scholarly journals Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

scholarly journals Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.

scholarly journals Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.

scholarly journals Applications of FACTS devices for improving power system transient stability

2015 ◽  
Vol 18 (3) ◽  
pp. 47-54
Author(s):  
Khanh Tuan Dang ◽  
Liem Van Nguyen
Keyword(s):  
Power Systems ◽  
Power System ◽  
Transient Stability ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Flexible Ac Transmission ◽  
Facts Devices ◽  
In Series ◽  
Rotor Angle Stability ◽  
Ac Transmission

As the power demand has been increasing rapidly, today’s modern power system becomes to be more complex and faces many challenges. It is envisaged that transient stability will play the important role in ensuring the steady state operation of power systems in the event of three phases fault or switching of lines. This paper investigates models of Flexible AC Transmission Systems (FACTS) and applications of FACTS devices for improving the rotor angle stability. FACTS devices are applicable in shunt connection Static Var Compensator (SVC), in series connection Thyristor-Controlled Series Capacitor (TCSC), or in the combination of both. Mathematical models of power systems having FACTS devices are set of Differential - Algebraic Equations (DAEs). Trapezoidal rule and Newton - Raphson method are applied to solve DAEs. The simulation results of rotor angles demonstrate the effectiveness and robustness of proposed the SVC and TCSC on transient stability enhancement of power systems.

scholarly journals Load area aggregation considering integration of electric vehicles to the system

2015 ◽  
Vol 35 (1Sup) ◽  
pp. 42-49 ◽  
Author(s):  
Luis Fernando Rodríguez-García ◽  
Sandra Milena Pérez-Londoño ◽  
Juan José Mora-Flórez
Keyword(s):  
Power Systems ◽  
Power System ◽  
Electric Vehicles ◽  
System Analysis ◽  
Original System ◽  
Computational Effort ◽  
Computational Technique ◽  
Equivalent Network ◽  
Optimal Dispatch ◽  
Equivalent Load

<span>Current electric power systems have an increasing penetration of electric vehicles, and its effect has to be considered in different <span>studies, such as optimal dispatch or voltage stability, among others. Additionally, considering that power system analysis becomes <span>complex when the number of buses increase, this paper presents a methodology for aggregation of load areas that use a measurement-based load modeling approach based on an evolutionary computational technique and a classical reduction method. This aggregate <span>load area model is proposed to reduce areas that consider electric vehicle (EV) load models. The proposed method provides a static <span>equivalent load model and an equivalent network that can be used to reduce the computational effort required by power system<br /><span>studies. In order to validate the application of the proposed methodology, a 30-bus power system considering several disturbances <span>and levels of penetration of the electric vehicles was used. The results show that the equivalent network model allows the reproduction <span>of different events with an acceptable accuracy when it is compared to the original system behavior.</span></span></span></span></span></span></span><br /><br class="Apple-interchange-newline" /></span>

scholarly journals Studying State Convergence of Input-to-State Stable Systems with Applications to Power System Analysis

Energies ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 92 ◽  
Author(s):  
Antonio T. Alexandridis
Keyword(s):  
Nonlinear Systems ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Nonlinear Models ◽  
Sufficient Conditions ◽  
Stability And Convergence ◽  
Convergence To Equilibrium ◽  
Analysis Tool ◽  
Wide Range

In stability studies, the response of a system enforced by external, known or unknown, inputs is of great importance. Although such an analysis is quite easy for linear systems, it becomes a cumbersome task when nonlinearities exist in the system model. Nevertheless, most of the real-world systems are externally enforced nonlinear systems with nonzero equilibriums. Representative examples in this category include power systems, where studies on stability and convergence to equilibrium constitute crucial objectives. Driven by this need, the aim of the present work is twofold: First, to substantially complete the theoretical infrastructure by establishing globally valid sufficient conditions for externally enforced nonlinear systems that converge to nonzero equilibriums and, second, to deploy an efficient method easily applicable on practical problems as it is analyzed in detail on a typical power system example. To that end, in the theoretical first part of the paper, a rigorous nonlinear analysis is developed. Particularly, starting from the well-established nonlinear systems theory based on Lyapunov techniques and on the input-to-state stability (ISS) notion, it is proven after a systematic and lengthy analysis that ISS can also guarantee convergence to nonzero equilibrium. Two theorems and two corollaries are established to provide the sufficient conditions. As shown in the paper, the main stability and convergence objectives for externally enforced systems are fulfilled if simple exponential or asymptotic converging conditions can be proven for the unforced system. Then, global or local convergence is established, respectively, while for the latter case, a novel method based on a distance-like measure for determining the region of attraction (RoA) is proposed. The theoretical results are examined on classic power system generation nonlinear models. The power system examples are suitably selected in order to effectively demonstrate the proposed method as a stability analysis tool and to validate all the particular steps, especially that of evaluating the RoA. The examined system results clearly verify the theoretical part, indicating a rather wide range of applications in power systems.

scholarly journals Controlled Impedance-Admittance-Torque Nonlinear Modeling and Analysis of Modern Power Systems

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2461
Author(s):  
Panos C. Papageorgiou ◽  
Antonio T. Alexandridis
Keyword(s):  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Power Converter ◽  
Lyapunov Methods ◽  
Duty Ratio ◽  
System Response ◽  
Power Electronic ◽  
Dynamic Representation ◽  
Dynamic Description

Modern power systems are continuously transformed into decentralized ones where distributed generation (DG) plays a key role. Almost all the different distributed energy resources (DERs) are connected in geographically dispersed places through controlled power electronic interfaces in a manner that essentially affects the dynamic performance and control of the whole power system. Simultaneously, rotating machines in power production or absorption, dominate the system response and stability. In this new frame, this paper proposes a novel generalized dynamic representation and full scale modeling of a modern power system based on the well-known impedance-admittance (IA) network model for the electricity grid, substantially extended to include in detail both the power converter devices by considering the controlled power electronic dynamics and the electrical machines by inserting their full electromechanical dynamics. This formulation results in a holistic nonlinear dynamic description, defined here as controlled impedance-admittance-torque (CIAT) model of the whole system which features common structural characteristics. The model is deployed in state space, involves all the controlled inputs in DG, namely the duty-ratio signals of each power converter interface, all the other external inputs affecting the system, namely all the known or unknown voltage, current, and torque inputs. As shown in the paper, the proposed CIAT model retains its fundamental properties for any DG and network topology, standard or varying. This enables the compression of the accurate analytic power system dynamic description into a matrix-based generic nonlinear model that can be easily used for analysis studies of such large-scale systems. Taking into account the nonlinear nature of the CIAT matrix-based model and the persistent action of the external inputs, Lyapunov methods deployed on recently established input to state stability (ISS) notions are systematically applied for the system analysis. Hence, the traditionally used small-signal model-based analysis that suffers from the intermittent and continuously changing operation of DERs is completely substituted by the proposed formulation. A modern power system example with different DERs involved is analyzed by this way and is extensively simulated to verify the validity of the proposed method.

Performance of the Grid-Connected PV System in LV Microgrid Operation

2012 ◽  
Vol 512-515 ◽  
pp. 137-142
Author(s):  
Yan Li ◽  
Li Wang ◽  
Pan Pan Jing ◽  
Bin Bin Zhong ◽  
Bu Han Zhang ◽  
...  
Keyword(s):  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Low Voltage ◽  
Environmental Benefits ◽  
Pv System ◽  
Load Curve ◽  
Power System Analysis ◽  
Pv Penetration ◽  
Flexible Operation

Microgrids are a future power system configuration providing clear economic and environmental benefits compared to the legacy power systems, as the Grid-Connected PV penetration increases, its reaction in Low Voltage (LV) microgrid has to be taken into account during relative system studies. This paper presents a mathematical model for the Grid-Connected PV, it’s developed by User Define (UD) module on Power System Analysis Software Package (PSASP), PV behavior under several typical weather and typical 1-day load curve is studied in detail, Flexible Operation Strategy to achieve the reasonable voltage level are both considered, PSASP simulation environment is used to analyze the probable operation scenarios of LV microgrid, useful conclusions are summarized at last.

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