scholarly journals Analysis of the most common methods for determining the stability of energy systems

2021 ◽  
pp. 17-26
Author(s):  
Andrii Hnatov ◽  
Shchasiana Arhun ◽  
Ruslan Bagach ◽  
Hanna Hnatova ◽  
Valentina Tarasova ◽  
...  
Keyword(s):  
Power Systems ◽  
Lyapunov Method ◽  
Direct Method ◽  
Energy Systems ◽  
Energy System ◽  
Mathematical Function ◽  
Direct Lyapunov Method ◽  
First Approximation ◽  
Differential Methods ◽  
The Stability

Problem. There are many methods for determining the stability of the energy system. In normal operating condition (normal rated mode), the power system must reliably ensure the consumption of electricity of normalized quality. However, in addition to the normal state, there are emergency and transient states caused by various transients. This is due to the fact that the energy system is constantly changing its parameters. Such changes are determined by variations in the amount of power produced and consumed, as well as the changes in system configuration. Goal. The goal is studying the possibilities of various methods of determining the power systems stability and drawing up the general algorithm of actions for maintenance of their stability. Methodology. When determining the stability of energy systems by the Lyapunov method, two methods can be used: the direct method and the first approximation method. Lyapunov direct method refers to differential methods. To conclude about the stability of the system we do not find a general or particular solution of differential equations, but with their help we find a mathematical function, the complete derivative of which over time allows to obtain a conclusion about the stability of the system. Results. Many methods can be used to determine whether a sustainable energy system is stable or not. The most common are the Lyapunov methods and the Moiseev method. It is determined that the direct Lyapunov method refers to differential methods. The application of the direct Lyapunov method for energy problems is limited. Currently, it can be used only for some individual cases. The method of the first approximation (Lyapunov first method) has received wider application in the solution of power problems. When applying this method, which belongs to the group of methods of full integration, the right-hand sides of the equations are decomposed into power series. Originality. It is determined that one of the perspective directions of increasing the efficiency of the mathematical device work is using the methods of the second order in modeling and optimization of operating modes of electric power systems. This allows you to increase the speed and reliability of the convergence of iterative processes. Practical value. Based on the analysis of various existing methods for solving the problems of stability of energy systems, an algorithm of actions is proposed and developed, which will help to solve the problem of stability in practice.

scholarly journals Managing Wind Power Generation via Indexed Semi-Markov Model and Copula

Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4246 ◽  
Author(s):  
Guglielmo D’Amico ◽  
Giovanni Masala ◽  
Filippo Petroni ◽  
Robert Adam Sobolewski
Keyword(s):  
Power Generation ◽  
Power Systems ◽  
Wind Energy ◽  
Output Power ◽  
Wind Turbines ◽  
Wind Farm ◽  
Energy Systems ◽  
Wind Farms ◽  
Energy System ◽  
Spatial Dependencies

Because of the stochastic nature of wind turbines, the output power management of wind power generation (WPG) is a fundamental challenge for the integration of wind energy systems into either power systems or microgrids (i.e., isolated systems consisting of local wind energy systems only) in operation and planning studies. In general, a wind energy system can refer to both one wind farm consisting of a number of wind turbines and a given number of wind farms sited at the area in question. In power systems (microgrid) planning, a WPG should be quantified for the determination of the expected power flows and the analysis of the adequacy of power generation. Concerning this operation, the WPG should be incorporated into an optimal operation decision process, as well as unit commitment and economic dispatch studies. In both cases, the probabilistic investigation of WPG leads to a multivariate uncertainty analysis problem involving correlated random variables (the output power of either wind turbines that constitute wind farm or wind farms sited at the area in question) that follow different distributions. This paper advances a multivariate model of WPG for a wind farm that relies on indexed semi-Markov chains (ISMC) to represent the output power of each wind energy system in question and a copula function to reproduce the spatial dependencies of the energy systems’ output power. The ISMC model can reproduce long-term memory effects in the temporal dependence of turbine power and thus understand, as distinct cases, the plethora of Markovian models. Using copula theory, we incorporate non-linear spatial dependencies into the model that go beyond linear correlations. Some copula functions that are frequently used in applications are taken into consideration in the paper; i.e., Gumbel copula, Gaussian copula, and the t-Student copula with different degrees of freedom. As a case study, we analyze a real dataset of the output powers of six wind turbines that constitute a wind farm situated in Poland. This dataset is compared with the synthetic data generated by the model thorough the calculation of three adequacy indices commonly used at the first hierarchical level of power system reliability studies; i.e., loss of load probability (LOLP), loss of load hours (LOLH) and loss of load expectation (LOLE). The results will be compared with those obtained using other models that are well known in the econometric field; i.e., vector autoregressive models (VAR).

Stable Control of Multi-link Manipulator Using Collision Phenomena

1991 ◽  
Vol 3 (6) ◽  
pp. 482-490
Author(s):  
Yasumasa Shoji ◽  
◽  
Makoto Inaba ◽  
Toshio Fukuda ◽  
Hidemi Hosokai ◽  
...  
Keyword(s):  
Lyapunov Method ◽  
Direct Method ◽  
Type Model ◽  
Lyapunov Direct Method ◽  
Loss Parameter ◽  
Flexible Wall ◽  
Stabilization Effect ◽  
The Stability ◽  
The Impact ◽  
Stable Control

In this paper, a methodology using the Lyapunov direct method is proposed to analyze the stability of a multi-link manipulator system, which is positioned on a flexible wall, with collision phenomenon. The stability and response of the system are examined by parameter studies of numerical simulation. Because industrial demands for rapid motion of robotics have been increasing in order to achieve higher efficiency, collision has become a problem because every task involves contact when a manipulator interacts with an object. However, few research has been initiated to overcome this problem. In this paper, we employ a Hertz-type model which includes an energy loss parameter to express the impact force between the manipulator and the wall. Using this model, we have verified the stabilization effect of collision by the Lyapunov method. The effect has been confirmed by simulation. As a result, stable positioning of the manipulator on a flexible wall is assured, and the use of collision is sometimes effective to control the manipulator to performs tasks with rapid contact.

scholarly journals On the stability of solutions of fractional non conformable differential equations

2020 ◽  
Vol 65 (4) ◽  
pp. 495-502
Author(s):  
Paulo M. Guzman ◽  
Luciano M. Lugo Motta Bittencurt ◽  
Juan E. Napoles Valdes
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Method ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Direct Lyapunov Method ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
The Stability

In this note we obtain sufficient conditions under which we can guarantee the stability of solutions of a fractional differential equations of non conformable type and we obtain some fractional analogous theorems of the direct Lyapunov method for a given class of equations of motion.

scholarly journals Energy System Monitoring Based on Fuzzy Cognitive Modeling and Dynamic Clustering

Energies ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5848
Author(s):  
Vadim Borisov ◽  
Maksim Dli ◽  
Artem Vasiliev ◽  
Yaroslav Fedulov ◽  
Elena Kirillova ◽  
...  
Keyword(s):  
Fuzzy Clustering ◽  
Cognitive Modeling ◽  
Cluster Structure ◽  
Energy Systems ◽  
Energy System ◽  
Dynamic Clustering ◽  
Clustering Methods ◽  
Cognitive Approach ◽  
Combined Use ◽  
The Stability

A feature of energy systems (ESs) is the diversity of objects, as well as the variety and manifold of the interconnections between them. A method for monitoring ESs clusters is proposed based on the combined use of a fuzzy cognitive approach and dynamic clustering. A fuzzy cognitive approach allows one to represent the interdependencies between ESs objects in the form of fuzzy impact relations, the analysis results of which are used to substantiate indicators for fuzzy clustering of ESs objects and to analyze the stability of clusters and ESs. Dynamic clustering methods are used to monitor the cluster structure of ESs, namely, to assess the drift of cluster centers, to determine the disappearance or emergence of new clusters, and to unite or separate clusters of ESs.

scholarly journals Robust operation of microgrid energy system under uncertainties and demand response program

2020 ◽  
Vol 17 (2) ◽  
pp. 1005
Author(s):  
Sahar Seyyedeh Barhagh ◽  
Amin Mohammadpour Shotorbani ◽  
Behnam Mohammadi-Ivatloo ◽  
Kazem Zare ◽  
Ali Farzamnia
Keyword(s):  
Power Systems ◽  
Demand Response ◽  
Optimization Problems ◽  
Energy Systems ◽  
Stochastic Scheduling ◽  
Energy System ◽  
Optimization Method ◽  
Operating Conditions ◽  
Mixed Integer ◽  
Demand Response Program

<span>Microgrid energy systems are one of suitable solutions to the available problems in power systems such as energy losses, and resiliency issues. Local generation by these energy systems can reduce the role of the upstream network, which is a challenge in risky conditions. Also, uncertain behavior of electricity consumers and generating units can make the optimization problems sophisticated. So, uncertainty modeling seems to be necessary. In this paper, in order to model the uncertainty of generation of photovoltaic systems, a scenario-based model is used, while the robust optimization method is used to study the uncertainty of load. Moreover, the stochastic scheduling is performed to model the uncertain nature of renewable generation units. Time-of–use rates of demand response program (DRP) is also utilized to improve the system economic performance in different operating conditions. Studied problem is modeled using a mixed-integer linear programming (MILP). The general algebraic modeling system (GAMS) package is used to solve the proposed problem. A sample microgrid is studied and the results with DRP and without DRP are compared. It is shown that same robustness is achieved with a lower increase in the operation cost using DRP.</span>

UNIFORM APPROACH FOR STABILITY ANALYSIS OF FAST SUBSYSTEM OF TWO-TIME SCALE NONLINEAR SYSTEMS

2007 ◽  
Vol 17 (11) ◽  
pp. 4195-4203 ◽  
Author(s):  
LUÍS F. C. ALBERTO ◽  
HSIAO-DONG CHIANG
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Power Systems ◽  
Time Scale ◽  
Stability Region ◽  
Direct Method ◽  
System Stability ◽  
Fast Subsystem ◽  
Theoretical Support ◽  
The Stability

A new uniform methodology to study the fast subsystem stability of general two-time scale nonlinear systems is developed. It consists of a direct method that provides estimates of the stability region of the fast subsystem that are uniform with respect to the slow variables, which are treated as uncertainties. The methodology is illustrated on small power systems leading to much improved results in estimating the stability region, critical clearing times as compared to traditional methods. As a by-product, it gives the required theoretical support to justify and to correct the heuristic approaches used in power system stability analysis literature.

scholarly journals Technical Condition Management for a PV-Based Distributed Energy System

2021 ◽  
Vol 1 ◽  
Author(s):  
Sebastian Schulz ◽  
Jörg Reiff-Stephan
Keyword(s):  
Power Systems ◽  
Energy Systems ◽  
Energy System ◽  
Technical Condition ◽  
Success Factor ◽  
Distributed Energy ◽  
Distributed Energy System ◽  
Low Performance ◽  
Infrastructure Maintenance ◽  
Education Culture

Distributed energy systems are a key success factor for the future and self-determined living in undeveloped or emerging regions. Education, culture and economic growth are significantly influenced by energy processes. In order to be able to use a built-up infrastructure, maintenance and condition control of the systems along their entire life cycle are indispensable. However, this can only be achieved if an independent technical condition management system can be established. Event-based data and warnings can be transmitted or retrieved at any time. Due to this, decisions can be made on the basis of the information obtained, which then lead to the maintenance of the targeted functional scope of the power systems. In the following paper, a TCM for pv-based distributed energy systems is presented. It consists of a low performance single board computer which can be connected to a cloud system with mobile communication and transmits essential data.

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