This paper investigates the impact of electric vehicle (EV) aggregator with communication time delay on stability regions and stability delay margins of a single-area load frequency control (LFC) ...system. Primarily, a graphical method characterizing stability boundary locus is implemented. For a given time delay, the method computes all the stabilizing pro-portional-integral (PI) controller gains, which constitutes a stability region in the parameter space of PI controller. Secondly, in order to complement the stability regions, a frequency-domain exact method is used to calculate stability delay margins for various values of PI controller gains. The qualitative impact of EV aggregator on both stability regions and stability delay margins is thoroughly analyzed and the results are authenticated by time-domain simulations and quasi-polynomial mapping-based root finder (QPmR) algorithm.
This paper investigates the effect of gain and phase margins (GPMs) on stability delay margin of a two-area load frequency control (LFC) system with constant communication delay. A gain-phase margin ...tester (GPMT) is introduced to the LFC system as to take into GPMs in delay margin computation. A frequency domain exact method, Rekasius substitution, is proposed to compute the GPMs-based stability delay margins. The method aims to calculate all possible purely complex roots of the characteristic equation for a finite positive time delay. The approach first transforms the characteristic polynomial of the LFC system with transcendental terms into a regular polynomial. Routh-Hurwitz stability criterion is then implemented to compute the purely imaginary roots with the crossing frequency and stability delay margin. For a wide range of proportional–integral controller gains and GPMs, time delay values at which LFC system is both stable and has desired stability margin measured by GPMs are computed. The accuracy of complex roots and delay margins are verified by using an independent algorithm, the quasi-polynomial mapping-based root finder and time-domain simulations. Simulation studies indicate that delay margins must be determined considering GPMs to have a better dynamic performance in term of fast damping of oscillations, less overshoot and settling time.
This paper presents a comprehensive stability analysis of a single-area load frequency control (LFC) system with constant communication delays. First, an exact method that takes into account both ...gain and phase margins is proposed to determine stability delay margins in terms of system and controller parameters. The method implements an elimination procedure to transform transcendental characteristic equation into a standard polynomial of the crossing frequency. The real roots of this new standard polynomial exactly match with the purely imaginary roots (crossing frequencies) of the original characteristic equation with transcendental terms. Secondly, an effective and simple graphical method is implemented to compute all stabilizing Proportional Integral (PI) controller gains for a given time delay. The approach is based on extracting stability region and the stability boundary locus in the PI controller parameter space having user defined gain and phase margins, and relative stability. The time-domain simulation studies indicate that the proposed scheme improves dynamic performance gain and phase margins are included in delay-dependent stability analysis of single-area LFC with communication delays.
This work presents the delay-dependent stability analysis using eigenvalue tracing method for the multi-area load frequency control system that includes both electric vehicles aggregator (LFC-EVs) ...and incommensurate time delays in each control area. The LFC-EVs systems face inevitable communication time delays that affect the frequency stability. Although communication infrastructures are necessary to maintain system stability and reliability, a large amount of delay exceeding the allowable limit leads to system instability. In this study, stability delay margin values of a time-delayed LFC-EVs system are computed by a simple method finding the critical eigenvalues. By tracing eigenvalue loci of a transformation matrix, the method easily determines critical eigenvalues on the imaginary axis and obtains stability regions in time delay space. Stability delay margins depicted as a stability region in the delay space are determined for various system parameters and verified by time-domain simulations. Results indicate that more accurate stability delay margins are obtained as compared to ones using Lyapunov–Krasovskii Functionals with different linear matrix inequalities.
This paper investigates the impact of electric vehicles (EVs) aggregator with communication time delay on stability delay margin of a two-area load frequency control (LFC) system. A frequency-domain ...exact method is used to calculate stability delay margins for various values of proportional-integral (PI) controller gains. The proposed method first eliminates the transcendental terms in the characteristic equation without using any approximation and then transforms the transcendental characteristic equation into a regular polynomial using a recursive approach. The key result of the elimination process is that real roots of the new polynomial correspond to imaginary roots of the transcendental characteristic equation. With the help of new polynomial, delay-dependent system stability and root tendency with respect to the time delay is determined. An analytical formula is then developed to compute delay margins in terms of system parameters. The qualitative impact of EVs aggregator on stability delay margins is thoroughly analysed and the results are verified by time domain simulations and quasi-polynomial mapping-based root finder (QPmR) algorithm.
The utilization of communication linkages generates delays that degrade system dynamic performance and cause fluctuations in the system frequency while the extensive integration of renewable energy ...sources may cause further increase in the frequency oscillations owing to low inertia. By considering the inclusion of the virtual inertia and damping (VID) control in load frequency control (LFC) systems with time delays, this article investigates the impacts of the VID control on the stability delay margins (SDMs) of two-area LFC systems. For this purpose, an exact method, which is based on recursively removing exponential terms from the characteristic equation, is first implemented to compute SDMs of the two-area LFC system enhanced by VID control for a wide range of controller gains. Secondly, the effect of the VID parameters on the SDMs is investigated by employing the exact method. Theoretical results clearly illustrate that SDMs significantly increase as VID parameters increase. Furthermore, simulation analysis elucidates that with the VID incorporation, the performance of the LFC system with low inertia is enhanced and the rate of change of the frequency and frequency nadir are remarkably decreased, improving the stability of time-delayed LFC systems.
Abstract
This study focuses on analyzing the robust stability regions and robustness margin of a time‐delayed load frequency control (LFC) system with Electric Vehicles (EVs) using the Kharitonov ...Theorem. Communication time delays in LFC systems can jeopardize stability and reliability, leading to suboptimal controller performance. Integrating EVs into LFC systems enhances dynamical stability but introduces additional complexity. Therefore, it is crucial to employ robust analysis and controller design techniques to ensure system stability. In this study, we utilize the Kharitonov Theorem to determine the robust stability regions and stability boundaries in the parameter plane of the Proportional‐Integral (PI) controller. By considering communication time delays and parametric uncertainties in the LFC system with EVs (LFC‐EVs), the robust PI controller gains using these methods are efficiently computed. To evaluate the performance of the theoretically computed robust controller parameters, time‐domain simulations are conducted.
This paper investigates the effect of gain and phase margins (GPMs) on the delay-dependent stability analysis of the pitch control system (PCS) of large wind turbines (LWTs) with time delays. A ...frequency-domain based exact method that takes into account both GPMs is utilized to determine stability delay margins in terms of system and controller parameters. A gain-phase margin tester (GPMT) is introduced to the PCS to take into GPMs in delay margin computation. For a wide range of proportional–integral controller gains, time delay values at which the PCS is both stable and have desired stability margin measured by GPMs are computed. The accuracy of stability delay margins is verified by an independent algorithm, Quasi-Polynomial Mapping Based Rootfinder (QPmR) and time-domain simulations. The time-domain simulation studies also indicate that delay margins must be determined considering GPMs to have a better dynamic performance in term of fast damping of oscillations, less overshoot and settling time.
As a result of the increase in energy demand and government subsidies, the usage of wind turbine system (WTS) has increased dramatically. Due to the higher energy production of a variable-speed WTS ...as compared to a fixed-speed WTS, the demand for this type of WTS has increased. In this study, a new method for the calculation of the power output of variable-speed WTSs is proposed. The proposed model is developed from the S-type curve used for population growth, and is only a function of the rated power and rated (nominal) wind speed. It has the advantage of enabling the user to calculate power output without using the rotor power coefficient. Additionally, by using the developed model, a mathematical method to calculate the value of rated wind speed in terms of turbine capacity factor and the scale parameter of the Weibull distribution for a given wind site is also proposed. Design optimization studies are performed by using the particle swarm optimization (PSO) and artificial bee colony (ABC) algorithms, which are applied into this type of problem for the first time. Different sites such as Northern and Mediterranean sites of Europe have been studied. Analyses for various parameters are also presented in order to evaluate the effect of rated wind speed on the design parameters and produced energy cost. Results show that proposed models are reliable and very useful for modeling and optimization of WTSs design by taking into account the wind potential of the region. Results also show that the PSO algorithm has better performance than the ABC algorithm for this type of problem.
PDF
