Power Flow Method Research Articles

A new combined analytical–numerical probabilistic method for assessing the impact of DERs on the voltage stability of bulk power systems

The integration of distributed energy resources (DERs) and unpredictable loads has increased uncertainty in power systems. Traditional methods struggle to assess performance under these uncertainties, and existing probabilistic methods face challenges with complexity and accuracy. This paper introduces a new combined analytical–numerical probabilistic method to assess the impact of DERs on voltage stability. Using Bayesian Parameter Estimation (BPE), the method derives the analytical properties of random variables (RVs) associated with DERs and loads, obtaining posterior distributions. The Metropolis–Hastings sampling technique then estimates these posteriors numerically, enabling accurate predictions of DERs and load outputs. Voltage stability analysis was performed using the continuation power flow method and validated on the IEEE 59-bus test system in MATLAB/Simulink. The results show that integrating DERs significantly improves voltage stability. The proposed method outperforms the Monte Carlo simulation (MCS)-based method in accuracy and computational speed, increasing DERs penetration and voltage stability limits by 3%. It closely matches MCS voltage estimates but requires fewer iterations (500 per loading increment) compared to MCS’s 1000, leading to faster computation times (a few hours to one day versus up to three days for MCS). This method provides an efficient solution for managing uncertainties in power systems.

The Calibrated Safety Constraints Optimal Power Flow for the Operation of Wind-Integrated Power Systems

As the penetration of renewable energy sources (RESs), particularly wind power, continues to rise, the uncertainty in power systems increases. This challenges traditional optimal power flow (OPF) methods. This paper proposes a Calibrated Safety Constraints Optimal Power Flow (CSCOPF) model that uses the Improved Acceleration Coefficient-Based Bee Swarm algorithm (IACBS) in combination with the equivalent current injection (ECI) model. The proposed method addresses key challenges in wind-integrated power systems by ensuring preventive safety scheduling and enabling effective power incident safety analysis (PISA). This improves system reliability and stability. This method incorporates mixed-integer programming, with continuous and discrete variables representing power outputs and control mechanisms. Detailed numerical simulations were conducted on the IEEE 30-bus test system, and the feasibility of the proposed method was further validated on the IEEE 118-bus test system. The results show that the IACBS algorithm outperforms the existing methods in both computational efficiency and robustness. It achieves lower generation costs and faster convergence times. Additionally, the CSCOPF model effectively prevents power grid disruptions during critical incidents, ensuring that wind farms remain operational within predefined safety limits, even in fault scenarios. These findings suggest that the CSCOPF model provides a reliable solution for optimizing power flow in renewable energy-integrated systems, significantly contributing to grid stability and operational safety.

Data-model driven probability model of branch power flow for distribution networks and its application to analysis of overload and line loss

The fluctuation of highly penetrated distributed generations (DGs) in distribution networks (DNs) increases branch overload risks, which makes the analysis uncertainty of branch power flow more complex. The probability analysis of branch power can grasp the power flow operation characteristics under uncertain conditions, which supports the power flow optimization management and ensures the safe and economic operation of DNs. Therefore, this paper proposes a data-model driven probability analysis method for branch power flow in DNs. An approximate branch power model is first derived to reveal the analytical relationship between branch power and node power. Then, based on the branch power approximation model and the forecasting error, the datasets of branch apparent power are constructed to capture the complex nonlinear characteristics of the power flow. The non-Gaussian distribution characteristics of branch apparent power and line loss are described by the optimal probability fitting method. Finally, the probability level of branch overload is evaluated and the probability distribution of line loss is analyzed. The case studies demonstrate that the branch power approximation model is highly accurate, and the probability distribution of the branch apparent power presents different characteristics. The proposed method can quickly and accurately calculate the branch overload probability level.

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.

Transmission and Dissipation of Vibration in a Dynamic Vibration Absorber-Roller System Based on Particle Damping Technology

The research of rolling mill vibration theory has always been a scientific problem in the field of rolling forming, which is very important to the quality of sheet metal and the stable operation of equipment. The essence of rolling mill vibration is the transfer of energy, which is generated from inside and outside. Based on particle damping technology, a dynamic vibration absorber (DVA) is proposed to control the vertical vibration of roll in the rolling process from the point of energy transfer and dissipation. A nonlinear vibration equation for the DVA-roller system is solved by the incremental harmonic balance method. Based on the obtained solutions, the effects of the basic parameters of the DVA on the properties of vibration transmission are investigated by using the power flow method, which provides theoretical guidance for the selection of the basic parameters of the DVA. Furthermore, the influence of the parameters of the particles on the overall dissipation of energy of the particle group is analyzed in a more systematic way, which provides a reference for the selection of the material and diameter and other parameters of the particles in the practical application of the DVA. The effect of particle parameters on roll amplitude inhibition is studied by experiments. The experimental results agree with the theoretical analysis, which proves the correctness of the theoretical analysis and the feasibility of the particle damping absorber. This research proposes a particle damping absorber to absorb and dissipate the energy transfer in rolling process, which provides a new idea for nonlinear dynamic analysis and stability control of rolling mills, and has important guiding significance for practical production.

Simulation-Based Hybrid Energy Storage Composite-Target Planning with Power Quality Improvements for Integrated Energy Systems in Large-Building Microgrids

In this paper, we present an optimization planning method for enhancing power quality in integrated energy systems in large-building microgrids by adjusting the sizing and deployment of hybrid energy storage systems. These integrated energy systems incorporate wind and solar power, natural gas supply, and interactions with electric vehicles and the main power grid. In the optimization planning method developed, the objectives of cost-effective and low-carbon operation, the lifecycle cost of hybrid energy storage, power quality improvements, and renewable energy utilization are targeted and coordinated by using utility fusion theory. Our planning method addresses multiple energy forms—cooling, heating, electricity, natural gas, and renewable energies—which are integrated through a combined cooling, heating, and power system and a natural gas turbine. The hybrid energy storage system incorporates batteries and compressed-air energy storage systems to handle fast and slow variations in power demand, respectively. A sensitivity matrix between the output power of the energy sources and the voltage is modeled by using the power flow method in DistFlow, reflecting the improvements in power quality and the respective constraints. The method proposed is validated by simulating various typical scenarios on the modified IEEE 13-node distribution network topology. The novelty of this paper lies in its focus on the application of integrated energy systems within large buildings and its approach to hybrid energy storage system planning in multiple dimensions, including making co-location and capacity sizing decisions. Other innovative aspects include the coordination of hybrid energy storage combinations, simultaneous siting and sizing decisions, lifecycle cost calculations, and optimization for power quality enhancement. As part of these design considerations, microgrid-related technologies are integrated with cutting-edge nearly zero-energy building designs, representing a pioneering attempt within this field. Our results indicate that this multi-objective, multi-dimensional, utility fusion-based optimization method for hybrid energy storage significantly enhances the economic efficiency and quality of the operation of integrated energy systems in large-building microgrids in building-level energy distribution planning.

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.

An Enhanced Continuation Power Flow Method Using Hybrid Parameterization

The rapid integration of renewable energy sources and the increasing complexity of modern power systems urge the development of advanced methods for ensuring power system stability. This paper presents a novel continuation power flow (CPF) method that combines two well-known parameterization techniques: natural parameterization and arc-length parameterization. The proposed hybrid approach significantly improves computational efficiency, reducing processing time by 32.76% compared to conventional methods while maintaining high accuracy. The method enables faster and more reliable stability assessments by efficiently managing the complexities and uncertainties, particularly in grids with high penetration of renewable energy.

Multi-fidelity graph neural networks for efficient power flow analysis under high-dimensional demand and renewable generation uncertainty

The modernization of power systems faces uncertainties due to fluctuating renewable energy sources, electric vehicle expansion, and demand response initiatives. These uncertainties require consideration in power flow analyses by calculating power flow across a spectrum of generation and load values. Traditional power flow methods, which rely on iterative solutions of non-linear equation sets, become computationally burdensome under these uncertain conditions. Surrogate models have been used to reduces the computational cost of power flow analysis under uncertainty. Recently, graph neural networks (GNNs) have gained increasing attention as surrogates for power system simulations. However, GNNs, similar to other machine learning models, require significant amounts of training data. This paper proposes an innovative approach combining a multi-fidelity methodology with a GNN-based surrogate model for efficient power flow calculations. This model is trained using both high-fidelity power flow simulations and low-fidelity power flow simulations. Our multi-fidelity GNN model not only reduces the cost of generating training data, but also outperforms both single-fidelity GNN models trained solely on high-fidelity data and conventional neural network models. Additionally, the proposed model exhibits robustness to minor topology changes and achieves reasonable performance with unseen topologies. The model’s effectiveness is validated through simulations on standard IEEE systems.

Optimal planning of photovoltaic and distribution static compensators in medium-voltage networks via the GNDO approach

This research employs the generalized normal distribution optimizer (GNDO) to address the simultaneous integration of solar photovoltaic (PV) sources and distribution static compensators (D-STATCOMs) in medium-voltage distribution networks. Through a discrete-continuous codification process, the GNDO method determines the optimal locations (nodes) and capacities (sizes) of PV systems and D-STATCOMs. A power flow approach based on the successive approximations method is used to solve the power flow equations and assess the solution's technical characteristics, including voltage profiles and power injections. Using a master-slave optimization strategy, the GNDO and the power flow method are used to address the studied problem. Numerical results in the 33- and 69-bus grids demonstrate the effectiveness of the proposed approach, showing superior performance compared to the vortex search algorithm (VSA) and the sine-cosine algorithm (SCA). The results indicate reductions of approximately 35.5554% and 35.6839% when using the GNDO in both test feeders. Additionally, the GNDO reduces the computational efforts required to find solutions in both test feeders, in comparison with the VSA and the SCA. All numerical validations were performed using MATLAB 2024a.

Optimal integration of PV generators and D-STATCOMs into the electrical distribution system to reduce the annual investment and operational cost: A multiverse optimization algorithm and matrix power flow approach

In this work, we address the problem of optimally integrating photovoltaic distributed generators (PV) and distributed static compensators (D-STATCOMs) in distributed electrical systems (DES). Previous methods have struggled with the complexities of non-linear mathematical models and the integration of operating and investment costs while meeting the operational constraints of these devices. We propose a solution using a master-slave methodology that combines a discrete-continuous version of the multiverse optimization algorithm (MVO), with a matrix power flow method based on successive approximation (MAX). This approach aims to reduce annual costs by efficiently managing the grid’s operating costs and the investment and operational costs of PV and D-STATCOMs. Various researchers have suggested methodologies for solving the problem of optimal D-STATCOM integration in DES, focusing on minimizing investment and operating costs as the objective function. However, these studies often lack comparative methodologies and statistical analysis to validate the performance of their proposed approaches. Additionally, they do not consider the impact of variable power demand. We compared our methodology with other master-slave approaches that utilize different optimization algorithms, including the vortex search algorithm (VSA), crow search algorithm (CSA), a continuous genetic algorithm (GA), and the particle swarm optimization algorithm (PSO). These comparisons were made using two test systems with 33 and 69 nodes, which incorporate variations in power demand and PV production from a region in Colombia. Our statistical analysis included evaluations of the best and average solutions, standard deviations, differences between the best and average solutions, and a dispersion analysis using box-and-whisker plots. The results demonstrate that MVO outperforms other methods, providing the best results with reduced processing times in both test systems.

An Active Learning Local Control Method for Optimal Power Flow in Low Voltage Distribution Networks Considering Missing Data

An Active Learning Local Control Method for Optimal Power Flow in Low Voltage Distribution Networks Considering Missing Data

Development of a Plate Linear Ultrasonic Motor Using the Power Flow Method.

Linear ultrasonic motors can output large thrust stably in a narrow space. In this paper, a plate linear ultrasonic motor is studied. Firstly, the configuration and operating principle of the Π-type linear ultrasonic motor is illustrated. Then, two slotting schemes are put forward for the stator to enlarge the amplitude of the driving foot and improve the output performance of motor. After that, a novel optimization method based on the power flow method is suggested to describe the energy flow of stator, so as to estimate the slotting schemes. Finally, the prototypes are manufactured and tested. The experimental results show that the output performance of both new motors are excellent. The maximum output thrust of the arc slotted motor is 76 N/94 N, and the corresponding maximum no-load speed is 283 mm/s/213 mm/s, while the maximum output thrust of V-slotted motor reaches 90 N/120 N, and the maximum no-load speed reaches 223 mm/s/368 mm/s.

An efficient modelling and hosting capacity analysis of a distribution system integrating PVs supported by the V2G technology

Over the past decade, the production of photovoltaic (PV) systems has increased owing to the rising demand for electricity generation. Recently, the vehicle-to-grid (V2G) technology of electric vehicles (EVs) has also gained interest as a clean and green energy source to support PVs providing sustainable energy. However, this necessitates the efficient modelling of PV output generation and V2G scheme for integration in the distribution system. Despite the advantages of PV and V2G technology, excessive integration potential affects the distribution system. To circumvent these problems, an accurate evaluation of hosting capacity (HC) is essential. This study proposes efficient modelling and a novel, improved analytical-optimal power flow method for HC analysis of distribution systems with PV and V2G integration considering uncertainties. Furthermore, the effects of increasing integration and optimal allocation of PVs and V2G technology on the voltage profile and power losses, respectively, were analysed. The IEEE 33-bus and 69-bus distribution systems were employed to perform the simulation test to obtain results of HC that validated the effectiveness and robustness of the proposed method compared with those of conventional methods. The proposed method provides an accurate, robust, and global-optimum solution. The integration of V2G technology enhances the overall HC of distribution system.

An intelligent analysis method for power flow of bulk power grid based on fusion of indicator system feature and image feature

Abstract At present, the adjustment of power flow non-convergence in large power grid is still mostly based on manual trial and error, which relies heavily on expert experience and is inefficient. Therefore, an intelligent power flow analysis method based on index system and image feature fusion is proposed. Firstly, the power flow index system is constructed according to the actual demand, which can provide data support for the following power flow convergence judgment problems. Secondly, taking into account the constraints of similarity and ternary loss, the image feature information is used to guide the output of the information feature representation and to realize the organic interaction of the two modal features. On this basis, the calculation result of the index is correlated with the actual state of power flow to judge the convergence of power flow. Finally, the proposed method is verified on the CEPRI36 nodes system and a large power grid in China. The simulation results show that the accuracy of power flow convergence judgment is 100% for CEPRI36 nodes system and 99.83% for some domestic large power grid. It can effectively predict the convergence of the power flow before the calculation of the power flow required by the project and can provide the basis and theoretical support for the power flow optimization adjustment based on the indicator data.

Quadratic functions for efficient load balancing in the terminals of a substation of a three-phase asymmetric network with power loss reduction capabilities

This research addresses the problem of optimal load balancing in terminals of the three-phase substation by proposing three quadratic objective functions. These objective functions are formulated considering active, reactive, and apparent power consumptions aggregated at the terminals of the substation. The proposed formulation belongs to the mixed-integer quadratic models’ family, which can be solved globally with specialized mixed-integer convex tools. To evaluate the effect of load redistribution in the substation terminals, the 15- and 35-bus grids are tested using each of the proposed quadratic functions. In addition, Broyden's unbalanced power flow method is used to determine the extent of power loss reduction and enhancement of voltage profile. Numerical results confirm the effectiveness of the proposed mixed-integer quadratic model in enhancing electrical performance in three-phase asymmetric networks through load balancing at the substation terminals. After solving each quadratic function for the 15-bus grid, power losses were reduced between 12.9624% and 17.2550%, and these reductions were between 5.0771% and 7.7389% in the 35-bus grid.

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.

Decentralized Operations of Industrial Complex Microgrids Considering Corporate Power Purchase Agreements for Renewable Energy 100% Initiatives in South Korea

With the rise of environmental policies and advanced technologies, power systems are transitioning from centralized to decentralized systems, incorporating more distributed energy resources (DERs). This shift has increased interest in the operational functions of microgrids (MGs). The “Renewable Energy 100%” (RE100) campaign is pushing companies to adopt renewable energy. In South Korea, industrial complex microgrids (ICMGs) aim to achieve RE100 through corporate power purchase agreements (PPAs) with renewable energy providers. ICMGs need to operate in both grid-connected and islanded modes, facing challenges in power transactions due to different operating agents. This study proposes a decentralized optimal power flow (OPF) method using the separable augmented Lagrangian relaxation (SALR) algorithm to solve these power transaction problems without disclosing internal information. The proposed method decomposes the centralized OPF problem into subproblems for each ICMG and solves them in a distributed manner, sharing only transaction prices and amounts. Numerical results from the case study validate the effectiveness of the proposed method.

Adaptive convergence enhancement strategies for Newton–Raphson power flow solutions in distribution networks

AbstractThis study introduces a series of strategies to enhance convergence in the Newton–Raphson power flow method for unbalanced distribution networks. The proposed approach incorporates graph theory, Kron reduction, and current injection techniques. The network components, including transmission conductors, power transformers, power conductors, shunt capacitors/reactors, and demand loads, were merged into the bus impedance matrix. Using two identification processes (based on mismatches for bus voltages and bus power injections) and optimal multipliers (μ), the proposed approach estimates the initial bus voltages by approximating the converged solutions. To verify the effectiveness of the proposed approach, the authors performed a comparative analysis of five IEEE test feeders in various scenarios. The results confirmed the effectiveness of the proposed approach, particularly for unbalanced distribution systems with diverse transformer connections.

Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow

Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow