Power Flow Calculation Method Research Articles

Optimal power flow in hybrid AC-DC systems considering N-k security constraints in the preventive-corrective control stage

The optimal power flow methods for AC-DC systems containing VSC-HVDC generally only consider the economy during normal operation, overlooking the distribution of line transmission power in fault conditions. As a result, lines that continue to operate after a fault may experience overloading or operate at full capacity. Thus, a method for optimal power flow calculation is proposed that incorporates N-k security constraints in the preventive-corrective control stage for secure and economic operation of hybrid AC-DC systems. This method ensures that the line transmission power in the system meets the limits in the normal, short-term fault, and long-term fault states. In addition to the optimal power flow in the normal state, the method incorporates the system's imbalance as an indicator to evaluate system resilience. It combines this indicator with the economic, network loss, and performance metrics of the system, forming a two-stage bi-level multi-objective optimization model. Furthermore, to address the curse of dimensionality in anticipating system fault sets, a method for generating the anticipated fault set using non-sequential Monte Carlo simulation is proposed, along with a fault scenario search approach based on robust thinking to identify the most severe faults. Finally, the traditional IEEE 30-bus system was improved, and simulation verification was conducted using examples of an AC/DC system with a three-terminal DC network and a wind-solar-storage hybrid AC/DC system with a three-terminal DC network. The simulation results indicate that the proposed optimal power flow method considering the preventive-corrective control stage with N-k security constraints can effectively enhance system resilience. Furthermore, it improves the economic efficiency while ensuring the secure operation of the system.

Identification and Evaluation of Vulnerable Links in a Distribution Network with Renewable Energy Source Based on Minimum Discriminant Information

With the increase in the proportion of photovoltaic and wind power access, the scale and form of distribution networks are becoming more and more complex. The traditional single distribution network vulnerability assessment method is difficult to use to identify the vulnerable links in the distribution network. Therefore, this paper proposes a method for identifying and evaluating vulnerable links in distribution networks based on minimum discriminant information. First, considering the influence of distributed grid connection, an improved probabilistic power flow calculation method is proposed, which improves the calculation efficiency and accuracy. Second, considering the correlation degree, transmission capacity, and voltage stability of branches in the distribution network, the identification index of vulnerable lines is defined. Based on power quality and operating state, the identification index of vulnerable nodes in a distribution network is defined. Finally, based on the indicators of vulnerable nodes and vulnerable lines, the vulnerable links in the distribution network are comprehensively evaluated based on the principle of minimum discriminant information, and the vulnerable links of the entire distribution network are evaluated according to different degrees of vulnerability. The rationality and effectiveness of the proposed method are verified via an example analysis of actual power grid data.

A Virtual Graph Constrained Learning Method for Power Flow Calculation

A Virtual Graph Constrained Learning Method for Power Flow Calculation

A Neural Network Approach to Physical Information Embedding for Optimal Power Flow

With the increasing share of renewable energy in the power system, traditional power flow calculation methods are facing challenges of complexity and efficiency. To address these issues, this paper proposes a new framework for AC optimal power flow analysis based on a physics-informed convolutional neural network (PICNN) approach, which enables the neural network to learn solutions that follow physical laws by embedding the power flow equations and other physical constraints into the loss function of the network. Compared with the traditional power flow calculation method, the calculation speed of this method is improved by 10–30 times. Compared to traditional neural network models, the method provides higher accuracy, with an average increase in accuracy of up to 2.5–10 times. In addition, this paper introduces a methodology to extract worst-case guarantees for violations of the neural network’s predicted power generation constraints, determining the worst possible violation that could result from any neural network output across the entire input domain, and taking appropriate measures to reduce the violation. The method is experimentally shown to be highly accurate and reliable for the AC optimal power flow (AC-OPF) analysis problem, while reducing the dependence on a large amount of labelled data.

Fast power flow calculation for distribution networks based on graph models and hierarchical forward-backward sweep parallel algorithm

IntroductionIn response to the issues of complexity and low efficiency in line loss calculations for actual distribution networks, this paper proposes a fast power flow calculation method for distribution networks based on Neo4j graph models and a hierarchical forward-backward sweep parallel algorithm.MethodsFirstly, Neo4j is used to describe the distribution network structure as a simple graph model composed of nodes and edges. Secondly, a hierarchical forward-backward sweep method is adopted to perform power flow calculations on the graph model network. Finally, during the computation of distribution network subgraphs, the method is combined with the Bulk Synchronous Parallel (BSP) computing model to quickly complete the line loss analysis.Results and DiscussionResults from the IEEE 33-node test system demonstrate that the proposed method can calculate network losses quickly and accurately, with a computation time of only 0.175s, which is lower than the MySQL and Neo4j graph methods that do not consider hierarchical parallel computing.

A Method for Power Flow Calculation in AC/DC Hybrid Distribution Networks Considering the Electric Energy Routers Based on an Alternating Iterative Approach

With the advancement of new power system construction, distribution networks are gradually transforming from being a simple energy receiver and distributor to being an integrated power network that integrates sources, networks, loads, and energy storage with interactive and flexible coupling with the upper-level power grid. However, traditional distribution networks lack active control and distribution capabilities, failing to meet the demands of network transformation and upgrading. To address this issue, this paper proposes a method for solving AC/DC power flow calculation considering an electric energy router (EER) based on an alternating iterative method. Initially, the model for the multi-port EER and three types of power flow models for the AC distribution network, DC distribution network, and EER are constructed. By leveraging the properties of the EER and the hybrid power flow calculation model, a method is proposed for calculating the power flow in the AC/DC hybrid distribution network considering the EER. Finally, by solving the power flow in a medium- and low-voltage AC/DC distribution system, the adaptability of the proposed method is compared. The results demonstrate that the AC/DC hybrid distribution network power flow calculation method established in this paper, which incorporates the EER, possesses high accuracy and adaptability, with an error margin of less than 0.05%.

Dynamic Calculation Method for Zonal Carbon Emissions in Power Systems Based on the Theory of Production Simulation and Carbon Emission Flow Theory

Power systems are the main source of carbon emissions. Currently, coordinated operation strategies of the source–grid–load–storage model considering carbon emissions is primarily expanded from the generation side. For practical power systems, where multiple types of generating units coexist at a single node, it is difficult to develop unit combination strategies that simultaneously consider carbon emission factors and power flow constraints. Therefore, a new power flow calculation method based on connectivity matrix theory was proposed, aiming to address the issues of existing approaches that are too coarse and unable to accurately represent the operating states of multiple units under each node. Furthermore, a new method for dynamic calculation of regional carbon emission based on connectivity matrix and carbon emissions flow was introduced to improve the accuracy of carbon emission measurements. Firstly, a simulation model for a coordinated optimization operation based on the minimum system cost for the source–grid–load was established and an optimal flow calculation method using a connectivity matrix was introduced. Second, a dynamic carbon emission calculation method, considering electricity sources, was developed by combining the results of the optimal power flow calculation with carbon emission flow theory. Finally, the effectiveness of the approach in this article was verified by the IEEE 14-bus system example and a provincial power grid, ensuring strict adherence to the conservation principle of carbon emissions between the supply and demand sides and satisfying power flow constraints.

Optimal power flow method with consideration of uncertainty sources of renewable energy and demand response

Optimal power flow (OPF) calculation methods are important for the power system operation and mainly focus on the deterministic power flow calculation, neglecting the impact of demand response on online security calculation of power systems with renewable energy sources. Therefore, this paper proposes an OPF calculation method that considers the uncertainties of wind power, photovoltaic (PV) power generation and demand-side response. Firstly, the research focuses on the renewable energy grid, considering the uncertainties of wind power and PV power generation, and establishes uncertainty models for wind power and PV output. Secondly, based on cloud model theory, an uncertainty model for demand response is established. According to the established models, an efficient OPF model is constructed with a linearized submodels considering multiple uncertainties. By testing on the IEEE 30-bus system as a typical example, we found the effectiveness and superiority of the proposed OPF calculation method can benefit the power system economic operation and demand side resource utilization.

Research on harmonic power flow calculation method of distribution network with large-scale distributed grid-connected inverter

Research on harmonic power flow calculation method of distribution network with large-scale distributed grid-connected inverter

A novel stochastic power flow calculation and optimal control method for microgrid based on multivariate stochastic factors fusion – Sensitivity

The stochasticity of power flow of distributed generations (DGs) and load in the microgrid has great influence on power flow distribution and voltage quality of the distribution network. For improving the voltage quality of the distribution network, the questions need to be further studied, which include the description of the stochasticity of the power flow in the microgrid and the impact of the microgrid into the distribution network on the power flow. Therefore, a novel stochastic power flow calculation and optimal control method for the microgrid based on multivariate stochastic factors fusion-sensitivity (MSFF-sensitivity) is proposed in this paper. Firstly, the multivariate stochastic factors fusion (MSFF) function is developed by using the probability density function to extract the stochasticity and correlation of power flow among different stochastic factors in the microgrid, which are effectively unified. Furthermore, the fusion-sensitivity (F-sensitivity) of the power flow in the microgrid integrated into the distribution network is constructed to accurately characterize the influence degree of various stochastic factors in the microgrid on the power flow of the distribution network. Based on this, the output power of the stochastic factor is adjusted to optimally control the power flow of the distribution network. Finally, the algorithm verification suggests that, compared with the conventional power flow methods, the method proposed in this paper is more suitable for the microgrid. The influence of stochastic power flow on the distribution network can be effectively reduced and the voltage quality of the distribution network can be improved by optimizing control of the power flow in the microgrid integrated into the distribution network.

Power Flow Calculation for AC/DC Power Systems with Line-Commutated Converter–Modular Multilevel Converter (LCC-MMC) Hybrid High-Voltage Direct Current (HVDC) Based on the Holomorphic Embedding Method

To harness the strengths and mitigate the limitations of line-commutated converter (LCC) and modular multilevel converter (MMC) HVDC systems, the LCC-MMC hybrid HVDC system has been developed. This paper proposes a holomorphic embedding (HE)-based power flow calculation method for AC/DC power systems with the LCC-MMC hybrid HVDC system. Firstly, the methodology involves establishing the mathematical model of the LCC-MMC hybrid HVDC system and its control modes. Subsequently, the HE formulation for the constructed LCC-MMC model is derived using the HE method. The proposed method simplifies the HE formulation using substitute variables, making it adaptable to various control modes. The designed HE formulation facilitates the derivation of the germ solution and the calculation of high-order power series coefficients. A sequential solution flow chart compatible with AC power flow algorithms is constructed to enhance the practicality of the HE method for real-world large-scale systems. The accuracy and effectiveness of the proposed method are verified through numerical tests on the modified IEEE 14-bus, IEEE 57-bus, and large 2383-bus system. The proposed method provides a reliable and efficient solution for power flow analysis in hybrid HVDC systems.

Research on data-driven power flow calculation method based on undirected-graph delooping-backtracking

As the scale of the power grid expands and distributed energy sources are integrated, along with the emergence of random loads, topological control of distribution networks has become a novel means of control. Therefore, data-driven power flow calculations must be capable of rapidly and accurately computing power flow results even when there are changes in the network’s topology. In this paper, a data-driven power flow calculation method is proposed to take topological changes into account. Based on initial loop data, we employ an undirected-graph delooping-backtracking method to generate a set of feasible topological samples. Using the Monte Carlo method on this basis, we generate feasible samples for the network’s topology and power injection, thereby establishing a training dataset. By training a deep neural network on these samples and adjusting network parameters, we effectively address power flow calculations in the presence of topological changes. Case study results demonstrate that the data-driven power flow calculation method, considering topological changes, can rapidly and accurately compute power flow results when topology alterations occur.

Probabilistic Voltage Optimization Considering Load Static Voltage Characteristics

In the conventional power flow calculation, the load is mostly treated as a constant power node. When the voltage deviation occurs, the static voltage characteristics of the load will change, resulting in the change of the power flow calculation. This situation is more likely to occur in the distribution network with distributed power supply. Therefore, it is very important to consider the static voltage response characteristics of the load in the power flow calculation. In the existing literature, when evaluating and optimizing voltage stability, deterministic indicators are usually used to evaluate the voltage level of the system. In the active distribution network with uncertain new energy output, this method has its limitations. Based on the above analysis, this paper uses the power flow calculation method considering the static voltage characteristics of the load to solve the node voltage distribution of the distribution network system. Considering the uncertainty of new energy output and load, the semi-invariant method is used to analyze the probabilistic power flow. An evaluation index considering the digital characteristics of voltage deviation distribution is proposed. The voltage optimization model is established according to the proposed index, and the genetic algorithm is used to solve the problem. The IEEE33 node standard example is simulated to verify the correctness and feasibility of the proposed method.

Optimal Cooperative Eco-Driving of Multitrain With TLET Comprehensive System

Aiming to minimize the total electricity usage in realistic operation of urban rail transit (URT) trains, this paper establishes the coupled model for the train-line-electric network-timetable (TLET) comprehensive system, and proposes a multi-train cooperative eco-driving method to achieve the system energy optimal. The dynamic power flow within the DC railway system with multiple trains is analyzed by modeling the traction power supply system (TPSS), and an improved power flow calculation (PFC) method is proposed to calculate the dynamic power flow distribution. To achieve the total substation energy minimization, a space-time-speed (STS) three-dimensional network is presented to transform continuous train motion process into discrete states on space-speed plane, and a multiple individuals dynamic programming (MIDP) algorithm is throughly developed to cooperatively optimize the multi-train trajectories along the time horizon, with which the optimal speed profiles and timetables of each train can be obtained simultaneously. Moreover, a computationally efficient heuristic algorithm together with a train-to-train (T2T) communication policy are developed as a comparative study. Numerical experiment with field data from Guangzhou Metro Line 8 is implemented, to illustrate the energy-saving performance of the proposed methods.

Convergence criterion of power flow calculation based on graph neural network

In order to solve the problem of current data-driven power flow calculation methods rarely consider the divergence of power flow, which always maps a false system power flow when a divergence power flow case was given, a data-driven power flow convergence method based on DGAT-GPPool graph neural network classifier is proposed. Firstly, to solve the problem that the classical graph convolution method does not consider the edge attribute, a double-view graph attention convolution layer is constructed based on line admittance. Secondly, to solve the existing pooling method also does not consider the edge attribute and the loss of physical meaning of the coarse graph obtained from pooling, a grid partition pooling layer is constructed based on the electrical distance between nodes. Finally, 10000 system samples containing different network topologies are generated based on the IEEE 14-node system and its extended system, the accuracy reaches 99.3% in the testing set after training, and the effectiveness of the improvements in graph convolution and graph pooling is verified by comparative experiments.

Optimal power flow calculation method for regional integrated energy system based on double-layer optimization

In this paper, a two-layer optimization calculation method is proposed to improve the practical application efficiency of the integrated energy system and to improve the different problems of power flow calculation. Firstly, the power flow model is constructed and the optimization function is established based on indicators such as economy and environmental protection. The two-layer optimization method is proposed by combining the quadratic programming method and the particle swarm algorithm. Then, the obtained operating conditions of each energy equipment are used as the input of the power flow. The processing of each device and the energy flow of the power flow network are calculated and the effectiveness of the algorithm is verified by MATLAB power analysis.

Distribution network power flow calculation based on the BPNN optimized by GA‐ADAM

AbstractPower system operation and control are based on power flow calculations. In order to solve the uncertainty of the increasing penetration of renewable energy, the voltage fluctuation at the load point increases in the distribution network, and the inaccuracy of the power flow calculation due to the insufficient power flow data collection capability of the traditional power system. In this paper, a data‐driven power flow analysis model is proposed, a back propagation neural network combined with genetic algorithm (GA) and adaptive moment estimation (ADAM) optimization algorithm model is constructed to analyze the power flow calculation method of distribution networks under stochasticity. Firstly, the power flow initial value information, topology characteristics, and power factor index are introduced to construct a training set, and the mapping relationship between bus voltage and power is fully explored by training the regression model. Second, the GA‐ADAM algorithm is used to optimize the initial values and weight parameters of the model. Finally, it is verified based on IEEE‐33 bus distribution model, and the model is used for power flow calculation, and compared with other methods through each relevant error evaluation indicators. The results show that the model constructed in this paper has small error indicators and high accuracy, which improves the efficiency and accuracy of power flow calculation.

Optimal siting of substations of traction power supply systems considering seismic risk

The traction power supply system (TPSS) is a critical infrastructure that provides electrified railways with power. However, its safe and reliable operation is threatened by earthquake disasters. Due to the strong randomness, uneven spatial distribution, and destructive risk of earthquake disasters, it is crucial to develop reasonable planning schemes to mitigate seismic risks of the system. This paper proposes a substation optimal siting method considering seismic risks. By establishing the chain circuit model of the TPSS and employing the dynamic power flow calculation method, the power loss of the system is obtained. By integrating the earthquake scenario simulation and substation fragility analysis, the substation seismic risk is calculated through Monte Carlo simulation. On this basis, the optimization model for substation site selection is formulated, aiming to minimize both the system power loss and the substation seismic risk while adhering to constraints of construction cost, operating safety, and geographical locations. The Pareto optimal solutions are then obtained. Simulation analysis based on actual system parameters shows that compared with traditional site selection methods, the proposed method can effectively mitigate system seismic risks while considering system power loss, providing theoretical bases for the disaster prevention and mitigation in the TPSS planning.

Linearized power flow calculation of bipolar DC distribution network with multiple flexible equipment

The bipolar direct current distribution network (BDCDN) has the advantages of high reliability, large transmission, and high efficiency. However, voltage unbalance is a crucial power quality problem of BDCDN. On one hand, flexible equipment, such as DC electric spring, DC power flow controller, and DC transformer, can effectively suppress unbalanced voltage. On the other hand, the diversity of topology and control methods of multiple types of flexible equipment complicates power flow calculation. In this study, a linear power flow algorithm is proposed. First, the structural characteristics of a BDCDN with multiple types of flexible equipment are analyzed. Second, a linear ZIP load model based on Taylor expansion is derived. The steady-state model of multiple types of flexible equipment is established by analyzing the topological structure and control mode. Third, a network modeling and power flow calculation method of BDCDN with multiple types of flexible equipment are proposed. Finally, the modified IEEE14-node case and IEEE33-node case are used to verify the validity and correctness of the proposed algorithm. The effectiveness of flexible equipment on the power quality issue is demonstrated through comparison studies of power flow distributions.

Vulnerable Area Identification of Islanded Combined Electrical and Heat Networks Based on Static Sensitivity Analysis

In combined electrical and heat networks (CEHNs) under the Islanded mode, the district heating network (DHN) is more vulnerable to fluctuations in the electrical load, resulting in the transgression of the CHEN power flow. Identifying vulnerable areas in islanded CEHNs is necessary. In this paper, we introduce a static sensitivity analysis method into islanded CHENs, which can identify vulnerable areas susceptible to these impacts, and explore the energy interaction mechanisms between the electrical network (EN) and DHN. We established a power flow model of the islanded CEHN, and developed the sensitivity matrix. Then, the decomposition model is solved, based on which the static sensitivity matrices can be calculated. The case study shows that the sensitivity can effectively represent the impact of EN load changes on the mass flow rate of the DHN, thus we can locate the weak areas of the CEHN. It can provide auxiliary information for the safe and stable operation of an islanded CEHN, with fewer calculations compared to the power flow calculation method. In addition, the results present the enhancement of islanded CHEN stability by using a kind of combination of CHP units.