Power Flow Calculation Research Articles

Multi-Objective Power Supply Restoration in Distribution Networks Based on Graph Calculation and Information Collected by Multi-Source Sensors

With the increasing complexity of the distribution network structure, enhancing the efficiency and reliability during fault restoration has become a focal point. Based on the multi-source information collected by traditional sensors, such as CT and PT, and intelligent sensors, such as D-PMU, and the graph calculation model, the fault recovery problem of a multi-objective distribution network is studied. Firstly, a power flow calculation model and operation constraint adaptable to topology changes are proposed under the graph calculation framework. The minimum spanning tree theory is utilized to define the blackout range and recovery path set. Secondly, the intelligent sensor D-PMU is configured to collect fault information to ensure that at least one of any two connected load vertices is configured with D-PMU. Thirdly, a topological evolution model is established that considers repeated primary and secondary transfer in outage areas while exploring possible recovery strategies deeply. Finally, a distribution network in Shaanxi Province is taken as an example to verify the model. The experiment shows that the strategy in this paper dynamically adjusts the recovery strategy through four means—one transfer, one repeat transfer in the outage area, two transfers, and cutting off part of the outage load—and the overall recovery rate is increased by more than 20%.

LCC-MCC hybrid HVDC power flow calculation based on holomorphic embedding method

LCC-MCC hybrid HVDC power flow calculation based on holomorphic embedding method

Enhanced AC/DC optimal power flow via nested distributed optimization for AC/VSC-MTDC hybrid power systems

The deployment of voltage source converters (VSC) to facilitate flexible interconnections between the AC grid, renewable energy system (RES) and Multi-terminal DC (MTDC) grid is on the rise. However, significant challenges exist in exploiting coordinated operations for such AC/VSC-MTDC hybrid power systems. One of the most critical issues is how to achieve the optimal operation of such wide-area systems involving several power entities with as minimal communication burden as possible. To address this issue, an enhanced AC/DC optimal power flow (OPF) is specifically proposed. Firstly, a mixed-integer convex AC/DC OPF model is explicitly formulated to describe the optimal operation of such hybrid power systems. Subsequently, a nested distributed optimization method with double iteration loops is developed to offer optimal system-wide decision-making through a more “thorough” distributed communication architecture. In the outer iteration, the original AC/DC OPF problem is decomposed into several slave problems (SPs) associated with systems (including the AC grid and RESs) and one master problem (MP) associated with the integrated VSC-MTDC grid. Generalized Benders decomposition (GBD) serves to solve the master and slave problems iteratively. Techniques such as multi-cut generation and asynchronous updating are utilized to upgrade the GBD performance of computation efficiency and address communication delays. In the inner iteration, the master problem is continuously decomposed into multiple sub-MPs associated with individual VSCs. The alternating direction method of multipliers (ADMM) is employed to solve these sub-MPs iteratively. Proximal terms and heuristic approaches are embedded to enable parallel computation and handling of integer variables. Numerical experiment results finally validate the effectiveness of the proposed enhanced AC/DC OPF. The constructed AC/DC OPF model exhibits acceptable accuracy in terms of power flow calculation, and the developed nested distributed optimization method showcases decent convergence rate and solution optimality performances.

GENETIC ALGORITHM-BASED OPTIMIZATION OF DISTRIBUTED GENERATOR PLACEMENT IN DISTRIBUTION NETWORKS TO MINIMIZE POWER LOSSES

An increase in electrical energy can lead to an increase in power losses and a decrease in voltage in the system. One of the efforts made to reduce power losses that occur in the distribution network is by placing the optimal Distributed Generation (DG) in the right location. Installation of DGs with suboptimal capacity and placement location can result in greater active power losses and further reduce voltage stability. This study discusses the optimization of DG placement in the electric power distribution network using genetic algorithm methods that are known to be effective in solving complex optimization problems. The IEEE 33 bus distribution system, which is a standard system frequently employed in power flow research, was the subject of the case study. The Newton-Raphson method is a commonly used iterative method for power flow analysis due to its accuracy in calculating power flow in electrical networks. The research findings indicate that the most suitable location for two DG units with an injection power of 6,626 MW is on buses 3 and 4. The placement of this DG has the potential to substantially mitigate power losses within the distribution network. The placement of two DG units on buses 3 and 4 results in a more significant improvement in system power losses than the placement of DG units on other buses. Power losses of buses 3 and 4 experienced power losses of 67724.69 MW, while system losses were reduced by 1137621.21 MW, or 5.61 percent.

A multi-task learning based line parameter identification method for medium-voltage distribution network

Accurate line parameters are critical for and dispatch in distribution systems. External operating condition variations affect line parameters, reducing the accuracy of state estimation and power flow calculations. While many methods have been proposed and obtained results rather acceptable, there is room for improvement as they don’t fully consider line connections in known topologies. Furthermore, inaccuracies in measurement devices and data acquisition systems can introduce noise and outliers, impacting the reliability of parameter identification. To address these challenges, we propose a line parameter identification method based on Graph Attention Networks and Multi-gate Mixture-of-Experts. The topological structure of the power grid and the capabilities of modern data acquisition equipment are utilized to capture. We also introduce a multi-task learning framework to enable joint training of parameter identification across different branches, thereby enhancing computational efficiency and accuracy. Experiments show that the GAT-MMoE model outperforms traditional methods, with notable improvements in both accuracy and robustness.

Physics-informed line graph neural network for power flow calculation.

Power flow calculation plays a significant role in the operation and planning of modern power systems. Traditional numerical calculation methods have good interpretability but high time complexity. They are unable to cope with increasing amounts of data in power systems; therefore, many machine learning based methods have been proposed for more efficient power flow calculation. Despite the good performance of these methods in terms of computation speed, they often overlook the importance of transmission lines and do not fully consider the physical mechanisms in the power systems, thereby weakening the prediction accuracy of power flow. Given the importance of the transmission lines as well as to comprehensively consider their mutual influence, we shift our focus from bus adjacency relationships to transmission line adjacency relationships and propose a physics-informed line graph neural network framework. This framework propagates information between buses and transmission lines by introducing the concepts of the incidence matrix and the line graph matrix. Based on the mechanics of the power flow equations, we further design a loss function by integrating physical information to ensure that the output results of the model satisfy the laws of physics and have better interpretability. Experimental results on different power grid datasets and different scenarios demonstrate the accuracy of our proposed model.

Application of simplifying jacobian matrix and introducing iterative threshold to improve newton-raphson method in three-phase power flow calculation

Abstract With the expansion of the scale and complexity of the power system, traditional three-phase power flow calculation methods are facing dual challenges of computational efficiency and accuracy. Power flow calculation is a mathematical method for analyzing the power flow of an electrical system. And the Newton-Raphson (NR) method is an effective algorithm for solving nonlinear problems. However, updating the Jacobian matrix in the NR method can take a lot of time. Based on the asymmetry in three-phase power systems and the time-consuming nature of the NR method, an enhanced version of the NR method is proposed in this paper that improves the efficiency of power flow calculations by simplifying the Jacobian matrix and optimizing the iteration speed. Furthermore, in order to minimize the number of iterations in the NR method, it is proposed to use the PO method to determine the ideal iteration threshold.

Physics Embedded Graph Convolution Neural Network for Power Flow Calculation Considering Uncertain Injections and Topology.

Probabilistic analysis tool is important to quantify the impacts of the uncertainties on power system operations. However, the repetitive calculations of power flow are time-consuming. To address this issue, data-driven approaches are proposed but they are not robust to the uncertain injections and varying topology. This article proposes a model-driven graph convolution neural network (MD-GCN) for power flow calculation with high-computational efficiency and good robustness to topology changes. Compared with the basic graph convolution neural network (GCN), the construction of MD-GCN considers the physical connection relationships among different nodes. This is achieved by embedding the linearized power flow model into the layer-wise propagation. Such a structure enhances the interpretability of the network forward propagation. To ensure that enough features are extracted in MD-GCN, a new input feature construction method with multiple neighborhood aggregations and a global pooling layer are developed. This allows us to integrate both global features and neighborhood features, yielding the complete features representation of the system-wide impacts on every single node. Numerical results on the IEEE 30-bus, 57-bus, 118-bus, and 1354-bus systems demonstrate that the proposed method achieves much better performance as compared to other approaches in the presence of uncertain power injections and system topology.

Research on power flow calculation methods applicable to new energy generating station area

Abstract With the construction and development of new distribution networks, more and more new components such as distributed power supply and active loads have been connected to the new energy generation station area, posing new requirements for operational control in the new energy generation station area. However, the power supply and load coexist in the new energy generation station area, with both single-phase and three-phase, significant power fluctuations, inaccurate calculation parameters, and incomplete measurement information. Therefore, achieving accurate and efficient calculations plays an important role. This article proposes a power flow calculation method suitable for new energy generation station areas. Firstly, the three parts of this method are explained: overall scheme, stationary correction link, and generalized scene mapping; Secondly, the correctness and applicability of this method were verified through simulation.

Holistic analysis of the dynamic stability of the Southern Cameroon Interconnected grid in contingency situations

The Southern Cameroon Interconnected Network (SIG) is depicted as a large-scale power system that has shown significant instability due to a series of blackouts in recent years. These blackouts are primarily attributed to major disruptions in transmission lines and energy deficits between supply and demand. The imbalance between power supply and demand necessitates the grid to operate near its stability limits, increasing the risk of blackouts. The necessity of investigating the dynamics of SIG behavior in response to observed contingency situations serves as the primary motivation for this study. To achieve this objective, the SIG was modeled using saturated generators with ZIP static loads. Through Newton-Raphson based power flow calculations, voltage magnitude profiles of the grid were obtained for each generation scenario. An N-1 contingency consisting of a standard Newton-based continuation power flow (CPF) analysis has identified line 5–6 as the most frequent worst case of line outage. Additionally, a short-term transient analysis was conducted under three-phase short-circuit, line outage and generator outage scenarios. In the event of a short-circuit, the Mangombe-225 bus experienced the most significant impact. Concerning line outages, line 1–5 had the most adverse effect on the grid's frequency stability. However, generation outages had a lesser impact on frequency stability compared to other disturbances. Lastly, modal analysis revealed that the grid exhibited weak stability with a critical mode identified at a frequency of 4.0267 Hz, exceeding typical values. This underscores the necessity of damping the grid oscillations for enhanced stability.

Power Flow Analysis in Unbalanced Three-Phase Distribution Systems using Backward/Forward Sweep and Current Injection Methods

The electrical power distribution system is a part of the power system that distributes electricity from the transmission network to customers. In the distribution system, imbalances often occur due to the varying load profiles in each phase. This can cause voltage imbalances in the distribution system. This study aims to compare two power flow analysis methods, Backward/Forward Sweep and Current Injection. The study analyses the voltage and power loss conditions on each phase at each bus and line in the three-phase distribution system under unbalanced conditions. Simulations were conducted on two IEEE test buses, IEEE 19-Bus and IEEE 33-Bus with radial configurations. The power flow calculation results using the Backward and Forward Sweep method showed that in the IEEE 19-Bus system, the highest voltage drop percentage occurred on phase b at bus 19, at 3.14%, the highest voltage imbalance percentage occurred at bus 19, at 0.1409%, and the total active and reactive power losses were 7.352 kW and 3.164 kVAR. In the IEEE 33-Bus system, the highest voltage drop percentage occurred on phase c at bus 18, at 5.85%, the highest imbalance percentage occurred at bus 15, at 0.2077%, and the total active and reactive power losses were 19.107 kW and 8.22 kVAR. The percentage difference between the two methods used is less than one percent, indicating that both methods are sufficiently accurate in analyzing power flow in an unbalanced distribution system.

A multi-objective robust dispatch strategy for renewable energy microgrids considering multiple uncertainties

The demand for low-carbon transformations and the uncertainty of renewable energy sources and loads present significant challenges for the optimal dispatch of microgrid. This study proposed a multi-objective robust dispatch strategy to reduce the risks associated with the uncertainty of renewable energy source output and loads while promoting low-carbon and economical microgrid operation. The economic emission dispatch problem for a microgrid was formulated as a multi-objective robust dual-layer optimization model. Consequently, a high-dimensional adjustable linear polyhedral uncertainty set was proposed to describe the uncertainty of renewable energy sources and loads. This study transformed the original model into an easy-to-solve single-layer second-order cone programming optimal power flow optimization model by employing second-order cone relaxation and duality transformation. Thereafter, a synthetic membership function was proposed to determine the optimal compromise solution. To determine the charging and discharging statuses of the battery storage system and the electricity traded between the microgrid and the external power grid, a battery storage system control strategy based on time-of-use electricity prices and real-time power flow calculations was proposed. Simulations conducted on a modified IEEE-30 bus system demonstrated that the proposed strategy effectively reduced the economic costs and carbon emissions of the microgrid by 8.23 % and 2.43 %, respectively.

Power flow analysis and volt/var control strategy of the active distribution network based on data-driven method

In order to solve the problems of low power flow calculation accuracy and voltage overcrossing of the distribution network caused by large-scale distributed power supply, a data-driven power flow analysis and volt/var optimization control strategy for distribution network are proposed in this paper. Firstly, a data-driven power flow analysis model for the distribution network is proposed, and the nonlinear mapping relationship between the distribution network state and power flow results is described from the data-driven perspective. Secondly, the paper analyzes the influence of photovoltaic power supply on the voltage of the distribution network, and establishes the volt/var optimization model based on photovoltaic power supply. Then, on the basis of data-driven power flow analysis of the distribution network, the distribution network reactive voltage optimization strategy based on data-driven power flow analysis is proposed to ensure the safe and stable operation of distribution network voltage, reduce the operating network loss of distribution network, and realize the distribution network reactive voltage optimization is not affected by factors such as distribution network line parameters. Finally, IEEE 33 node power distribution system is used to verify the effectiveness of the proposed strategy.

Dynamic Determination Method of Line Drop Compensator Parameters for Voltage Regulators Based on Mixture of Experts Using Real‐Time Information

In this paper, a method for determining line drop compensator (LDC) parameters for step voltage regulators and on‐load tap changers is proposed to avoid voltage violations in distribution systems with voltage fluctuations due to photovoltaic (PV) generation and electric vehicle (EV) charging. Distribution system operators need to effectively solve voltage problems caused by the widespread installation of distributed energy resources with the existing voltage regulators to construct an efficient and rational infrastructure. Our focus was on improving the method for determining the LDC parameters for the existing voltage regulators based on LDC control. A mechanism to dynamically change the LDC parameters depending on the situations in the distribution system was developed by using a mixture of experts, one of the machine learning techniques, and real‐time voltage and power flow information from information technology switches. The power flow calculations were performed using a distribution system model constructed based on the topology, loads, and generation characteristics of an actual distribution system in the Hokuriku region. The effectiveness of the proposed method was evaluated in terms of its improved effect on PV and EV hosting capacity, as well as the impact on the frequency of tap operations of voltage regulators. © 2024 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

A long-term power system state calculation method using sequential power and holomorphic embedding

Traditional Power Flow (PF) calculations struggle to support the data analysis requirements as the power system develops. Therefore, this paper introduces a non-sequential and non-iterative PF calculation method to enhance the computational speed and analytical efficiency of power system state variables over long time scales. Firstly, a Power Sequential Division (PSD) method is proposed, representing the power curve using hierarchical energy with temporal characteristics. Next, based on the Fast and Flexible Holomorphic Embedding (FFHE) method, the paper explores the incremental properties of Voltage Power Series Coefficients (VPSC) and proposes an Incremental Holomorphic Embedding (IHE) method. Finally, by combining PSD and IHE, this study introduces a Power Sequential Flow (PSPF) method for rapid computation of power system state variables over long time scales. Unlike traditional PF methods, PSPF method shifts away from time-series calculations and instead analyzes the distribution of power system state variables over long time scales from an energy perspective. Various test cases are set up to analyze the performance characteristics of IHE and PSPF from multiple perspectives. The results indicate that the proposed methods significantly outperform traditional PF methods in terms of computational speed, adaptability to test cases, and analytical efficiency.

Single and multi-threaded power flow algorithm for integrated transmission-distribution-residential networks

The rapid development of renewable sources has significantly increased interdependencies between electricity networks of all voltage levels, leading to bidirectional flows between transmission and distribution networks, and requiring analysis of Integrated Transmission-Distribution (ITD) network. The interconnectivity is further amplified by additional coupling with electricity, gas, heat and hydrogen networks, on both national and regional levels. Moreover, installation of solar, wind and storage on customers’ premises has indicated that residential networks need to be included in the overall integrated model, called Integrated Transmission-Distribution-Residential (ITDR) network. The main goal of the paper is to develop a general model of the ITD/ITDR networks and to solve the power-flow problem on large-scale networks in an efficient way. The general model includes three-phase transmission and multi-phase distribution models, as well as accurate control strategies for traditional and electronically coupled electricity resources. The proposed model is solved via novel single-threaded power flow procedure, which incorporates new network elements’ models and the developed algorithm for integrated power flow calculations in different domains. This is further improved by developing a multi-threaded approach. Analyses on a small-scale ITD network have shown that single- and multi-threaded approaches are, respectively, (1.5–4) and (2–5) times faster compared to the state-of-the-art procedures. As network size increases, the efficiency of the proposed multi-threaded procedure becomes more pronounced compared to the single-threaded one (up to 2.39 times).

A Fully Analytical Approach for the Real-Time Dynamic Reliability Evaluation of Composite Power Systems with Renewable Energy Sources

Renewable energy sources (RES) have strong uncertainties, which significantly increase the risks of power imbalance and load shedding in composite power systems. It is thus necessary to evaluate the operational reliability for guiding economic dispatch and reducing the risks. Current methods cannot meet the requirement for the operational timeliness of reliability evaluations due to the high computational complexity of the optimal power flow (OPF) calculations of massive contingencies. This paper proposes a fully analytical approach to construct fast-to-run analytical functions of reliability indices and avoid reassessments when the load and RES change. The approach consists of uniform design (UD)-based contingency screening and a modified stochastic response surface method (mSRSM). The contingency screening method is used to select critical contingencies while considering the uncertainties. The mSRSM is used to construct the analytical functions of the load shedding to the load and RES generation for the selected contingencies. An analytical function of a smooth virtual variable that maps to the load shedding is established in such a way that, when the load and RES vary, the reliability can be assessed within a very short time rather than using laborious OPF calculations. Case studies illustrate the excellent performance of the proposed method for real-time reliability evaluation.

Optimal Power Flow Calculation Based on Improved Crossover Algorithm

Abstract Aiming at the optimization problem of power flow distribution in power system, this paper puts forward a method for calculating the optimal power flow of power network based on the improved crisscross algorithm. The fast convergence crisscross optimization algorithm (FCSO) is based on the traditional crisscross optimization algorithm (CSO) to improve the efficiency and accuracy of solving the Optimal Power Flow, OPF) problem. Based on the original double crossover operator, the improved algorithm puts forward a brand-new operator-central crossover operator, which alternates with transverse crossover operator according to certain rules, In order to improve the quality of single search and accelerate convergence, each individual in the population performs crossover operation with the current optimal individual in turn, and then performs competition operator to selectively approach the current global optimal individual. Finally, combined with experimental verification, the optimal power flow calculation of reactive power optimization based on FSCO has obvious practical effects in improving network voltage quality and reducing line loss, The average voltage increase ratio of 220kV bus and 110kV bus is 0.676% and 0.855% respectively, and the loss reduction rate reaches 3.51%, Compared with CSO, the convergence and calculation speed of FSCO proposed in this paper is faster, the convergence curve is smoother, and the average time consumption is increased to 59.53% compared with CSO, In the case of obtaining the same precision solution, the optimization time is obviously shortened, the timeliness of the optimal solution in regulation operation is effectively improved, and the problem of reactive power optimization in power system can be well solved.

Discrete-time distributed algorithms for solving linear equations via layered coordination

This paper is concerned with the problem of designing discrete-time distributed algorithms for solving large-scale linear equations via layered coordination. A row-column decomposition and a column-row decomposition are provided to partition the augmented matrix associated with the linear equations into several block matrices, respectively. By assigning an equation solver layer to computation and a data integration layer to data exchanges, a row-column decomposition-based discrete-time distributed algorithm and a column-row decomposition-based discrete-time distributed algorithm are proposed for solving large-scale linear equations, respectively. It is shown that the distributed algorithms proposed can reach a consensus exponentially on one of the solutions of linear equations. Finally, the effectiveness of the distributed algorithms proposed is validated via the numerical simulation of the power flow calculation of power systems and the problem of solving the large-scale linear equations.

Optimal Placement of HVDC-VSC in AC System Using Self-Adaptive Bonobo Optimizer to Solve Optimal Power Flows: A Case Study of the Algerian Electrical Network

Modern electrical power networks make extensive use of high voltage direct current transmission systems based on voltage source converters due to their advantages in terms of both cost and flexibility. Moreover, incorporating a direct current link adds more complexity to the optimal power flow computation. This paper presents a new meta-heuristic technique, named self-adaptive bonobo optimizer, which is an improved version of bonobo optimizer. It aims to solve the optimal power flow for alternating current power systems and hybrid systems AC/DC, to find the optimal location of the high voltage direct current line in the network, with a view to minimize the total generation costs and the total active power transmission losses. The self-adaptive bonobo optimizer was tested on the IEEE 30-bus system, and the large-scale Algerian 114-bus electric network. The obtained results were assessed and contrasted with those previously published in the literature in order to demonstrate the effectiveness and potential of the suggested strategy.