of increasing active power loss in the whole network. So, In order to ensure the safe and economic operation of power grid, it is necessary to coordinate the relationship between active power loss and the constraints of control equipment’s action. This paper has positive reference significance for power system dispatching.

In the distribution network containing distributed generators (DG), both DG and capacitors can be adjusted for reactive power, and there is a strong complementarity between the two. If the reactive power compensation ability of each grid-connected DG can be fully utilized, it will effectively reduce the voltage fluctuation and the number of equipment actions, which will help to improve the operation level of the distribution network. In this paper reactive power optimization of distribution networks containing distributed power sources has studies. An improved evolutionary programming (EP) method is proposed to solve the optimization goal, using a variable step-size evolution method and optimization strategy with small population and high convergence accuracy. The algorithm improves the random dynamic step method. In different stages of optimization, different step sizes are used to improve the optimization effect. At the same time, considering that some wind farms are equipped with AVC and some wind farms are equipped with capacitor banks, the evolutionary operator is improved. The operator evolves directly on the integer, so it is easier to find the global optimal solution. This paper has used IEEE33 bus system to verification. Results show that the DG can reduce active power loss in distribution network and ameliorate the voltage level. Meanwhile, the improved evolutionary programming method has good optimization effect, fast convergence speed and high search efficiency.

The dimension of control variables in dynamic reactive power optimization would increase rapidly with the enlargement of power system. A two-phase optimization method was proposed in this paper to confine the regulation times of control equipments. In the first phase, a static optimal model solved by the improved genetic algorithm was established for each time-interval to find several optimal states for the second phase optimization. In the second phase, dynamic programming and genetic algorithm were used to determine the shortest transition path of states to meet the restrictions of regulation times. Furthermore, this method can implement parallel computing easily to be suitable for online applications. The results of test system show the proposed method has a good performance in convergence speed and global optimization.

As it is a new challenge for reactive power optimization reactive power optimizationto bring distributed generators (DGs) into electric distribution network, this paper researches the reactive power optimizationin electric distribution network including DGs. The randomness of DG output results in the randomness of the node voltage in the electric distribution network including DGs, the DG's incorporation into grid, therefore, becomes very significant to the uncertainty analysis of electric power system. Random power flow algorithm is adopted in this paper to figure out the probability distribution of each node, and the model, with the objective function of active network loss minimization based on the chance constraints, is established, under the condition of the secure voltage margin. Improved gravitational search algorithm (IGSA) is adopted to conduct the simulation analysis in the IEEE-33 node standard test system, and the result indicates that, compared with the routine gravitational search algorithm (GSA), IGSA can effectively solve the reactive power optimization problem in electric distributed network, avoiding the premature convergence.

With the increasing penetration of inverter-based photovoltaic (PV) generation, utility-scale grid-connected PV plants are frequently exposed to voltage regulation and voltage stability challenges driven by intermittent irradiance and limited reactive power flexibility under operating constraints. Conventional static Volt/VAR control schemes are typically designed for quasi-steady conditions and therefore struggle to respond to fast variations in PV output and network states. This paper presents a digital twin (DT)-enabled framework for dynamic Volt/VAR optimization in large PV plants. A four-layer DT architecture is developed to achieve real-time cyber-physical synchronization through multi-source data acquisition, secure transmission, fusion, and quality control. To balance model fidelity and computational efficiency, a hybrid physics–data-driven model is constructed, and a local voltage stability L-index is incorporated as an explicit security constraint. A multi-objective optimization problem is formulated to minimize node voltage deviations and reactive power losses while maximizing the static voltage stability margin. The problem is solved using an adaptive parameter particle swarm optimization (AP-PSO) algorithm with dynamic inertia and learning coefficients. Case studies on modified IEEE 33-bus and 53-bus systems demonstrate that the proposed method reduces the voltage profile index by up to 68.9%, improves the static voltage stability margin by 76.5%, and shortens optimization time by up to 30.3% compared with conventional control and representative meta-heuristic or learning-based baselines. The framework further shows good scalability and robustness under practical uncertainties, including irradiance forecast errors and measurement noise. Overall, the proposed approach provides a feasible pathway to enhance operational security and efficiency of grid-connected PV plants under high-penetration scenarios.

The new power system effectively integrates a large number of distributed renewable energy sources, such as solar photovoltaic, wind energy, small hydropower, and biomass energy. This significantly reduces the reliance on fossil fuels and enhances the sustainability and environmental friendliness of energy supply. Compared to distribution networks in traditional power systems, the new-generation distribution network offers notable advantages in improving energy efficiency, reliability, environmental protection, and system flexibility, but it also faces a series of new challenges. These challenges include potential harmonic issues introduced by the widespread use of power electronic devices (such as inverters for renewable energy generation systems and electric vehicle charging stations) and the voltage fluctuations and flickering caused by the intermittency and uncertainty of renewable energy generation, which may affect the normal operation of electrical equipment. To address these challenges, this study proposes an optimization model aimed at minimizing network losses and voltage deviations, utilizing traditional capacitor adjustments and static var compensators (SVCs) as optimization measures. Furthermore, this study introduces an improved version of the multi-objective particle swarm optimization (MOPSO) algorithm, specifically enhanced to address the unique challenges of reactive power optimization in modern distribution networks. The test results show that this algorithm can effectively generate a large number of Pareto optimal solutions. The application of this algorithm on a 33-node network case study demonstrates its advantages in reactive power optimization. The optimization results highlight the effectiveness and feasibility of the proposed improved algorithm in the application of distribution network reactive power optimization, offering users a uniform and diverse range of reactive compensation solutions.

In the context of the energy crisis and environmental problems, renewable energy has burgeoned in recent years. However, with the increasing proportion of wind power access, the dynamic reactive power reserve and support capacity of the system is sharply reduced, and the problem of system voltage stability is prominent. As one of the essential auxiliary means for the power system, the traditional reactive power optimization plays a vital role in improving power quality and reducing active power loss. Wind power and storage devices can output not only active power but also has excellent reactive power output capacity. This paper establishes a wind power and energy storage system (ESS) combined reactive power optimization model and analyzes the effects of the model on the modified IEEE 24-BUS system under the objective function of minimizing the system loss and the wind power curtailment. The results show that the wind and ESS combined reactive power optimization is conducive to the stability of the power grid and can maximize the accommodation of renewable energy.

In order to meet the high permeability and the access of large scale distributed generation, at present and in the future, active distribution network becomes the trend of smart grid research. This paper introduces the influence of distribution network voltage distribution and stability of distributed energy access based on active distribution network; The reactive power and voltage optimization control method of active power distribution network is summarized from the aspects of optimal voltage regulation measure, voltage regulation measure of power network equipment, reactive power optimal dispatch of power system, and so on. Analysis of the current status of the research, and summarized the existing active distribution network with a distributed power pickup distribution network reactive power and voltage control of the existence of some problems and the insufficiency still some problems that must be solved in the study of reactive power and voltage optimization control of active distribution network are pointed out.

A mathematical model considering reactive power cost is proposed for dynamic reactive power optimization in electricity market. To solve this complicated problem, this paper presents a mixed optimization strategy that sufficiently combines the advantages of immune theory and genetic algorithm (GA). By simulating homeostatic mechanism of antibody in immune system, the density of individuals is restrained and promoted automatically. Further more, in order to obtain the heuristic GA, variable region and stable region of antibody are studied in this paper, and an expert knowledge based on effective variety of load is proposed for gene recombination of individuals. The proposed model and algorithm are applied to IEEE30 system, and the numerical results verify the correctness and validity of them.

Voltage violations are the main problem faced in distribution networks (DN) with a higher penetration of inverter-based generations (IBG). Active and reactive power control from smart inverters (SI) can mitigate such violations. Optimal power flow (OPF)-based control provides more accurate operating set points for the coordinated operation of SIs. Therefore, this paper presents a three-phase OPF-based control on SI-enriched unbalanced distribution networks. To consider this, first three-phase model using the current injection model (CIM) is developed. Later, the optimal active and reactive power set points for SIs are obtained by solving a quasi-dynamic optimization problem. The uniqueness of the proposed method is that it regulates the voltage at the affected nodes by obtaining the optimal set points for the smart inverter. The OPF is implemented with a mathematical CIM in Pyomo and solved using the Knitro solver. The proposed method is compared with the sensitivity-based Volt-Var Control (VVC), Volt-Watt Control (VWC), and combined VVC and VWC methods. The effectiveness of the proposed method is verified in a European low-voltage and CIGRE medium-voltage distribution network with 100% penetration. The analysis shows that the OPF-based control optimizes with less network loss and can maintain voltage violations with less reactive power support.

This paper presents a comprehensive distribution robust optimization model based on the distribution network risk index to address the distributional uncertainties of distributed generations (DGs) and loads. To analyze the security of active distribution network (ADN) systematically, a risk assessment method based on improved semi-invariant method and clustering technique is proposed. The risk assessment method is performed on the integrated dynamic reconfiguration and reactive power optimization model. This method can consider the correlation between distributed power sources, and when the injected power is large, the calculation results with higher accuracy can be obtained Case studies on the PG&E 69-bus system verify the robustness and feasibility of the proposed model.

In the context of "dual carbon" strategy, PV power generation will play a very important role, but the distribution network is increasingly affected by the uncertainty of PV power output. This paper proposes a dual-objective distribution network reactive power optimization method based on the adaptive equalization optimizer (AEO) algorithm, which uses adaptive inertia weighting to improve the convergence speed and accuracy of the algorithm based on the basic equalization optimizer algorithm. The AEO algorithm is established to solve the IEEE 33-node distribution network containing PV access with minimum network loss and minimum voltage deviation as the objective function, and finally, the effectiveness and superiority of the proposed algorithm are verified by simulation analysis.