scholarly journals Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 106 ◽  
Author(s):  
Ioannis Dassios ◽  
Andrew Keane ◽  
Paul Cuffe
Keyword(s):  
Spectral Analysis ◽  
Electrical Engineering ◽  
Laplacian Matrix ◽  
Electrical Network ◽  
Electrical Networks ◽  
Eigenvalues And Eigenvectors ◽  
Admittance Matrix ◽  
Current Flows ◽  
Matrix Spectrum

Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These insights should permit the functioning of electrical networks to be understood in the context of spectral analysis.

scholarly journals Optimal feeder reconfiguration in distributed generation environment under time-varying loading condition

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Yanrenthung Odyuo ◽  
Dipu Sarkar ◽  
Lilika Sumi
Keyword(s):  
Graph Theory ◽  
Distributed Generation ◽  
Spanning Tree ◽  
Voltage Stability ◽  
Electrical Network ◽  
List Type ◽  
Network Reconfiguration ◽  
Time Varying ◽  
Electrical Networks ◽  
Tree Algorithm

Abstract The development and planning of optimal network reconfiguration strategies for electrical networks is greatly improved with proper application of graph theory techniques. This paper investigates the application of Kruskal's maximal spanning tree algorithm in finding the optimal radial networks for different loading scenarios from an interconnected meshed electrical network integrated with distributed generation (DG). The work is done with an objective to assess the prowess of Kruskal's algorithm to compute, obtain or derive an optimal radial network (optimal maximal spanning tree) that gives improved voltage stability and highest loss minimization from among all the possible radial networks obtainable from the DG-integrated mesh network for different time-varying loading scenarios. The proposed technique has been demonstrated on a multiple test systems considering time-varying load levels to investigate the performance and effectiveness of the suggested method. For interconnected electrical networks with the presence of distributed generation, it was found that application of Kruskal's algorithm quickly computes optimal radial configurations that gives the least amount of power losses and better voltage stability even under varying load conditions. Article Highlights Investigated network reconfiguration strategies for electrical networks with the presence of Distributed Generation for time-varying loading conditions. Investigated the application of graph theory techniques in electrical networks for developing and planning reconfiguration strategies. Applied Kruskal’s maximal spanning tree algorithm to obtain the optimal radial electrical networks for different loading scenarios from DG-integrated meshed electrical network.

scholarly journals Predicting the influence of the non-sinusoidal network mode on power transformers

2019 ◽  
Vol 114 ◽  
pp. 04005
Author(s):  
Ngo Van Cuong ◽  
Lidiia I. Kovernikova
Keyword(s):  
Service Life ◽  
Electric Power ◽  
Power Quality ◽  
Electrical Equipment ◽  
Operating Conditions ◽  
Transformer Oil ◽  
Power Transformers ◽  
Electrical Network ◽  
Electrical Networks ◽  
Current Harmonics

The parameters of electrical network modes often do not meet the requirements of Russian GOST 32144-2013 and the guidelines of Vietnam. In the actual operating conditions while there is the non-sinusoidal mode in electrical networks voltage and current harmonics are present. Harmonics result in overheating and damage of power transformers since they cause additional active power losses. Additional losses lead to the additional heat release, accelerating the process of insulating paper, transformer oil and magnetic structure deterioration consequently shortening the service life of a power transformer. In this regard there arises a need to develop certain scientific methods that would help demonstrate that low power quality, for instance could lead to a decrease in the electrical equipment service life. Currently we see a development of automated systems for continuous monitoring of power quality indices and mode parameters of electrical networks. These systems could be supplemented by characteristics calculating programs that give out a warning upon detection of the adverse influence of voltage and current harmonics on various electrical equipment of both electric power providers and electric power consumers. A software program presented in the article may be used to predict the influence of voltage and current harmonics on power transformers.

Study of the influence of overvoltage on the quality of electricity in energy systems.

2020 ◽  
Vol 23 (2) ◽  
pp. 52-58
Author(s):  
S. SKRYPNYK ◽  
Keyword(s):  
Power Supply ◽  
Fire Hazard ◽  
Lightning Discharge ◽  
Quality Standard ◽  
Normal Operation ◽  
Electrical Network ◽  
Modern World ◽  
Electrical Networks ◽  
The World

Our world with its high technologies has long been deeply dependent on the quality of electricity supply. In most countries of the world there are national power grids that combine the entire set of generating capacity and loads. This network provides the operation of household appliances, lighting, heating, refrigeration, air conditioning and transport, as well as the functioning of the state apparatus, industry, finance, trade, health services and utilities across the country. Without this utility, namely electricity, the modern world simply could not live at its current pace. Sophisticated technological improvements are firmly rooted in our lives and workplaces, and with the advent of e-commerce began the process of continuous transformation of the way individuals interact with the rest of the world. But with the achievement of intelligent technologies, an uninterrupted power supply is required, the parameters of which exactly meet the established standards. These standards maintain our energy security and create a reliable power system, that is maintaining the system in a trouble-free state. Overvoltage is the deviation of the rated voltage from the value of the corresponding quality standard (frequency, sinusoidal voltage and compliance of harmonics). Overvoltage in terms of fire hazard is one of the most dangerous emergency modes of electrical equipment, which causes conditions that in most cases are sufficient for the occurrence of fire hazards (exceeding the allowable voltage leads to disruption of normal operation or possible ignition). Against the background of deteriorating engineering systems, increased power consumption and poor maintenance, power supply of electrical installations, the main causes of overvoltage in electrical networks are thunderstorms (atmospheric overvoltage), switching switches, uneven phase load in electrical networks, etc. The physical picture of internal overvoltage is due to oscillatory transients from the initial to the established voltage distributions in the conductive sections due to the different situation in the electrical circuit. In the conditions of operation of electric networks planned, mode or emergency situations are possible. Therefore, the ranges of overvoltage are determined by the range from several hundred volts to tens and hundreds of kilovolts, and depend on the types of overvoltage. Atmospheric overvoltage is considered to be one of the most dangerous types of emergency modes of operation of the electrical network. This overvoltage occurs as a result of lightning discharge during precipitation by concentrating electricity on the surface of the object, the introduction of potential through engineering networks and

scholarly journals Calculations, norming and reducing of electrical energy losses in city electrical networks

2019 ◽  
Vol 21 (3) ◽  
pp. 46-54
Author(s):  
A. V. Lykin ◽  
E. A. Utkin
Keyword(s):  
High Voltage ◽  
Power Transmission ◽  
Low Voltage ◽  
Demand Curve ◽  
Electrical Energy ◽  
Electrical Network ◽  
Energy Losses ◽  
Capital Investments ◽  
Electrical Networks

The article considers the feasibility of changing the structure of a distribution electrical network by transferring points of electricity transformation as close to consumers as possible. This approach is based on installation of pole-mounted transformer substations (PMTS) near consumer groups and changes the topology of the electrical network. At the same time, for groups of consumers, the configuration of sections of the low-voltage network, including service drops, changes. The efficiency of approaching transformer substations to consumers was estimated by the reduction in electrical energy losses due to the expansion of the high-voltage network. The calculation of electrical losses was carried out according to twenty-four hour consumer demand curve. To estimate the power losses in each section of the electrical network of high and low voltage, the calculated expressions were obtained. For the considered example, the electrical energy losses in the whole network with a modified topology is reduced by about two times, while in a high-voltage network with the same transmitted power, the losses are reduced to a practically insignificant level, and in installed PMTS transformers they increase mainly due to the rise in total idle losses. The payback period of additional capital investments in option with modified topology will be significantly greater if payback is assessed only by saving losses cost. Consequently, the determination of the feasibility of applying this approach should be carried out taking into account such factors as increasing the reliability of electricity supply, improving the quality of electricity, and increasing the power transmission capacity of the main part of electrical network.

scholarly journals Development of Optimum Repair Schedule of Electrical Network Equipment to Improve the Reliability of its Functioning

2019 ◽  
pp. 4-11
Author(s):  
Sergey V. Belyaev ◽  
Aleksey V. Malafeev ◽  
Evgeniy Ya. Omelchenko
Keyword(s):  
Power Supply ◽  
Technical Condition ◽  
Electrical Network ◽  
Steady Increase ◽  
Electrical Networks ◽  
Number Of Factors ◽  
Network Equipment ◽  
Long Time ◽  
Planning Algorithm ◽  
Labor Resources

To ensure uninterrupted power supply to consumers, maintenance of the electrical networks in a working condition is today carried out through the use of a system of preventive maintenance. In the general case such a system allows building equipment repair schedules based on repair cycles for a long time predetermining the list of necessary material and labor resources in advance. However, in practice, the use of this system is rather difficult and not always effective. This is due to the need to change the repair schedule for emergency or urgent repairs taking into account the seasonality of work performed and the organizational structure of the production department of electrical networks and related departments as well as taking into account the specific features of the operation of specific equipment. Taking into account the current pace of development of electrical networks with a steady increase in the number of consumers (which also leads to a complication of the configuration of electrical networks) this is impossible without the use of appropriate mathematics and software that automates the planning processes for the maintenance and repair of electrical networks with a large number of factors. The minimum equipment downtime was taken as the main criterion for optimality, as a factor that largely determines the reliability of power supply. A planning algorithm has been developed that takes into account the ranking of works in order of importance, the possibility of their shift in time and the likely adjustment of the schedule based on the results of assessing the technical condition of the equipment. A method for minimizing the downtime of repair crews by using them in adjacent areas as well as a technique for identifying a set of equipment that may be under repair in the same period of time are proposed.

A Model of Voltage Distribution and Change of Current in the Network Containing Unaccounted Electricity Consumption

Vestnik MEI ◽  
2021 ◽  
pp. 91-99
Author(s):  
Ivan M. Kazymov ◽  
◽  
Boris S. Kompaneets ◽  
Keyword(s):  
Graphical Representation ◽  
Low Voltage ◽  
Electricity Consumption ◽  
Distribution Networks ◽  
Electrical Network ◽  
Electrical Networks ◽  
Voltage Distribution ◽  
Electrical Grids ◽  
Proposed Model ◽  
Nominal Voltage

The aim of the study is control of commercial losses in electrical grids, especially in low voltage grids, which is one of the priority lines of activities conducted by electric network companies. The complexity of solving this problem is stemming from the difficulty of exactly locating the commercial loss occurrence place under the conditions of extensively branched low and medium voltage electrical networks. Various methods are currently used to determine the commercial loss occurrence places. However, no effective methods have been created for determining the fact and place of unaccounted electricity consumption in networks under the conditions of performing remote analysis of networks based on the data from modern electricity meters used in the automated fiscal electricity metering system. These difficulties can be overcome by developing a model of voltage distribution and change of current in distribution networks of the 0.4--35 kV nominal voltage levels. A model of voltage distribution and changes of current for a network containing unaccounted electricity consumption is proposed. The effectiveness of using the proposed model has been theoretically substantiated; its applicability limits are defined, and the accuracy of the obtained results is estimated. Graphical representation of the proposed model, which is one of the electrical network digital imaging forms, can be used to analyze electrical networks for revealing if there is unaccounted electricity consumption in them. By using the proposed model of voltage distribution and change of current in the network, it is possible to represent the electrical network as a set of electrical parameters to analyze electrical networks for the presence of commercial losses.

Approach to the location of distributed generation sources in the structure of electrical networks

2021 ◽  
pp. 75-86
Author(s):  
A. Gai ◽  
◽  
V. Gulevich ◽  
Keyword(s):  
Electric Power ◽  
Quality Indicators ◽  
Distributed Generation ◽  
Power Supply ◽  
Alternative Energy ◽  
Electric Power Industry ◽  
Energy System ◽  
Electrical Network ◽  
Electrical Networks

Today, the electricity supplier is not able to declare the possible level of quality of electricity supply, and the consumer simply does not have the opportunity to buy such "high-quality" electricity. In such conditions, a differentiated approach to tariff formation is inevitable, which has been implemented in practice today, albeit in its infancy. Further improvement of the tariff-forming mechanism is impossible without creating a "flexible" dependence of the tariff on the quality indicators of the consumer's power supply. Quality indicators, in turn, are based, on the one hand, on the methods and approaches for their determination, and on the other, on statistically reliable data on the elements that make up the equipment in the "generation-consumer" chain. In recent years, there has been a tendency to change the concept of development of the electric power industry, since preference is given to the development of sources of distributed generation. Distributed generation is understood as a source of electrical energy directly connected to the distribution electrical network or connected to it by consumers. Ensuring the socio-economic stability of society and a decent quality of life for the population largely depends on the reliability and efficiency of the functioning of the infrastructure for the supply of fuel and energy resources, in particular, electricity. Excessive losses of electricity during its production, transportation and distribution, as well as an unacceptable level of harmful emissions into the atmosphere, are the cause of interruptions in power supply to consumers and even the threat of systemic accidents in the United Energy System (UPS) of the country. The introduction of alternative energy sources in electric power systems, in addition to reducing the harmful impact on the environment and solving the problems associated with waste pollution during electric power generation, will reduce the use of natural resources and relieve the backbone and distribution power lines. As part of the scientific search, an approach was proposed, which is the basis for calculations to determine the optimal installation locations for sources of distributed generation of an average overhead line. The results obtained are presented in the framework of a joint technical meeting of leading specialists of operating enterprises, the customer and the staff of the Department of Power Supply named after V.M. Sinkova NULES of Ukraine.

SPECTRAL ANALYSIS FOR WEIGHTED ITERATED TRIANGULATIONS OF GRAPHS

Fractals ◽  
2018 ◽  
Vol 26 (01) ◽  
pp. 1850017 ◽  
Author(s):  
YUFEI CHEN ◽  
MEIFENG DAI ◽  
XIAOQIAN WANG ◽  
YU SUN ◽  
WEIYI SU
Keyword(s):  
Spectral Analysis ◽  
Closed Form ◽  
Structural Properties ◽  
Spanning Trees ◽  
Laplacian Matrix ◽  
Kirchhoff Index ◽  
Successive Generations

Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a first study on the spectra of the normalized Laplacian of weighted iterated triangulations of graphs. We analytically obtain all the eigenvalues, as well as their multiplicities from two successive generations. As an example of application of these results, we then derive closed-form expressions for their multiplicative Kirchhoff index, Kemeny’s constant and number of weighted spanning trees.

EIGENTIME IDENTITY OF THE WEIGHTED KOCH NETWORKS

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850042 ◽  
Author(s):  
YU SUN ◽  
JIAHUI ZOU ◽  
MEIFENG DAI ◽  
XIAOQIAN WANG ◽  
HUALONG TANG ◽  
...  
Keyword(s):  
Transition Matrix ◽  
Small World ◽  
Laplacian Matrix ◽  
Block Matrix ◽  
The Other ◽  
Small World Networks ◽  
Eigenvalues And Eigenvectors ◽  
Two Factors ◽  
Analytical Research ◽  
Definition Of

The eigenvalues of the transition matrix of a weighted network provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to biased walks. Although various dynamical processes have been investigated in weighted networks, analytical research about eigentime identity on such networks is much less. In this paper, we study analytically the scaling of eigentime identity for weight-dependent walk on small-world networks. Firstly, we map the classical Koch fractal to a network, called Koch network. According to the proposed mapping, we present an iterative algorithm for generating the weighted Koch network. Then, we study the eigenvalues for the transition matrix of the weighted Koch networks for weight-dependent walk. We derive explicit expressions for all eigenvalues and their multiplicities. Afterwards, we apply the obtained eigenvalues to determine the eigentime identity, i.e. the sum of reciprocals of each nonzero eigenvalues of normalized Laplacian matrix for the weighted Koch networks. The highlights of this paper are computational methods as follows. Firstly, we obtain two factors from factorization of the characteristic equation of symmetric transition matrix by means of the operation of the block matrix. From the first factor, we can see that the symmetric transition matrix has at least [Formula: see text] eigenvalues of [Formula: see text]. Then we use the definition of eigenvalues and eigenvectors to calculate the other eigenvalues.

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