Power Flow Calculation Research Articles

Sequencing paths of optimal control adjustments determined by the optimal reactive dispatch via Lagrange multiplier sensitivity analysis

Optimal power flows play a key role in power system operation planning. While most papers in the literature focus on attaining optima, sequencing paths of optimal control adjustments that lead the system from an initial operating point towards the optimum remain scarcely accounted for. Thus, this work proposes a practical framework based upon power system steady-state analysis for sequencing strictly feasible paths of optimal control adjustments determined by the Optimal Reactive Dispatch (ORD) via Lagrange multiplier sensitivity analysis. The proposed framework is methodologically founded on the reformulation of the ORD in terms of optimal control adjustments rather than optimal control values, successive Newton’s power flow calculations to assure a strictly feasible path from the initial operating point towards the optimum, and successive resolutions of the reformulated ORD’s associated dual problem to determine Lagrange multipliers along such sequence path. Thus, pondering optimal control adjustments by their respective Lagrange multipliers indicates which control action must be realised. Numerical results for IEEE test-systems with up to 300 buses with an increased number of controllable variables are obtained to validate and illustrate the efficiency and robustness of the proposed framework.

Method for the Analysis of Three-Phase Networks Containing Nonlinear Circuit Elements in View of an Efficient Power Flow Computation

The present paper is devoted to applying the Hănțilă method for solving nonlinear three-phase circuits characterized by different reactance values on the three sequences (positive, negative and zero). Nonlinear elements, which are components of the circuit, are substituted by real voltage or current sources, whose values are an iteratively corrected function of the voltage across or the current through them, respectively. The analysis is carried out in the frequency domain and facilitates an easy evaluation of the power transfer on each harmonic. The paper presents numerical implementations of the method for two case studies. For validation, the results are compared against those obtained using the software LTspice in the time domain. Finally, the power flow on the harmonics and the overall power balance are analyzed.

An Asynchronous Forward-Backward-Splitting Power Flow Algorithm of Coupled Transmission and Active Distribution Systems

Considering that the conventional synchronous splitting (MSS) method for power flow calculation of coupled transmission and active distribution (TDC) systems has limitations in efficiency and convergence due to the penetration of distributed generations (DGs) and loop operation, this paper proposes an asynchronous forward-backward-splitting power flow algorithm of TDC systems. In this algorithm, the transmission system operator (TSO) acts as a coordinator and processes forward steps while the distribution system operators (DSOs) act as agents and process backward steps. Two first-in-first-out queues are introduced to realize an asynchronous mechanism, and thus, the TSO does not have to wait for the slowest DSO to complete its power flow calculation and power injection update before the next iteration can proceed. This asynchronous mechanism has a higher efficiency compared with a synchronous one when communication delays exist. In addition, the conventional fixed-point iteration in the MSS method is replaced with the Krasnosel’skii-Mann iteration. The proposed algorithm with appropriate settings will achieve better convergence, especially when active distribution networks are considered, where volt-walt-control-typed and volt-var-control-typed DGs are penetrated. The linear convergence of the proposed algorithm is proved under several assumptions and the parameter tuning issue is discussed with numerical experiments.

Study of power flow in electricity system using extreme learning machine

Load Flow or Power Flow Analysis in the power system in used to determine the power system parameters such as voltage, current, active power, and reactive power contained in the power grid. The method that has long been used in the calculation of load flow or power flow is the Newton-Raphson iteration method. As for its development, to complete the power flow study, it is carried out by implementing the Artificial Intelligence method, one of which is the Extreme Learning Machine method. This method is used in the simulation of the simple 39 Bus system calculation from IEEE. In this Extreme Learning Machine, the testing analysis is carried out with 2 inputs, 1 hidden layer, 5 neurons, and 2 outputs and the number of datasets is 39 to produce MAE and MAPE respectively 2.02 and 0.76% and with a very fast processing time of 0.010s

Risk Assessment for Alternating Current / Direct Current (AC/DC) Hybrid Systems with Renewables Penetration

In this paper, a risk assessment method is proposed for AC/DC hybrid systems with renewables penetration, considering the effect of renewables penetration and the application of DC transmission. The sequential Monte Carlo method is introduced to simulate the output of renewables generators, and the unified iterative method is used to solve the problem of AC/DC hybrid system power flow calculation. By establishing the quantized risk assessment indices, the risk of AC/DC hybrid systems with renewables penetration can be analysed. The results of EPRI of China 6-machine-22-bus Test case show that the proposed method can effectively evaluate the risk level of AC/DC hybrid systems with renewable energy penetration and provide reference for power grid planning and the actual operation in advance.

Impact assessment framework of PV‐BES systems to active distribution networks

Passive distribution networks tend to become active, due to the high penetration of photovoltaic units, battery energy storage utilization and their combined active participation to distribution network operation. In this paper, a framework for the assessment of the impact of photovoltaic and battery energy storage systems on voltage profiles, power losses and reverse power flow phenomena of active distribution networks is proposed. Also, the utilization of photovoltaic and battery energy storage systems is evaluated. The proposed methodology is applied to statistically analyse results obtained from annual timeseries power flow calculations in a real 18-bus low-voltage network over a range of operating conditions; the obtained results are quantified using a set of probabilistic indices. The proposed framework can be a useful tool for distribution system operators to identify operational challenges and ensure the optimal exploitation of end-user and network assets.

State solutions for distribution systems and switching event using a neural network

Power flow calculations are an essential stage in many planning and control applications for distribution systems.To use these in control applications, however, the calculation time needs to be improved, and this can be done by the use of a trained ANN. This paper presents the considerations for constructing ANNs for DSs, and describes a method for training the system in order to support switching events representing a change in topology. The solutions for three DSs, balanced as well as unbalanced, are presented and the various considerations affecting the most appropriate ANN construction are discussed. The results are compared to the solution from the classical complex Newton-Raphson and the fixed-point iterative methods. The solutions have very high precision and good results are found for switched laterals. The computational performance is also compared and an improvement of two orders of magnitude is observed.

GPU accelerated power flow calculation of integrated electricity and heat system with component-oriented modeling of district heating network

Due to its advantage of improving energy efficiency and promoting sustainable development, integrated electricity and heat system (IEHS) has been widely studied in recent decades. However, the traditional network-oriented district heating network (DHN) model in IEHS could only deal with DHNs of supply-return-parallel topologies, and the employ of constant thermodynamic properties could incur inaccurate power flow results. With the increasing requirements on operation flexibility and system resilience of IEHS, it has become a necessity to develop a superior power flow model of DHN. This study presents a novel component-oriented modeling method in which the models of the three basic components in DHN, the pipelines, pressure sources and junctions, are investigated in detail. Formulas of the fundamental physical processes including pressure, temperature loss and enthalpy transfer are derived based on the variable thermodynamic state of the fluid rather than predetermined constants in the traditional simplified models. Variables associated with these basic components are discussed in detail and their respective constraints are expounded. To overcome the huge amount of computation in the IEHS analyzing process, GPU is introduced as a coprocessor and a parallel algorithm is designed accordingly. The versatility of the proposed model, including providing accurate, more detailed power flow results and analyzing DHN of general topologies, is presented in a small-scale DHN case. And the practicality of the proposed model is demonstrated in the ensuing practical-scale IEHS case. Meanwhile, the proposed GPU-based parallel algorithm has attained more than 3 times of performance boost compared to single CPU computing.

Active/reactive power management in islanded microgrids via multi-agent systems

This paper deals with the power management problem in islanded microgrids. The paper proposes a two-stage strategy to ensure the proper operation of islanded microgrids under different operating conditions. The first stage is an operational planning stage for optimal power scheduling of the microgrid assets. The objective is to minimize the power losses if the generation is expected to be higher than the demand, otherwise, the objective is to minimize the shed loads. This stage is based on the forecasted generation/demand data and is performed periodically. The second stage aims to operate the microgrid in real-time based on the scheduled powers and deals with the possible deviations due to the forecasting errors of the first stage. The proposed strategy is designed using a hierarchical approach to ensure close to optimal operation and fast response in real time operation. In addition, guidelines for calculating the execution time of the proposed strategy are presented in the paper to help in selecting the suitable communication system to sustain the islanded microgrid. The multi-agent system is used in this paper to implement the proposed strategy in the JADE environment while the power flow calculations are performed using Matlab platform. Several case studies are presented, and detailed results are included to demonstrate the effectiveness of the proposed strategy.

Power flow adjustment for smart microgrid based on edge computing and multi-agent deep reinforcement learning

In current power grids, a massive amount of power equipment raises various emerging requirements, e.g., data perception, information transmission, and real-time control. The existing cloud computing paradigm is stubborn to address issues and challenges such as rapid response and local autonomy. Microgrids contain diverse and adjustable power components, making the power system complex and difficult to optimize. The existing traditional adjusting methods are manual and centralized, which requires many human resources with expert experience. The adjustment method based on edge intelligence can effectively leverage ubiquitous computing capacities to provide distributed intelligent solutions with lots of research issues to be reckoned with. To address this challenge, we consider a power control framework combining edge computing and reinforcement learning, which makes full use of edge nodes to sense network state and control power equipment to achieve the goal of fast response and local autonomy. Additionally, we focus on the non-convergence problem of power flow calculation, and combine deep reinforcement learning and multi-agent methods to realize intelligent decisions, with designing the model such as state, action, and reward. Our method improves the efficiency and scalability compared with baseline methods. The simulation results demonstrate the effectiveness of our method with intelligent adjusting and stable operation under various conditions.

Online Probabilistic Power Flow with Tie-line Power Transfer: A Stacked Denoising Auto-Encoders Method

Based on stacked denoising auto-encoders (SDAE) and combined with the Monte-Carlo simulation (MCS) method, this paper proposes a hybrid algorithm (SDAE-Based-PPF, SPPF) for online calculation of probabilistic power flow (PPF) with tie-line power transfer. By incorporating the deep structure and reconstructive strategy of SDAE, this paper extracts high-level features of nonlinear power flow equations, thereby constructing SDAE-based power flow models. Then, the parameters of SDAE-based power flow models, with improved training speed and accuracy, are optimized by mini-batch gradient descent algorithm, momentum learning rate and introduced cross-entropy loss function. The SDAE-based power flow models are developed to approximate power flow equations with unidirectional extracted high-level features, so as to enable non-iterative solvability judgment and calculation of power flow, therefore fast and accurate. Benefiting from the parallelizability, speed and accuracy of SDAE, the proposed SDAE-based power flow models, with unsolved random samples generated by the MCS method, are able to calculate all samples simultaneously, and this enables PPF to be calculated online. Finally, numerical results are implemented on three standard IEEE test cases to verify the effectiveness of proposed SDAE-based power flow models and SPPF method.

Cooperative Eco-Driving of Multi-Train Under dc Traction Network

Cooperative eco-driving of multi-train combined with dc railway system can achieve energy saving at the substation level for the metro system. This article presents an integrated optimization method for eco-driving by combining energy-efficient train control and dc traction power supply system (TPSS) model, to minimize the substation energy consumption. The coupled time-varying TPSS models for single train and multi-train are established, and a novel power flow calculation (PFC) method is proposed, to directly obtain the precise power flow distribution without iterations. Then, customized dynamic programming (DP) algorithms for specific TPSS models are developed, and optimal speed profiles of the tracking train and the preceding train can be respectively obtained by the multi-phase DP method. The former maximizes the utilization of a distributed regenerative braking energy (RBE), and the latter actively generates RBE to be fully utilized. Finally, the performance of the proposed method is analyzed by implementing the numerical experiments with field data from Guangzhou Metro Line 8, and the effectiveness is verified by comparing it with a previous study-based heuristic algorithm (HA). The simulation result indicates that the proposed method can also effectively reduce the lost energy on the catenary, suppress catenary voltage fluctuations, and precise match power during the RBE transmission phase.

Effective Parallelism for Equation and Jacobian Evaluation in Large-Scale Power Flow Calculation

This letter investigates parallelism approaches for equation and Jacobian evaluations in large-scale power flow calculation. Two levels of parallelism are proposed and analyzed: inter-model parallelism, which evaluates models in parallel, and intra-model parallelism, which evaluates calculations within each model in parallel. Parallelism techniques such as multi-threading and single instruction multiple data (SIMD) vectorization are discussed, implemented, and benchmarked as six calculation workflows. Case studies on the 70 000-bus synthetic grid show that equation evaluations can be accelerated by ten times, and the overall Newton power flow advances the state of the art by 20%.

Algorithm for optimal pairing of res and hydrogen energy storage systems

The global climate and environmental crisis dictate the need for the development and implementation of environmentally friendly and efficient technical solutions, for example, generation based on renewable energy sources. However, the annually increasing demand for electricity (according to the forecasts of the U.S. Energy Information Administration, the amount of energy consumed for the period 2006–2030 will increase by 44 %) cannot be fully provided by alternative energy. The main reason is not so much the high cost of these technologies, like unstable power generation, which determines the need for an additional reserve of regulated power.The solution to this problem can be the combined use of generation based on renewable energy sources with energy storage units of large capacity. Currently, a promising direction is the use of excess electricity for the production of hydrogen and its further accumulation in hydrogen storage. In this case an additional energy can be generated using industrial fuel cells (electrochemical generators) to compensate for the power shortage.At the same time, the distinctive advantage of hydrogen energy storage systems lies in the ability to accumulate a large amount of energy for long periods of time. This fact makes it possible to increase the reliability of the functioning of the electric power system, to provide power supply with a sufficiently long interruption (in case of faults) or allocation for isolated operation.With an increase in the unit capacity and the share of renewable generation in the total installed capacity, researches that aimed to systematic analysis of the impact of the implemented generation unit and the energy storage system on the parameters of the mode of the electric power system become more relevant. There are a number of tasks can be noted related to determining the optimal location and size of the generation unit and energy storage systems being implemented in terms of reducing power losses and maintaining an appropriate voltage level in the nodes of the electric power system. In this article, a variant of solving the optimization task for a typical 15-bus IEEE scheme is presented by means of software calculation using the bubble sorting method. To achieve this goal, the following tasks were solved: the objective function, which indicates the optimal location and size of the generation unit, and constraints, for example, the available deviation of voltage level, were formed; the software implementation of the algorithm for calculating power flows and power losses using the bubble sorting method was carried out. The results of the work of the program code for two scenarios are presented: for instance, installation of one renewable generation unit with a different range of possible capacities, and are compared with the data obtained in the MATLAB/Simulink software package.

Optimal power flow calculation of power grid based on reinforcement learning and crisscross PSO algorithm particle swarm optimization

针对电力系统最优潮流计算问题,提出了一种新的基于Q学习和纵横交叉搜索的粒子群算法.改进的算法在粒子群的寻优模式中引入纵横交叉算子进行优化,加强了全局收敛能力.同时,该改进算法引入Q学习的探索模式,使其在已知的解空间内进行发掘,从而更好地平衡探索与利用之间的关系.为解决Q学习算法的维度灾难问题,使用了状态-组合动作链的方法.IEEE57和IEEE118节点系统的仿真结果表明,所提算法可以增强传统粒子群算法的全局收敛性,有效求解大规模的最优潮流问题.

On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarrat’s method as applied to power flow calculation (PFC). Despite the 4th order of convergence of this technique, it is not competitive with the conventional solvers due to its very high computational cost. This paper addresses this issue by proposing two efficient modifications of the 4th order Jarrat’s method, which present the fourth and sixth order of convergence. In addition, continuous versions of the new proposals and the 4th order Jarrat’s method extend their applicability to ill-conditioned cases. Extensive results in multiple realistic power networks serve to sow the performance of the developed solvers. Results obtained in both well and ill-conditioned cases are promising.

Research on Power Flow Calculation of Distribution Network with Distributed Power Based on Optimal Multiplier

With a large number of distributed power connected to the grid, there are many new node types in the distribution network. The traditional power flow calculation method cannot be applied to the distribution network with multiple distributed generations. Three kinds of distributed power grid model such as synchronous machine, asynchronous machine and inverter are established, according to the characteristics of different distributed power. The P0 node model is proposed for nodes with reactive power output as active power output and terminal voltage function. To improve the condition number of Jacobian matrix included P0 node model, the optimal multiplier is introduced to correct Jacobian matrix. Through the simulation of a variety of operation mode in certain district grid, the results show that the introduction of distributed generation has effects on the process of power flow calculation. The optimal multiplier can effectively improve the ill-posed problem of power flow caused by P0 node model, and increase the fast convergence speed of power flow calculation.

Risk Assessment of Power Systems Dispatching Decision Considering Photovoltaic Systems Penetration

Grid-connected photovoltaic power generation is an important form of new energy utilization, which can effectively reduce the dependence of power system on traditional energy sources. However, the randomness and uncertainty of the output of photovoltaic power generation system will also pose some risks to power grid dispatching decision-making. The source of dispatching decision risk is analyzed, and a risk index system including line overload risk, reserve shortage risk, load shedding risk and light abandonment risk is established. Then a risk assessment model for optimal dispatch of grid-connected photovoltaic power generation is established. The time of power flow calculation is greatly simplified by using power flow distribution factor. Finally, through the risk assessment of IEEE RTS-79 system scheduling decision-making, the risk of scheduling decision-making under different photovoltaic acceptance is analyzed, and the feasibility of the model is verified.

Research on voltage reactive power optimization considering fuzzy load characteristics

For the distributed load output is uncertain, which leads to the over-limit of voltage and line power, this paper proposes a load representation method based on fuzzy set theory, and establishes a voltage reactive power optimization model based on fuzzy number. The influence of different control equipment on node voltage and reactive power is analyzed. Combined with the sensitivity analysis method, the selection rules of control equipment with heuristic method are developed. A method of Genetic calculation based on fuzzy power flow calculation is presented. Finally, this method is applied to build a 30-node model in Matlab for simulation calculation. The results of the example show that the proposed model and method can accelerate the convergence speed, reduce the solution space and reduce the network loss.

Research on the method of observing the safety level of the grid cascading trip based on node injection power

Cascading trips generally occur in the early stages of major power outages. They are usually caused by power flow shifts after the initial failure. Although their form is relatively simple and if they are not adequately evaluated in advance, which will cause disasters in the power grid. Aiming at the grid cascading trip, this paper discusses the relationship between the occurrence of cascading trip and the node injection power, and presents a method for evaluating the current operating status of the grid to the safety level of the cascading trip. For this method, this paper firstly gives the expression of the current operating status of the power grid to the safety level of the cascading trip, and then uses this expression to further give a mathematical model describing the safety level of the grid to the cascading trip state. This model is an optimization model. Based on the DC power flow calculation method and the particle swarm optimization algorithm, this paper gives the specific algorithm flow of the optimization model. Finally, the calculation examples are demonstrated on IEEE-39 node system and IEEE14-bus system, and the results of the cases show the effectiveness of the model and method.