Power Flow Calculation Research Articles

Investigation about Power Flow Algorithm for Distribution Network with Distributed Photovoltaic

To obtain the practical power flow algorithm for distribution network with distributed photovoltaic (PV), the change in phase and amplitude of calculated node voltage with number of iterations, and computation time of the Newton-Raphson algorithm, back/forward sweep algorithm and implicit Z bus Gaussian algorithm are obtained for 5-node circular distribution network with distributed photovoltaic. The results show that the Newton-Raphson algorithm can not converge and can not be used in the circular distribution network with PV. Both back/forward sweep algorithm and implicit Z bus Gaussian algorithm can converge and their results are consistent, but the computation time of the latter is almost 1/3 of the former. The latter is recommended for power flow calculation for annular distribution network with distributed PV.

Consider Carbon Emission Flow Analysis of Power System with Regards to Power Loss and Wind Power Uncertainty

A method for analyzing the impact of wind power uncertainty and active power loss on carbon emission flow in power systems is proposed. Based on the stochastic power flow calculation of wind power injection, the correlation function between wind power output and the total carbon injection rate into the system is determined. Meanwhile, the reverse power flow method is used to analyze the contribution of each unit to the active power flow in different parts of the system and calculate the corresponding carbon emissions. Under the assumption that wind power fluctuations are borne by balancing units, this method combines a conventional unit and a system node, branch, load, and active network loss correlation matrix calculation model to solve the average impact factor of wind power injection on other nodes and branches, thereby determining the uncertain characteristics of carbon emission flow in power systems under stochastic and intermittent wind power injection. The correctness and effectiveness of the method are proved by analyzing the IEEE 14-node standard example, providing new theoretical support and ideas for quantitatively evaluating the low-carbon contribution of wind power generation to the system.

A Real-Time Adaptive Energy Optimization Method for Urban Rail Flexible Traction Power Supply System

In urban rail traction power supply systems, the optimal power flow method is mostly utilized for energy optimization. Conventional power flow optimization adopts offline calculation methods to obtain the optimal strategy under given scenarios. However, this method cannot continuously realize the ideal optimization effect for the time-varying flexible traction power supply system. For this reason, this paper proposes a real-time adaptive energy optimization method to solve the problem above. Firstly, the control objective of the optimal power flow is determined based on analyzing the system power flow. Secondly, a hierarchical control system is designed to achieve adaptive optimal control for the flexible traction power supply system. Moreover, a swarm intelligence optimization algorithm-based optimal power flow calculation method is employed to realize the real-time optimal power flow. Finally, some simulations are performed to verify the effectiveness and accuracy of the proposed real-time optimal power flow. It is demonstrated that the real-time optimal power flow method makes it possible to consider the low delay and high accuracy of control commands at the same time. Compared with the conventional offline method, the proposed real-time method can reduce the input electricity consumption by 1.47%, which is valuable in practical applications.

Evaluation of the Influence of Thermal State and Mechanical State of Overhead Conductors on Power Flow

Overhead conductors’ thermal and mechanical states are the critical factors to determine their safe operation and have an impact on the power flow calculation. The thermal and mechanical state parameters of overhead conductors change the resistance parameters of the line on the one hand and change the line parameters through the tensile action of force on the line on the other hand. The parameters of the line are closely related to the power flow calculation of the power system. Based on two kinds of influence mechanisms and regional power systems, this paper quantitatively analyzes the influence of thermal state and mechanical state on power flow under light load and heavy load.

A bidirectional loss allocation method for active distributed network based on Virtual Contribution Theory

Loss Allocation is a crucial task in power transmission and distribution services, as it essential for reconciliation of generator-user settlement results. With the availability of distributed generation in recent years, power can flow in both directions along transformers and mainlines in the traditional distribution networks. This makes it difficult to calculate power losses in active distribution networks and correct transactions between generators and users. In this paper, we propose the concept of Virtual Contribution Theory and construct a virtual contribution matrix to illustrating how generators and loads use and occupy distribution networks. By combining Virtual Contribution Theory with Power Flow Tracing, a bidirectional loss allocation method based on the Virtual Contribution Theory is proposed to account for power losses in active distribution network. One key advantage of this method is that it eliminates many shortcomings of traditional loss allocation method, including cumbersome calculation processes, low solution efficiency, and limitations in bidirectional power flow calculations. This method can also fairly allocate power loss between generators and loads in the retail electricity market. We conducted tests on IEEE 33 and IEEE 69 systems to evaluate the feasibility and effectiveness of the proposed method.

Position-Capacity Optimization Method for Distributed Photovoltaic Accessing to Distribution Network Based on PV Load Uncertainty Quantification

As the proportion of photovoltaic grid-connected systems increases year by year, the uncertainty of photovoltaic output and load has an increasingly significant impact on the stable operation of the distribution network. In this paper, a photovoltaic access location-capacity optimization method in distribution lines based on the quantification of photovoltaic-load uncertainty is proposed, and the uncertainty propagation of the PV load model parameters in the distribution network power flow calculation node voltage output model is analyzed. This paper proposed an improved Sobol’s method based on polynomial development to quantitatively evaluate the uncertain impact of photovoltaic load parameters, constructed a photovoltaic access location-capacity evaluation model for distribution lines based on uncertainty quantitative assessment, optimized the access capacity of nodes by using the goal function of line loss minimization, and finally verified the feasibility and effectiveness of the proposed method by improving the IEEE33 node.

Parallel Scientific Power Calculations in Cloud Data Center Based On Decomposition-Coordination Directed Acyclic Graph

With the expansion scale of interconnected power systems and refined state perception, scientific power calculations become more complex and diverse. They need faster computation speed and better scalability to support power flow calculation, reactive power optimization, and static/transient stability analysis for unit scheduling. Therefore, this paper proposes a novel cloud data center task mapping algorithm of the Stoer-Wagner binary tree (SWBT) to support accelerated executions of these calculations. Firstly, based on the block bordered-diagonal form of the admittance matrix, high-time complexity scientific power calculations are transformed into a unified multi-task decomposition-coordination directed acyclic graph (DC-DAG). And then, the critical tasks in this DC-DAG are found and the virtual machines encapsulating them are matched with physical machines in the data center preferentially. Finally, on CloudSim, a cloud computing platform, the multi-job mixed experiments of 118-13659 bus power systems are carried out. In addition, real-time workload performance is enhanced in two very large real-world power systems. Studies illustrate that SWBT can improve the underlying physical machine resource utilization and reduce data interaction transmission hops to achieve better computing acceleration performance.

Development of a Three-Phase Power-Flow Calculation Method for Distribution Systems with Automatic Handling of Arbitrary Winding Connections of Transformers

Development of a Three-Phase Power-Flow Calculation Method for Distribution Systems with Automatic Handling of Arbitrary Winding Connections of Transformers

Optimal Capacity and Location for STATCOM with Seasonal Wind Power Prediction Using C-Vine Copula

This paper proposes a selection strategy for determining the optimal capacity and location of a static synchronous compensator (STATCOM) device under intermittent output variations of renewable energy sources using a multi-objective cuckoo search (MOCS) algorithm. The impact of seasonal output variations on the location and capacity of the STATCOM devices was analyzed based on the daily output variations of the wind turbines. Three objective functions were considered to determine the optimal location and capacity of the STATCOM devices: (1) minimizing the system line losses, (2) minimizing the transient voltage indicators, and (3) minimizing the total cost of the STATCOM capacity. MOCS was combined with the Pareto front to determine the non-dominated solution sets for the four seasons. The Manhattan distance method was used to select the most suitable installation locations and capacities within a specified time interval. Power flow calculations were performed using DIgSILENT Power Factory 2021 and MATLAB R2021b. To validate the proposed method, a test experiment was conducted using an IEEE 39 bus system.

An Improved Three-point Method for Power Flow Calculation based on Halton Sequence

With the development of electric power system, it is necessary to expand the scale of new energy power generation to meet the demand of peak cutting and valley filling. The new energy power generation presents intermittenity and volatility, so it is a hot research topic to use the theory of point estimation method to study the power system planning based on uncertainty quantity. This paper improved the three-point estimation method in probabilistic power flow calculation, combined with Halton sequence sampling method to make sampling samples more uniform, and then added a pair of estimation points on the basis of the three-point estimation method, so as to improve the precision of power flow calculation without calculating the fourth moment. The proposed method is verified on IEEE14 and IEEE33 node systems, and the results verify the rationality of the improved three-point method based on Halton sequence.

Physics-model-free heat-electricity energy management of multiple microgrids based on surrogate model-enabled multi-agent deep reinforcement learning

Reliability and cost-effectiveness in the operation of the multiple microgrid (MMG) system depend on the skillful management of its energy resources. Traditional energy management approaches are physics-model-based, which rely on the precise system parameters (e.g., line parameters) of the electricity and heat network. It is difficult to establish the precise system parameters in practice because they depend on a variety of factors. In this context, this paper proposes a physics-model-free control framework for the energy management of MMGs with heat-electricity energy, consisting of proposed surrogate model and multi-agent deep reinforcement learning (MADRL) approach. An important step is to use historical data to train a surrogate model in supervised manner that can imitate the realistic power and thermal flow calculations. Meanwhile, the energy management problem is reformulated as a Markov game. It is solved by the proposed MADRL-based approach by modeling each MG controller as an agent with a specific objective. The historical trajectories representation, parameter space technology, and deep dense architecture in reinforcement learning are introduced in MADRL to overcome the negative impact brought by the time series data from the input state on the decision-making process and construct an efficient exploration mechanism to overcome inefficient optimization of the MMG system in a multi-agent setting. During training period of MADRL, the trained surrogate models integrate into the environment of the MADRL, which can develop optimal energy management strategy based on the continuous interaction with the surrogate models. The proposed surrogate model enabled MADRL approach can reduce the reliance on precise physical systems and prevent having an impact on the real system while being trained involving trial and error process. Simulation results demonstrate the effectiveness of the proposed control framework.

Application of Phase-Shifting Transformer with Longitudinal and Transverse Voltage Regulation

This article was written to present a new solution for a phase-shifting transformer and to show that, in many aspects, the proposed device is more functional and improved when compared to the other currently available phase-shifting structures. The article shows the construction of the new phase-shifting transformer, with longitudinal and transverse voltage regulation. The proposed device’s functionality and available operation states are compared to other existing solutions. Selected steady-state variants of the operation of the proposed transformer were checked based on computer simulations and the laboratory model presented in detail in the article. Convergence between measurements and simulations was achieved. Power flow calculations were also performed in the five-node electrical power system model. In these calculations, two variants of the proposed device’s work were considered and compared with the asymmetric phase shifter. The tests confirmed in the proposed structure, both angle and voltage regulation, enabled maintaining a constant active power flow. The authors show that the proposed solution combines the advantages and functionality of various types of phase shifters while, at the same time, being characterized by a much simpler structure, which results in a two-times-lower cost of the device.

Study on Dynamic Interval Power Flow Calculation of Microgrid Based on Monte Carlo Algorithm

In order to effectively monitor the stability of the microgrid, based on the advantages of the Monte Carlo algorithm, a dynamic interval power flow calculation method for microgrid is designed. First, based on the multilayer complex structure of the microgrid, the hierarchical topology of its interval structure is analyzed. Then, the micropower flow model is designed, the affine algorithm is used to accurately describe the relationship between the variables in the microgrid structure, and the dynamic interval affine calculation is completed. Therefore, in the dynamic interval of the microgrid, the Monte Carlo probability method is applied to obtain more random data. Based on this, a model is established for the probability of wind power generation and photovoltaic power generation to simulate the output characteristics of the microgrid. Finally, the voltage variable, active power variable, and reactive power variable are calculated and embedded in the iterative algorithm to realize the stochastic power flow calculation of the microgrid. After experimental verification, the voltage amplitude calculated using the method proposed in this article has a small error value compared to the actual voltage, with a minimum error value of 0.2, close to 0. Under the condition of convergence accuracy of 10−6, the minimum convergence frequency is 3 times, and the power flow calculation process time does not exceed 38 seconds. This proves that the algorithm has high calculation accuracy, good convergence performance and timeliness, and can provide certain technical support for the stable operation of microgrids.

Peer-to-peer electricity trading considering voltage-constrained adjustment and loss allocation in blockchain-enabled distribution network

Interest in peer-to-peer (P2P) electricity trading has been growing, especially with respect to distributed energy resources (DERs) accommodation in distribution networks, which utilizes P2P trading mechanism to realize the decentralized operation of DERs. A key technology underpinning P2P electricity trading is the blockchain, which ensures that P2P trading is efficient and transparent. However, due to the limited calculation performance of blockchain, the blockchain-based P2P trading process has to be simplified, which makes on-chain grid security-constrained trading adjustment and on-chain power loss allocation become difficult to be solved. To address this challenge, a new on-chain P2P electricity trading framework with easy implementation is proposed. First, an on-chain linear power flow (OC-LPF) model is developed to reduce the difficulty of on-chain power flow calculation. Second, a novel self-adjustment loss allocation model with low complexity is proposed, which integrates the power loss into OC-LPF-based virtual power variable, and enables power flow calculation and power loss allocation to be performed synchronously. Third, a distributed market clearing algorithm with accelerated convergence based on the OC-LPF model is designed to improve the efficiency of on-chain convergence while protecting the privacy of participants. In addition, the effectiveness of the proposed mechanism has been verified with simulation studies on Ethereum.

A method for power flow calculation and optimal dispatch of gas–thermal–electricity multi energy system considering unit commitment

The optimal scheduling of integrated energy system considering unit commitment is a mixed integer nonlinear programming (MINLP) problem with 0-1 binary variables, and the efficient solution of MINLP has always been a research hotspot. In this paper, a power flow calculation method of gas thermal power multi energy coupling system is proposed. Considering the output of coal-fired, gas-fired and new energy units, a simplified unit commitment calculation model is established, which can greatly reduce the number of binary variables and constraints. At the same time, an optimal scheduling model with minimum economic cost and minimum carbon emission is established. For the nonlinear and non convex problem of air pressure equations, the incremental piecewise linearization method based on the idea of feasible region segmentation is used to transform it into MILP model, and the effective optimal solution is obtained. Finally, an example is given to verify the effectiveness and accuracy of the proposed algorithm.

Distributed bi-level optimal power flow calculation for SVSM interval of integrated transmission and distribution networks considering the uncertain renewables

To accurately and efficiently calculate the static voltage stability margin (SVSM) interval of integrated transmission and distribution networks (ITDNs) considering the uncertain fluctuation of renewables, a distributed bi-level optimal power flow (OPF) calculation method based on the alternating direction method of multipliers for the SVSM interval of ITDNs is proposed in this paper. Due to the different structure characteristics of transmission network (TN) and distribution network (DN), a hybrid node-branch OPF method for calculating the SVSM of ITDNs is proposed, which has better convergence than the traditional node OPF method. Different reactive power-voltage control modes of renewable energy stations (RESs) are also considered in the calculation. Considering the uncertain fluctuation of RESs, two distributed bi-level OPF models for calculating the upper and lower bounds of the SVSM interval of ITDNs are established. Based on the alternating direction method of multipliers, the SVSM interval bounds of ITDNs can be obtained by solving the sub-optimization models and transmitting the boundary coupling variables and the load growth parameter between the TN and multiple DNs iteratively until the given convergence criterion is satisfied. Test results on two ITDNs, the modified IEEE 39–33 & 69 bus system and an actual 2285-bus ITDNs, demonstrate the high computation accuracy and efficiency of the proposed distributed bi-level OPF method compared with other calculation methods.

A Power Flow Calculation Method Considering High-order Load Models

Given the popularity of new energy and the connection between large power electronic equipment and power system, the operation of power system becomes more complex and requires higher accuracy of power flow calculation. Therefore, a power flow calculation method considering high-order load model is proposed. On the basis of the Newton-Raphson method, when considering the load voltage characteristics, it is necessary to change the variables in the Newton-Raphson method power flow. Therefore, the established polynomial load model is introduced into the Newton-Raphson method, and the effect becomes more obvious with the increase of the order. Finally, constant power, constant current, constant impedance load and fifth order load models are tested in IEEE14-bus system respectively to verify the good accuracy and robustness of the proposed method.

Energy Saving and Loss Reduction Measures Optimization for Distribution Networks

High conversion rate energy plays an increasingly important role in the “double carbon” goal as well as the energy saving and emission reduction goals. The technology of loss reduction and energy saving has become the focus of modern power system construction. A technical line loss reduction technique is implemented in this work for feeders in the distribution network with abnormal losses in the technical circuit. Power flow calculations, analysis, and comparison are conducted using the Newton-Lafson method. Considering the best single investment benefit ratio measure under the same type of multi-measure loss reduction, the genetic mutation algorithm was used to sort the combination schemes, the efficient algorithm was used to solve the optimal scheme, and the multi-type measure solving model of the distribution network was established.

Efficient and Robust Power Flow Algorithm for Asynchronous Grids Coupled Through a VSC-MTDC System and Its Probability Analysis

With the interconnection of asynchronous ac grids through a voltage source converter-based multiterminal direct current (AGs/VSC-MTDC) system and the large-scale integration of renewable energy, it is important to resolve the power flow calculation problems efficiently and robustly for secure and economic operation of such system under stochastic context. Therefore, an improved sequential algorithm for deterministic power flow (DPF) of AGs/VSC-MTDC system is proposed first. This enhances the conventional manner of updating power losses of VSCs, which leads to a one-shot DPF solution of the ac/dc grid, thus boosting the efficiency; while the coupling of ac/dc systems is considered to remain high accuracy. In combination with the efficient DPF method for each sample, probabilistic power flow (PPF) analysis of the AGs/VSC-MTDC system is performed by using Zhao's three-point estimate method (Z-3PEM) with much fewer samples, thus achieving a higher efficiency with good accuracy. In addition, the PPF analysis of AGs/VSC-MTDC systems being more prone to the poor robustness in stochastic scenarios is effectively addressed, benefitting from the decreased nonconvergence of improved DPF and fewer extreme samples of Z-3PEM. Finally, the effectiveness and performance of works are verified through the results on an 11-terminal VSC-MTDC system with three asynchronous ac grids modified from different IEEE test systems.

Multiobjective Optimization of Traction Substation Converter Characteristic and Train Timetable in Subway Systems

Currently, power supply accidents and excessive energy consumption occur frequently in DC traction power systems of multitrain subway lines. Rail potential (RP) exceeds the standard limit frequently, energy consumption and fluctuation of the traction current are high, which are directly affected by the traction substation converter characteristic and train timetable. In this paper, multi-objective optimization of traction substation converter characteristic and train timetable is conducted to realize the safe and economic operation of subway systems. Firstly, a power flow calculation platform with multitrain running dynamically is established to work out the operating parameters of the system. Then, a multi-objective optimization model consisting of maximum RP, energy consumption and maximum traction current is designed. For the coordination of multiple goals to be optimized, an enhanced Non-Dominated Sorting Genetic Algorithm-III (NSGA-III) is proposed to obtain an optimal traction substation converter characteristic and train timetable. Finally, the multi-objective optimization is conducted with the data of Guangzhou Metro Line 2. Results indicate that three optimized objectives are dropped by 43.8%, 33.4% and 40.3% respectively based on the proposed optimization method, which will greatly enhance the energy conservation and power supply safety of subway systems.