Power Flow Calculation Research Articles

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.

Decomposing total power flows into contributions originating from power sources in loads, generators, and network elements

To thoroughly analyze the conditions in power lines, transformers or loads, it is essential to have knowledge of their active and reactive power flow contributions from each power source. Understanding these contributions allows for a detailed analysis of the impact of active and reactive power flow contribution from each power source on active and reactive power losses in each network element, as well as the determination of power participation of each source to every load. This paper provides the necessary equations and an adequate procedure for calculating power flow contributions. The method is suitable for meshed network and considers shunt elements, avoiding problematic simplifications. Furthermore, it ensures impartiality towards any network user, making it well-suited for application in deregulated environments. By offering valuable information useful, this method supports the creation of transparent and non-discriminatory agreements between network operator and users.

Optimal scheduling of active distribution network based on RBF-stochastic response surface method

As the high proportion of distributed generation (DG) and diversification of loads increase, the distribution network faces increasingly greater impact. To address the high-dimensional stochastic problems arising from the multi-dimensional uncertainty of power source and load, this paper proposes a two-stage optimization scheduling scheme for AC distribution networks based on RBF-stochastic response surface method (RBF-SRSM). This scheme takes into account economy, environmental protection and safety, and consists of day-ahead and intra-day stages. The day-ahead decision scheduling is based on an optimal low-carbon economy operation plan, while the intra-day reactive power optimization is achieved by converting nonlinear integral indicators into discrete linear indicators through probabilistic power flow calculation and the first moment derivation principle inspired by SRSM. The mixed integer second-order cone programming (MISOCP) method is used to solve the dispatching plan, and the results suggest that the proposed method is more efficient than the SRSM.

Optimizing Critical Overloaded Power Transmission Lines with a Novel Unified SVC Deployment Approach Based on FVSI Analysis

This paper proposes a novel methodology to improve stability in a transmission system under critical conditions of operation when additional loads that take the system to the verge of stability are placed in weak bus bars according to the fast voltage stability index (FVSI). This paper employs the Newton–Raphson method to calculate power flows accurately and, based on that information, correctly calculate the FVSI for every transmission line. First, the weakest transmission line is identified by considering N−1 contingencies for the disconnection of transmission lines, and then all weak nodes associated with this transmission line are identified. Following this, critical scenarios generated by stochastically placed loads that will take the system to the verge of instability will be placed on the identified weak nodes. Then, the methodology will optimally size and place a single static VAR compensator SVC in the system to take the transmission system to the conditions before the additional loads are connected. Finally, the methodology will be validated by testing the system for critical contingencies when any transmission line associated with the weak nodes is disconnected. As a result, this paper’s methodology found a single SVC that will improve the system’s stability and voltage profiles to similar values when the additional loads are not connected and even before contingencies occur. The methodology is validated on three transmission systems: IEEE 14, 30, and 118 bus bars.

On the operation and implications of grid-interactive renewable energy communities

The increasing installations of photovoltaic systems, electric vehicle chargers, heat pumps, and battery storage systems challenge distribution system operators to prevent critical grid operations. Nonetheless, flexibility potential from customer-owned assets remains untapped due to lacking federated coordination and incentives. In Europe, emerging renewable energy communities can address this challenge by facilitating collective optimal operation of flexible assets and providing grid services. This paper presents an approach for renewable energy communities to offer participants’ flexibility through grid-interactive operations. Distribution system operators then based on optimal power flow calculations request flexibility use to prevent voltage violations, transformer overloads, and line overloads. A case study with simulations for a future rural low-voltage grid is conducted. The results show that, compared to business-as-usual operations or renewable energy communities with fixed import and export limits, the grid-interactive approach ensures non-critical grid operations cost-efficiently and reduces curtailment by 60% to 90%, down to 1.1% of total generation. By providing both upward and downward flexibility and aligning with distribution system operators’ requirements, grid-interactive renewable energy communities can be key in enhancing the efficient use and stability of distribution grids.

Study on Reactive Power Optimization Including DSSC for New Energy Access to the Power Grid

The vigorous development of new energy has effectively reduced carbon emissions, but it has also brought fluctuating impacts on the carrying capacity of the power grid. In order to improve the voltage stability after integrating new energy sources and promote the scientific consumption of more new energy, this paper proposes the use of Distributed Static Synchronous Compensator (DSSC) devices for flexible and controllable voltage regulation in new energy integration. An improved particle swarm optimization algorithm is then developed to optimize the reactive power considering the regulation of DSSC. The paper conducts power flow calculations based on the DSSC power injection model and establishes a reactive power optimization mathematical model with objectives of minimizing active power loss, minimizing node voltage deviation, and maximizing voltage stability margin in the grid with new energy integration. The improved particle swarm optimization algorithm is utilized to achieve the reactive power optimization. Experimental simulations are conducted using the IEEE 33-node system to analyze the voltage improvement before and after adopting the improved particle swarm optimization algorithm considering the DSSC device in the grid with new energy integration. It is found that the proposed method effectively reduces active power loss and stabilizes voltage fluctuations, demonstrating its practical value.

Optimal configuration of distributed energy storage considering intending island recovery in faulty distribution networks

With the rapid development of distributed generation, represented by photovoltaic power, the access of a large number of distributed generation poses threats to the security and reliable operation of islanded distribution networks. However, relying on the distributed energy storage system can stabilize the island power supply, which can effectively improve the reliability of the island distribution network. To this end, under the premise of knowing photovoltaic output and load forecast curve, this paper proposes a distributed energy storage optimization configuration method in the active islanding operation mode of multi-source distribution network, which satisfies the “N-1″ safety criterion. First, this paper establishes an optimization configuration model for distributed energy storage with multiple objectives, including minimizing the load shedding in the non-fault loss of power zone, the initial investment cost of distributed energy storage, the node voltage deviation and the system frequency offset. Then, aiming at the islanded power flow calculation process mentioned above, an improved trust region algorithm is proposed, and integrating this method with the harmony search algorithm and ”N-1″ safety criterion solves the model. Finally, the IEEE 33-node distribution system is used to test the performance of the proposed algorithm. The results show that the proposed improved trust region algorithm has the advantages of fast convergence speed and short time-consumption compared with the traditional trust region algorithm. And the proposed optimization configuration scheme for distributed energy storage can satisfy the “N-1″ safety criterion of the distribution network under different fault scenarios.

Research on harmonic power flow calculation of novel urban distribution network considering the switching power supply harmonic and the correlation of impedance-frequency

Harmonic power flow calculation is the basis of harmonic analysis, tracing, and treatment. This paper focuses on the harmonic issues associated with the implementation of the “dual-carbon” plan in novel urban distribution networks. Due to the widespread integration of renewable energy generation into urban electrical grids, an increasing number of power electronic devices are being connected to the grid, which has a certain impact on harmonic power flow. Firstly, the harmonic components of 6-pulse and 12-pulse rectifiers are analyzed for the switching power supply model widely used in the distribution network. Secondly, the equivalent parameter models of the generator, the transformer, and the lines are reviewed. Finally, from the perspective of power balance, a harmonic power flow model considering the terminal switching power supplies and the correlation between impedance and frequency is proposed. Simulation verification is conducted to demonstrate the feasibility and accuracy of the proposed method.

Development of a New Modelling Concept for Power Flow Calculations across Voltage Levels

Development of a New Modelling Concept for Power Flow Calculations across Voltage Levels

Extended Newton–Raphson Algorithm for Accurate Power-Flow Calculation of Industrial Facilities Based on Induction Motor Catalog Information

Extended Newton–Raphson Algorithm for Accurate Power-Flow Calculation of Industrial Facilities Based on Induction Motor Catalog Information

Preventive-Security-Constrained Optimal Power Flow Model Considering IPFC Control Modes

The interline power flow controller (IPFC) is one of the most versatile integrated flexible alternating current transmission systems (FACTS) controllers and can realize power flow control for multiple transmission lines in modern power systems. However, control characteristics are ignored in conventional IPFC models, in which unreasonable assumptions about injected voltages may lead to security problems in realistic operation. Besides, preventive security constraints considering IPFC control modes are not included in optimal power flow (OPF) control of the system with IPFC, squandering IPFC control potential. To solve these problems, a preventive-security-constrained optimal power flow (PSCOPF) model considering IPFC control modes is proposed in this paper. IPFC control characteristics under different control modes are analyzed and employed as constraints of the optimization model. The iterative updates of converter output voltages for different control modes are derived respectively for power flow calculation, and the power and voltages required in the objective function and constraints of the proposed model can then be obtained. Through optimal selection of IPFC control modes and control parameters, the proposed model can better reconcile the economical and secure operation of the system. Numerical results demonstrate the efficient performance and superiority of the PSCOPF model considering IPFC control modes.

Dynamic microgrid formation for resilient distribution systems considering large-scale deployment of mobile energy resources

Microgrids (MGs) are promising solutions to improve power distribution system (PDS) resilience against natural disasters. However, the existing MG formation approaches based on the linearized Distflow (LinDistflow) model always demand MG roots and their corresponding topologies. This can result in an increased number of variables and constraints in the optimization problem, and deteriorate their computational performance. To this end, an adaptive LinDistflow model is proposed based on the single commodity flow model in graph theory in this paper. Specifically, we show that active and reactive powers can be represented as commodities, which are sent from one node to each of its adjacent nodes in the graph. Then, the power flow and nodal voltage calculation based on the commodity flow only requires adjacent node information of the original topology rather than various MG topologies caused by the dynamic deployment of mobile energy resources (MERs). Furthermore, by incorporating the adaptive LinDistflow model as constraints, a dynamic MG formation approach is proposed for resilient load restoration considering large-scale MER deployment. The problem is formulated as a mixed-integer nonlinear programming problem (MINLP). A linearization technique is proposed based on the propositional logic constraints. It employs the propositional logic that partitions the solution space into two separated regions. Accordingly, the region that the solution lies in can be selected linearly. The effectiveness of the proposed approach is demonstrated based on the IEEE 37-Node, 123-Node and 8500-Node Test Feeders.

Research on Improvement Calculation Method of Grid Power Losses Based on New Energy Access Model

This research presents an improved calculation method for grid power losses, particularly focusing on the challenges posed by new energy access models. With the integration of electric vehicles and the rise of data centers, the demand for electrical energy has surged, leading to increased strain on grid stations and subsequent power losses. The proposed model aimed at reducing these power losses, while also examining existing systems to mitigate and analyze such issues. A significant contribution of this work is the application of the Random Forest machine learning algorithm, which enables efficient and accurate power flow calculations essential for optimizing grid performance. The proposed method is expected to enhance the grid’s ability to handle future energy demands and contribute to the sustainable development of electrical energy 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.

Risk assessment of distribution network operation with scale distributed photovoltaics

In the context of large-scale photovoltaic integration into the distribution network, it is of great significance to comprehensively consider the uncertainty of photovoltaic output and load and scientifically and effectively evaluate the operational risks of the distribution network, in order to ensure the reliable and economic operation of the distribution network. At the same time, with the increase of distributed photovoltaic installed capacity, the small interference stability caused by it has an increasing impact on the operation of the distribution network. In this paper, we first establish a probabilistic model of photovoltaic output and load. Then, we propose a risk calculation method based on the non-sequential Monte Carlo method and probabilistic power flow calculation. Then, a risk analysis of large-scale photovoltaic access to the distribution network was carried out. A new small interference stability risk index was constructed to evaluate the risk of system oscillation caused by photovoltaic access. On this basis, the comprehensive risk value is calculated, and the risk levels are divided based on the voltage over-limit risk and power flow over-limit risk. Finally, the feasibility and effectiveness of the risk assessment model are verified through case analysis.

Calculation of probabilistic harmonic power flow based on improved three-point estimation method and maximum entropy as distributed generators access to distribution network

Uncertainty and volatility are the features of distributed generation (DG), which can impact greatly on the operational status of distribution network. Thus, an improved three-point estimation method and maximum entropy theory (ITPEM&ME) for calculating the probabilistic harmonic power flow in distribution network is proposed in this study. Firstly, the probabilistic model is constructed according to the uncertainty of input variables and the improved three-point estimate method is utilized to convert a probabilistic problem into a deterministic problem. Secondly, in order to obtain the distribution of the random harmonics in distribution network, the maximum entropy theory is adopted to reconstruct the statistical characteristics after the deterministic calculation is realized for each harmonic voltages. The case of an IEEE-33 system under various conditions is conducted. The results by the different algorithms indicate that the proposed method ITPEM&ME has a smaller error than the traditional method, as well as the fitting effect of the probability density function (PDF) is much closer to the practical engineering. It is feasible and accurate in dealing with probabilistic harmonic power flow problems.

Review of Applications of Quantum Computing in Power Flow Calculation

Review of Applications of Quantum Computing in Power Flow Calculation

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.