Power Flow In Distribution Networks Research Articles

Risk assessment of photovoltaic distribution network based on adaptive kernel density estimation and cumulant method

In order to efficiently and accurately evaluate the out of limit risk of photovoltaic power distribution network, the adaptive kernel density estimation (AKDE) method is introduced to fit the actual light intensity sequence, and the probability distribution model of photovoltaic power station output characteristics is established. At the same time, the Cornish–Fisher series combined with the cumulant method (CM) is used to calculate the probabilistic power flow of photovoltaic distribution network, the accuracy of probabilistic power flow calculation (PPFC) is verified by Monte Carlo Method (MCM), the system level voltage out of limit risk index (VOLRI) and branch power flow out of limit risk index (BPFOLRI) are established. Finally, MATLAB is used to verify the accuracy and efficiency of the algorithm for photovoltaic distribution network risk assessment.

A surrogate-assisted point estimate method for hybrid probabilistic and interval power flow in distribution networks

The uncertain power flow analysis is essential to assessing the operating states of distribution networks under various uncertainties. The power flow calculations considering the single uncertainty have been well developed. However, different types of uncertainties may coexist in power systems. In order to comprehensively assess the impacts of mixed uncertainties, this paper proposes a surrogate-assisted point estimate method to solve the hybrid probabilistic and interval power flow. By taking advantage of the point estimate method and high-fidelity surrogate model, the proposed method can accurately obtain the relevant results of power flow calculation with high efficiency. The numerical studies in IEEE 33-bus and 141-bus systems verify the accuracy and efficiency of the proposed method by comparing it with other well-known methods.

Multi-objective planning for voltage sag compensation of sparse distribution networks with unified power quality conditioner using improved NSGA-III optimization

Aiming at the voltage sag compensation of the long-distance sparse distribution network, this paper proposed a multi-objective optimization method based on improved S-CDAS dominance and NSGA-III genetic algorithm. Firstly, aiming at the difficulty of solving the power flow for distribution network with unified power quality conditioners (UPQC), an alternating iteration algorithm of power flow calculation was presented. Secondly, this paper proposed an adaptive controlling of dominance based on extreme solutions. The algorithm dynamically fitted the Pareto frontier according to the extreme solutions in the iterative process to strengthen the dominance region of the optimal set. The algorithm results showed that the improved S-CDAS dominance could improve the convergence speed and result of NSGA-III algorithm while preserving its diversity. Finally, through PSCAD simulation, the effectiveness of the proposed algorithms was proved, and the effect of UPQC on voltage sag in long-distance sparse distribution network was verified. In conclusion, the UPQC configuration method proposed in this paper can consider the diversity of convergence direction and speed, which plays an effective role in the voltage sag compensation of long-distance sparse distribution network.

Advanced studies for probabilistic optimal power flow in active distribution networks: A scientometric review

In the active distribution networks (ADNs), the emerging trend of high penetration of sustainable energy sources such as wind turbines, photovoltaics, and the forthcoming integration of energy storage devices and additional dynamic loads like plug-in-electric vehicles (PEVs) influences to change the nature of electric distribution networks. Consequently, it deteriorates power quality and reliability in terms of unacceptable voltage rise-drop, harmonic distortion, voltage unbalance, and excessive power loss. In this context of transition into the active distribution network, the probabilistic optimal power flow (P-OPF) in the ADN is considered an important tool that helps the distribution grid operators for defining the optimal settings of the system's control variables. However, the optimal solution of P-OPF becomes highly complex while considering the multiple variables, time-varying characteristics and operational uncertainties associated with sustainable resources, consumer behaviour and electricity market prices. This review aims at promoting the research and discussion of P-OPF studies in the context of ADNs characteristics and challenges. First, we perform a data-driven and visualized scientometric analysis of 1988 quality documents retrieved from the Scopus during the last ten years using VOSviewer software. Second, an in-depth investigation of the recent and emerging techniques for solving the P-OPF problem is presented. Third, a set of recommendations and highlights of future challenges for P-OPF in ADNs are offered. The review findings showed high interest among the scientific community in sustainable energy source integration, given the recent rise in publications and citations. Also, there is still a lack of innovative optimization techniques that can adequately handle the current issues associated with P-OPF and objectives with fair computational efficiency and accuracy. Finally, this paper offers a guide for P-OPF researchers to navigate the recent studies considering the sustainable sources, spot the new research frontiers, and identify the most impactful countries and publishers.

Line Loss Interval Algorithm for Distribution Network with DG Based on Linear Optimization under Abnormal or Missing Measurement Data

Data collection is more difficult in distribution network than transmission networks since the structure of distribution networks is more complex. As a result, data could be partly abnormal or missing, which cannot completely describe the operation status of distribution network. In addition, access of distributed generation (DG) to distribution network further aggravates the variability of power flow in distribution network. The traditional deterministic line loss calculation method has some limitations in accurately estimating the line loss of distribution network with DG. A line loss interval calculation method based on power flow calculation and linear optimization is proposed, considering abnormal data collection and distribution network power flow variability. The linear optimization model is established according to sensitivity of line loss to the injected power and sensitivity of transmission power of first branch to the injected power. Introducing the scheduling information into the optimization model, a reliable line loss fluctuation interval can be obtained which actual line loss locates. The effectiveness of the proposed algorithm is verified in IEEE 33-bus distribution network system.

Accelerated Probabilistic Power Flow in Electrical Distribution Networks via Model Order Reduction and Neumann Series Expansion

This paper develops a computationally efficient algorithm which speeds up the probabilistic power flow (PPF) problem by exploiting the inherently low-rank nature of the voltage profile in electrical power distribution networks. The algorithm is accordingly termed the Accelerated-PPF (APPF), since it can accelerate “any” sampling-based PPF solver. As the APPF runs, it concurrently generates a low-dimensional subspace of orthonormalized solution vectors. This subspace is used to construct and update a reduced order model (ROM) of the full nonlinear system, resulting in a highly efficient simulation for future voltage profiles. When constructing and updating the subspace, the power flow problem must still be solved on the full nonlinear system. In order to accelerate the computation of these solutions, a Neumann expansion of a modified power flow Jacobian is implemented. Applicable when load bus injections are small, this Neumann expansion allows for a considerable speed up of Jacobian system solves during the standard Newton iterations. APPF test results, from experiments run on the full IEEE 8500-node test feeder, are finally presented.

Topology and Impedance Identification Method of Low-Voltage Distribution Network Based on Smart Meter Measurements

In recent years, distributed photovoltaic facilities and distributed energy storage are widely connected to a low-voltage distribution network, which makes the topology of the low-voltage distribution network change faster, and the online identification and monitoring of the impedance of each branch are becoming more difficult. With the widespread installation of new distribution automation terminals and smart electricity meters, the technical gap of power data collection has been filled, the state perception ability of the distribution network has been improved, and the data support for further exploration of the topology and impedance of the distribution network has been provided. Therefore, the low-voltage distribution network topology and impedance identification method based on smart meter measurements, the physical topology model of distribution transformer-branch-meter box-user and the impedance exclusion model are proposed. Line loss and branch node power flow are calculated on the basis of the two models. Finally, the low-voltage distribution network topology recognition algorithm and power flow partition backtracking impedance estimation technology are developed based on the data mining method of distribution transformer terminal and smart meter. The example results show that the physical topology model of distribution transformer-branch-meter box-user and the impedance exclusion model proposed in this study can effectively identify the branch topology and impedance distribution in the low-voltage distribution network with a large amount of measurement information, realize the online perception of the distribution network, and provide the basis for the fine management of the power grid and line loss.

Model-augmented safe reinforcement learning for Volt-VAR control in power distribution networks

Volt-VAR control (VVC) is a critical tool to manage voltage profiles and reactive power flow in power distribution networks by setting voltage regulating and reactive power compensation device status. To facilitate the adoption of VVC, many physical model-based and data-driven algorithms have been proposed. However, most of the physical model-based methods rely on distribution network parameters, whereas the data-driven algorithms lack safety guarantees. In this paper, we propose a data-driven safe reinforcement learning (RL) algorithm for the VVC problem. We introduce three innovations to improve the learning efficiency and the safety. First, we train the RL agent using a learned environment model to improve the sample efficiency. Second, a safety layer is added to the policy neural network to enhance operational constraint satisfactions for both initial exploration phase and convergence phase. Finally, to improve the algorithm’s performance when learning from limited data, we propose a novel mutual information regularization neural network for the safety layer. Simulation results on IEEE distribution test feeders show that the proposed algorithm improves constraint satisfactions compared to existing data-driven RL methods. With a modest amount of historical data, it is able to approximately maintain constraint satisfactions during the entire course of training. Asymptotically, it also yields similar level of performance of an ideal physical model-based benchmark. One possible limitation is that the proposed framework assumes a time-invariant distribution network topology and zero load transfer from other circuits. This is also an opportunity for future research.

Development of New Admittance Matrix for Newton-Raphson Power Flow in Distribution Networks

Network modelling is a critical step in the analysis of distribution networks. It is used to relate the input currents and voltages with the output currents and voltages. This work aims to construct a new admittance matrix for distribution networks. The new admittance matrix is derived based on ABCD matrix, which presents the exact model of different types of power distribution networks considering the unbalance/balanced and single/three phase characteristics. The model takes into account shunt admittances to reflect the accurate performances of the components in the distribution networks, especially in the presence of distributed generation units. The importance of considering shunt admittance is due to the presence of capacitive charging current which can affect the node voltages. Application of the new admittance matrix of distribution networks in Newton-Raphson power flow analysis is performed. The standard IEEE 37 bus system is used to test the validity of the proposed approach. MATLAB environment is used to confirm the results. Simulation results show the accuracy of new network admittance matrix in power flow analysis.

A Simple and Efficient Power Flow for Distribution Networks

This paper presents an efficient power flow (PF) for distribution networks (DN). The proposed PF method uses basic circuit laws in deriving the final PF expression and appears like the classical Gauss-Seidel PF algorithm of transmission systems. It possesses the advantages of forward and backward sweeps (FBS) based PF methods but avoids the FBS and formation of a Jacobian matrix. It primarily depends on a constant transformation matrix, formed only once from the network topology and feeder parameters. The transformation matrix relates the node currents with effective feeder voltage drops, and helps to compute the node voltages directly from the given set of load powers. The proposed PF was studied on 15, 33 and 69 node DNs, and the study exhibited that the performances in terms of accuracy, robustness to different r/x ratios of distribution lines and computational efficiency of the proposed method are superior to those of existing methods.

Optimal locating method of edge computing device in cyber physical distribution system

With the development of interconnection of massive terminals, high maintenance of equipment data and complexity of network structure in distribution system, the traditional information processing mode based on single cloud master station has some disadvantages, such as high data transmission delay, high congestion, information far away from equipment and slow queuing processing. Edge computing can make local fast analysis and decision for data in the near terminal device side, which can effectively make up for the deficiency of cloud computing. As the cornerstone of edge computing, edge control processing node is the first premise to realize fast response control of cyber physical distribution system (CPDS). In this paper, a new method of edge computing node deployment is proposed for the distributed edge computing requirements of cyber physical distribution system, considering the cyber stability and power stability. The community theory based on distribution network power flow and line impedance is used to divide the edge computing autonomous region, and the calculation model of cyber stability and power stability of CPDS network is established, then the optimal deployment of CPDS edge computing nodes is solved by the hybrid entropy calculation of cyber and power. Finally, an improved standard example is used for simulation analysis. The simulation results show that the ECN deployment scheme proposed in this paper can effectively reduce network congestion, improve network response speed and realize optimal control of distribution network.

Data-adaptive robust coordinated optimization of dynamic active and reactive power flow in active distribution networks

The uncertainty of wind power brings security and economic issues in active distribution networks. As an effective solution to these problems, the active/reactive optimization aims at minimizing the total operation cost and network loss by controlling multiple resources. This paper proposes a two-stage data-adaptive robust optimization model for the dynamic active-reactive power flow. The dynamic correlation between the uncertainties of active and reactive power is analyzed at two kinds of power factor modes of wind turbines and then is described by a linear affine decision rule. To characterize these uncertainties, a data-adaptive multi-band uncertainty set is constructed based on historical data, which allows the number of bands and the corresponding weight coefficients to be adjusted under different confidence levels. Subsequently, the conic relaxation and linearization techniques are performed to reformulate the robust optimization model as a mixed-integer second-order cone programming problem. A two-level solution framework, consisting of a column-and-constraint generation algorithm and an outer approximation algorithm, is employed to solve this problem. Simulation results on a modified IEEE 33-bus system indicate that the variable power factor mode is more suitable for describing the dynamic correlation than the constant power factor mode. Besides, the proposed model and method also show better practicality and solution efficiency than the existing ones.

Collaborative Management of Multi-Type Energy for Optimal Control of Voltage and Loss of Distribution Systems with DGs and SVCs

Aiming at the deficiencies and shortcomings of traditional reactive power compensation devices in controlling and improving voltage quality, a bilevel programming model for the coordinated optimal allocation of active and reactive power capacity of photovoltaic power generation systems, wind-driven generators, shunt capacitors and static var compensators is established based on chance-constrained programming. In the optimization model, the randomness and intermittence of the output power of the distributed generation and the reactive power regulation ability of the distributed generation are considered. The correlation of illumination, wind speed and load fluctuation is considered and affected by seasonal variation. Latin hypercube sampling method is used to deal with the correlation of random variables. Monte Carlo probabilistic power flow method is used to calculate the power flow of distribution network with intermittent distributed generation systems. The location and capacity of active and reactive power sources in outer programming are optimized by adaptive artificial fish swarm algorithm, and the allocation scheme of active and reactive power sources determined by outer programming is optimized by inner adaptive artificial fish swarm algorithm. The two-layer nested adaptive artificial fish swarm algorithm is used to solve the optimal allocation problem constructed in this paper, and the optimal allocation scheme of active and reactive power supply capacity is determined. Taking IEEE33 distribution system as an example, the feasibility and applicability of the proposed model and algorithm are verified.

Discrete/continuous-time online algorithm application for time-varying optimal power flow in active distribution networks

This paper discusses and analyzes the latest online algorithm applications for time-varying optimal power flow problems in active distribution networks with numerous power-electronics-interfaced distributed energy resources, which bring significant time-varying characteristics to the optimal operation of active distribution networks. Conventional offline optimization algorithms are time-consuming and unable to track time-varying optimal solutions in highly variable environments. In contrast, online algorithms are characterized by fast calculation speeds and the ability to continuously track optimal solutions, thus having great potential in solving optimization problems that vary rapidly over time. In this paper, we design online time-varying optimal power flow algorithms based on the latest online algorithms, including three discrete-time algorithms (i.e., correction-only, prediction-correction, and correction-extra correction algorithms) and one continuous-time algorithm (i.e., prediction-correction interior-point method). According to our survey of the current applications of online algorithms, this study represents the first time that discrete-time prediction-correction and correction-extra correction algorithms have been applied in solving time-varying optimal power flow problems in active distribution networks. Detailed case studies, including correctness, validity, and sensitivity analysis, are carried out on a modified IEEE 33-node system. The numerical results reveal the advantages, disadvantages, and applicability of the proposed algorithms. Moreover, the characteristics of the discrete-time and continuous-time algorithms are compared intuitively. Finally, based on the numerical results, a guide for how to select an appropriate online time-varying optimal power flow algorithm for active distribution network optimization is provided, wherein the discrete-time prediction-correction optimal power flow algorithm is the most frequently recommended choice.

A New Second-Order Cone Programming Model for Voltage Control of Power Distribution System With Inverter-Based Distributed Generation

In this article, a novel second-order cone programming based branch flow model is proposed for optimal power flow (OPF) in radial distribution networks. The main advantage of the proposed architecture is that it can recover the bus voltage angle difference and, thus, control the reactive power flow (PF), leading to a better voltage regulation in the network. Based on the line PF and the line impedance, a convex equation is derived and included with the model to retrieve the bus voltage angle difference. Finally, using the retrieved bus voltage angle difference within the global optimal solution space, an algorithm is developed to control the reactive flow for voltage regulation. The proposed model has been tested on modified IEEE 32 bus (IEEE 33 bus network) and IEEE 123 bus power network systems for different test cases. The simulation results are verified with the OpenDSS PF and the MatPower nonlinear programming (NLP) based OPF solutions. The computational efficiency of the proposed model is superior to the NLP models. Also, the proposed reactive flow control algorithm improves the voltage regulation of a network and promises a globally optimal solution.

Digital Control of Electric Power Flows in Unbalanced Distribution Networks as Part of The Automated Metering and Control System

This paper aims to address the problem of controlling the electricity flows in power distribution networks (PDN) operating under current and voltage unbalance. As is known, the unbalance factor is responsible for significant losses of active power and, therefore, is detrimental to the PDN efficiency and technical and economic performance. The purpose of control is to minimize technical power losses in the distribution network. This is to be achieved by building an information control system (ICS) for balancing a three-phase network as part of the automated metering and control system (AMCS). The latter is currently being widely adopted to automate information processes in PDNs. However, the AMCS does not include technologies for solving the problem in question. We propose an algorithm of the digital controller operation for the ICS. Its primary function is to maintain phase power at a given level in real-time. The algorithm concept is based on the idea of required redistribution of electricity flows between the phases of the distribution network by appropriately switching single-phase loads of consumers (users) to ensure a minimum spread of phase powers relative to their required level. To achieve the goal of control, we construct criterion functions that determine qualitative indices of the ICS operation and develop computational schemes for their minimization. Control actions to be generated by the digital controller and performed on the facility represent a digital code that contains data on the coordinates of three-phase network loads to be switched to another phase.

A new power flow for multi-phase distribution networks with simultaneous phase interruptions

A new power flow for multi-phase distribution networks with simultaneous phase interruptions

Soccer game optimization-based power flow for distribution networks

PurposeThe purpose of the paper is to develop a simple, efficient and robust power flow (PF) method for ill-conditioned distribution networks (DNs).Design/methodology/approachIt first formulates the PF problem as an optimization problem of minimizing the node power mismatches, while treating the corrections of node voltages as problem variables and then uses soccer game optimization (SGO), an artificial intelligent algorithm simulating the behavior of soccer game players in scoring goals, in solving the formulated PF problem.FindingsIt studies the performances of the developed method on four standard test DNs and exhibits that the method is superior in respect of accuracy, robustness and computational speed than those of existing methods.Originality/valueIt suggests a novel and new PF method using SGO and portrays that the proposed method is as accurate as any other PF method, robust like non-Newton type of PF methods and faster than Newton type of PF methods.

Further Results on Newton-Raphson Method in Feasible Power-Flow for DC Distribution Networks

This letter analyzes the convergence of the Newton-Raphson method for the power-flow equation of a DC distribution network with constant power loads (CPLs). Specifically, this letter aims to: 1) determine the sufficient and necessary solvability condition of the power-flow equation; 2) derive the convergence condition of the Newton-Raphson (NR) method. For the first issue, the necessary and sufficient solvability condition for the power-flow equation is derived. On this basis, the convergence of the NR method is analyzed, and the convergence condition about the initial iterative value is obtained. Moreover, it is proved that the NR method under the proposed convergence condition is convergent as long as the power-flow equation is solvable. Finally, case studies verify the correctness of the presented theoretical analysis.

Optimal sizing and location of open-UPQC in distribution networks considering load growth

Voltage and current deficiencies in distribution network (DN) necessitate the improvement of power quality (PQ). Custom power devices (CPDs) compensate for these deficiencies. Recently, in presence of communication infrastructure in smart distribution network, open unified power quality conditioner (OUPQC) is attracted the attention of DN researchers and operators. OUPQC is utilized in DN to improve voltage and current deficiencies by operation of its series unit (SEU) and shunt units (SHU), respectively. Simultaneous compensation capability of voltage and current in distribution network increase its utilization by network operator. In steady state condition, the operation of SHUs compensate the reactive power flow in distribution network and the operation of SEU improve the voltage deficiencies in installation location. Hence, the optimum utilization of OUPQC result in maximization of its benefit for voltage and current improvement. In this regard, the planning of distribution network is performed considering the utilization of OUPQC and load growth. The optimum location, size and installation time of OUPQC is determined for minimizing the cost of distribution network during the planning horizon. Power loss reduction and voltage profile improvement are considered as benefits of the proposed planning approach. On the other hand, the added costs to the distribution network include the installation and maintenance costs of SEU and SHUs of OUPQC. The proposed planning approach is utilized to be tested on both standard IEEE 69-bus and practical Iranian 95-bus distribution networks. The results show that the proposed planning method is effective in term of economic and technical parameters of distribution networks and is useful for network planners.