scholarly journals Simplification of Mathematical Model of Double Fed Asynchronous Machine

2017 ◽  
Vol 1 (3) ◽  
Author(s):  
Rauf Ismail Mustafayev ◽  
Laman Hasan Hasanova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Power Systems ◽  
Voltage Drop ◽  
Renewable Energy Sources ◽  
Induction Machine ◽  
Sharp Change ◽  
Small Hydropower ◽  
Algebraic Differential Equations ◽  
Rotor Winding

Double Fed Asynchronous Machines in (DFAM) recent years have found wide application both as generators mainly in renewable energy sources (wind power, small hydropower), and as a motors embedded in various electric drives. In order to study the static and dynamic modes of operation of these machines as one of the most effective methods - the method of mathematical modeling is widely used. It was found that the algebraic-differential equations that make up the mathematical model of double fed induction machine are expediently represented in the d and q axes rotating with the rotor speed of the machine. Particularly this form allows relatively simple reproduction of control coordinates - amplitude and frequency converted to the rotor winding voltage. This mathematical model is based on the well-known Park equations for synchronous machines. It is proposed to simplify the algebraic-differential equations of the double-fed induction machine by reducing the transformer emf, the slip emf and the voltage drop on the stator winding of the machine. The results of calculations for the complete equations of the machine having the 6th order and on the simplified equations having the 4th order showed that the error in determining the regime parameters of the machine in steady-state conditions is in the range 0-7%, i.e. does not exceed 7 percent. The error in dynamic modes is also within acceptable limits. In the dynamics of the change in the regime parameters of DFIM with a sharp change in the disturbing influences slightly differ from each other, and with a sharp change in the control actions they make up 20-30%. This allows to recommend the proposed simplification for engineering calculations, especially when these machines operate in a group or in parallel with other machines and components of power systems. 

scholarly journals A mathematical model for the virtual simulator of the power unit electrical part

2022 ◽  
Vol 1216 (1) ◽  
pp. 012009
Author(s):  
P Baran ◽  
Y Varetsky ◽  
V Kidyba ◽  
Y Pryshliak
Keyword(s):  
Mathematical Model ◽  
Power Plant ◽  
Differential Equations ◽  
Power System ◽  
Real Time ◽  
Power Unit ◽  
Operating Conditions ◽  
Auxiliary System ◽  
Algebraic Differential Equations ◽  
Electrical Part

Abstract The mathematical model is developed for a virtual training system (simulator) of the power unit electrical part operators of a thermal (nuclear) power plant. The model is used to simulating the main operating conditions of the power unit electrical part: generator idling, generator synchronization with the power system, excitation shifting from the main unit to the backup one and vice versa, switching in the power unit auxiliary system, and others. Furthermore, it has been implemented modelling some probable emergency conditions within a power plant: incomplete phase switching, damage to standard power unit equipment, synchronous oscillations, asynchronous mode, etc. The model of the power unit electrical part consists of two interacting software units: models of power equipment (turbine, generator with excitation systems, auxiliary system) and models of its control systems, automation, relay protection and signalling. The models are represented by the corresponding algebraic-differential equations that provide real-time mapping power unit processes at the operator’s request. The developed model uses optimal solving algebraic-differential equations to ensure the virtual process behaviour in real-time. In particular, the implicit Euler method is used to solve differential equations, which is stable when simulating processes in significant disturbances, such as accidental disconnection of the unit from the power system, tripping and energizing loads, generator excitation loss, etc.

scholarly journals The Use of a Real-Time Simulator for Analysis of Power Grid Operation States with a Wind Turbine

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2327
Author(s):  
Zbigniew Kłosowski ◽  
Sławomir Cieślik
Keyword(s):  
Differential Equations ◽  
Power Systems ◽  
Wind Turbine ◽  
Real Time ◽  
Power Transformer ◽  
Power Grid ◽  
Induction Machine ◽  
Integration Step ◽  
Machine Model ◽  
The Real

The main issue in this paper is the real-time simulator of a part of a power grid with a wind turbine. The simulator is constructed on the basis of a classic PC running under a classic operating system. The proposed solution is expected and desired by users who intend to manage power microgrids as separate (but not autonomous) areas of common national power systems. The main reason for the decreased interest in real-time simulators solutions built on the basis of PC is the simulation instability. The instability of the simulation is due to not keeping with accurate results when using small integration steps and loss of accuracy or loss of stability when using large integration steps. The second obstacle was due to the lack of a method for integrating differential equations, which gives accurate results with a large integration step. This is the scientific problem that is solved in this paper. A new solution is the use of a new method for integrating differential equations based on average voltage in the integration step (AVIS). This paper shows that the applied AVIS method, compared to other methods proposed in the literature (in the context of real-time simulators), allows to maintain simulation stability and accurate results with the use of large integration steps. A new (in the context of the application of the AVIS method) mathematical model of a power transformer is described in detail, taking into account the nonlinearity of the magnetization characteristics. This model, together with the new doubly-fed induction machine model (described in the authors’ previous article), was implemented in PC-based hardware. In this paper, we present the results of research on the operation states of such a developed real-time simulator over a long period (one week). In this way, the effectiveness of the operation of the real-time simulator proposed in the paper was proved.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals Voltage Stability of Power Systems with Renewable-Energy Inverter-Based Generators: A Review

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 115
Author(s):  
Nasser Hosseinzadeh ◽  
Asma Aziz ◽  
Apel Mahmud ◽  
Ameen Gargoom ◽  
Mahbub Rabbani
Keyword(s):  
Renewable Energy ◽  
Power Systems ◽  
Voltage Stability ◽  
Reactive Power ◽  
Power Grid ◽  
Renewable Energy Sources ◽  
Electrical Power ◽  
System Stability ◽  
Special Issue ◽  
Synchronous Generators

The main purpose of developing microgrids (MGs) is to facilitate the integration of renewable energy sources (RESs) into the power grid. RESs are normally connected to the grid via power electronic inverters. As various types of RESs are increasingly being connected to the electrical power grid, power systems of the near future will have more inverter-based generators (IBGs) instead of synchronous machines. Since IBGs have significant differences in their characteristics compared to synchronous generators (SGs), particularly concerning their inertia and capability to provide reactive power, their impacts on the system dynamics are different compared to SGs. In particular, system stability analysis will require new approaches. As such, research is currently being conducted on the stability of power systems with the inclusion of IBGs. This review article is intended to be a preface to the Special Issue on Voltage Stability of Microgrids in Power Systems. It presents a comprehensive review of the literature on voltage stability of power systems with a relatively high percentage of IBGs in the generation mix of the system. As the research is developing rapidly in this field, it is understood that by the time that this article is published, and further in the future, there will be many more new developments in this area. Certainly, other articles in this special issue will highlight some other important aspects of the voltage stability of microgrids.

scholarly journals Special Issue: “Wind Power Integration into Power Systems: Stability and Control Aspects”

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3680
Author(s):  
Lasantha Meegahapola ◽  
Siqi Bu
Keyword(s):  
Power Systems ◽  
Wind Power ◽  
Renewable Energy Sources ◽  
Power Grids ◽  
Energy Sources ◽  
Low Carbon ◽  
Carbon Neutrality ◽  
Stability And Control ◽  
Wind Power Integration ◽  
And Control

Power network operators are rapidly incorporating wind power generation into their power grids to meet the widely accepted carbon neutrality targets and facilitate the transition from conventional fossil-fuel energy sources to the clean and low-carbon renewable energy sources [...]

scholarly journals A Method for Autonomous Navigation and Positioning of UAV Based on Electric Field Array Detection

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1146 ◽  
Author(s):  
Yincheng Li ◽  
Wenbin Zhang ◽  
Peng Li ◽  
Youhuan Ning ◽  
Chunguang Suo
Keyword(s):  
Mathematical Model ◽  
Power Systems ◽  
Transmission Lines ◽  
Autonomous Navigation ◽  
Strength Distribution ◽  
Field Source ◽  
Navigation Algorithm ◽  
Safety Warning ◽  
Positioning Algorithm ◽  
Navigation Equipment

At present, the method of using unmanned aerial vehicles (UAVs) with traditional navigation equipment for inspection of overhead transmission lines has the limitations of expensive sensors, difficult data processing, and vulnerable to weather and environmental factors, which cannot ensure the safety of UAV and power systems. Therefore, this paper establishes a mathematical model of spatial distribution of transmission lines to study the field strength distribution information around transmission lines. Based on this, research the navigation and positioning algorithm. The data collected by the positioning system are input into the mathematical model to complete the identification, positioning, and safety distance diagnosis of the field source. The detected data and processing results can provide reference for UAV obstacle avoidance navigation and safety warning. The experimental results show that the positioning effect of the positioning navigation algorithm is obvious, and the positioning error is within the range of use error and has good usability and application value.

scholarly journals Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods

2020 ◽  
Vol 34 (01) ◽  
pp. 630-637 ◽  
Author(s):  
Ferdinando Fioretto ◽  
Terrence W.K. Mak ◽  
Pascal Van Hentenryck
Keyword(s):  
Deep Learning ◽  
Power Systems ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Renewable Energy Sources ◽  
Electrical Power ◽  
Practical Applications ◽  
Fundamental Building Block ◽  
Optimal Power

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often solved repeatedly under various conditions, either in real-time or in large-scale studies. This need is further exacerbated by the increasing stochasticity of power systems due to renewable energy sources in front and behind the meter. To address these challenges, this paper presents a deep learning approach to the OPF. The learning model exploits the information available in the similar states of the system (which is commonly available in practical applications), as well as a dual Lagrangian method to satisfy the physical and engineering constraints present in the OPF. The proposed model is evaluated on a large collection of realistic medium-sized power systems. The experimental results show that its predictions are highly accurate with average errors as low as 0.2%. Additionally, the proposed approach is shown to improve the accuracy of the widely adopted linear DC approximation by at least two orders of magnitude.

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

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