Stability Delay Margins Research Articles

Determination of the robust stability delay margins for the load frequency control systems

Bu çalışma, zaman gecikmesi içeren Yük Frekans Kontrol (YFK) sistemlerinde parametrik belirsizliklerin olması durumunda sistemin gürbüz kararlılık gecikme payı değerlerini hesaplamayı amaçlamaktadır. YFK sistemlerinde frekans kararlılığının sürdürülmesi bakımından çeşitli elektrik verilerinin ölçülerek kontrol merkezine iletilmesi ve kontrol merkezinden frekans kontrol servisine katılım sağlayan santrallere kontrol sinyallerinin iletilmesi gerekmektedir. Bu süreçte, haberleşme ağlarında veri iletimi nedeniyle, zaman gecikmeleri kaçınılmaz hale gelmektedir ve sistemin dinamik performansı ve kararlılığı olumsuz etkilenmektedir. Ayrıca, YFK sisteminin modellenmesinden kaynaklı ve güç sisteminde oluşabilecek belirsizlikler nedeniyle sistem parametrelerinin belirsizlikleri dikkate alınarak haberleşme ağı tabanlı gözlemlenebilecek gecikme değerleri üzerinde böylesi belirsizliklerin etkisi incelenmelidir. Bu amaçla, YFK sisteminde üstel terimin yok edilmesi yöntemi ile Kharitonov Teoremi birlikte kullanılarak sistemin gürbüz kararlılığını sağlayabilen gürbüz zaman gecikme payı değerleri teorik olarak hesaplanmıştır. Teorik sonuçların doğruluğu Matlab/Simulink programı ve QPmR (Quasi Poliynomial Mapping Root Finder) algoritması kullanılarak gösterilmiştir.

Tradeoff Techniques for Stabilization of Network-Controlled DC Motor Speed Control System with Uncertainties

This paper details the development of a tradeoff techniques using the conventional time-domain method for stability assurance of network-controlled DC motor speed control system with uncertainties. The DC motor controlled using an open communication network introduces time-delays in the control loop. These time-delays are one of the factors that decides the stability and performance of the dynamical systems. Stabilization of network-controlled DC motor is achieved by tuning the network controller with concern to time-delay. The maximum extend of time-delay called delay margin is computed by developing stability criterion using Lyapunov–Krasvoskii functional and linear matrix inequality techniques. The impact of load disturbances on stability delay margins are investigated and further determining the relationship between delay margin and controller gains for network-controlled DC motor gives a tradeoff between stability and dynamic performance. Finally, proposed results for network-controlled DC motors are validated through Matlab simulation and experimental setup.

Impact of virtual inertia and damping control on stability delay margins of load frequency control systems with renewable energy sources

Impact of virtual inertia and damping control on stability delay margins of load frequency control systems with renewable energy sources

Investigation on the stability of networked-control integrated energy systems for frequency regulations

This paper presents the stability analysis of integrated energy systems under network environment. The networked-control integrated energy systems involve time-delay in the control loop. These time-delays are time-invariant or time-varying in nature. Further, it affects the stability and dynamic performance of the integrated energy systems. In this paper stability analysis of networked-control integrated energy systems are done using Lyapunov–Krasovskii functional and linear matrix inequality techniques. The maximum amount of time-delay that establishes the stability of the integrated energy systems is determined and controller is designed with concern to the time-delay. The effect of electric vehicles and battery energy storage system in stability delay margins of integrated energy systems is also addressed and the numerical simulations are done to verify the effectiveness of the presented results.

Analysis of Communication Simulation Model of Urban Comprehensive Energy Network Based on the Internet of Things

In urban construction, all energy infrastructures have been realized by the information structure. However, due to the non-uniform structure of each energy network, the data cannot be more compatible, and the communication guarantee based on the Internet of Things is one of the most urgent problems to be solved. In this paper, a reasonable network computing offloading model is designed in the edge computing layer, and the computing offloading algorithm is introduced. Considering the dependency between subtasks, an optimization problem is established, and a central scheduling algorithm is proposed to solve it. An optimized distributed unloading algorithm is proposed according to the solution idea of the classical distributed unloading algorithm. Simulation results show that the optimized distributed unloading algorithm proposed in this paper has good solving efficiency and performance, and reduces the task processing delay. At the same time, the experimental simulation proves that the efficiency of multiple edge servers in processing subtasks is higher than that of a single server. It is established that changing the convergence speed and communication delay stability margin of the system by changing the system eigenvalue is beneficial to design a better communication network structure to keep the system stable.

Time-delay Stability Analysis of the Distributed Economic Dispatch System of an Active Distribution Network

Distributed economic dispatch system has gained a lot of attention because it has better robustness, faster computation and less communication burden, but the system stability in the presence of communication delay is still researched at the fundamental level. By introducing the concept of virtual distributed generation, this paper develops a fully version of the distributed economic dispatching strategy for an active distribution network, and establishes the stability analysis model of the distribution network considering symmetric and asymmetric communication time-delay. The Lyapunov stability theorem and the free weight matrix method are comprehensively applied to derive the time-delay stability criterion of the system and solve the delay stability margin with a lower conservativeness. The distributed economic dispatch strategy in this paper under various operating conditions, the delay stability analysis method and delay stability margin solution are verified by the simulation results on an active distribution network modified based on the IEEE-14 system.

Stability delay margin computation of multi-area load frequency control system with electric vehicle using critical eigenvalue tracing method

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.

Enhancement of stability delay margins by virtual inertia control for microgrids with time delay

Large-scale deployment of renewable energy sources (RESs) contributes to fluctuations in the system frequency due to their inherent reduced inertia feature. Time delays have emerged as a major source of concern in microgrids (MGs) as a result of the broad adoption of open communication networks since significant delays inevitably reduce the controller?s performance and even cause instabilities. In this article, a frequency-domain direct method is used to evaluate the impact of the virtual inertia (VI) control on the stability delay margins of MG with communication delays. By avoiding approximation, the approach first removes transcendental terms from characteristic equations and turns the transcendental characteristic equations into regular polynomials. With this method, roots of the original characteristic equation on the imaginary axis correspond to exactly the positive real roots of the new regular polynomial not including any exponential term. This new polynomial can be used to find out whether the system stability is delay-dependent or not and enables us to compute stability delay margin for the delay-dependent stability case. The proposed analytical method is utilized for evaluating stability delay margins with regard to system parameters for various values of proportional-integral (PI) gains where the MG is marginally stable. Moreover, quantitative effect of virtual inertia and damping gains is comprehensively investigated. Based on the results, it is concluded that incorporating VI control enhances stability delay margins and enhances the MG's stability performance. Theoretical delay margin results are verified using time-domain simulations and quasipolynomial mapping-based root finder (QPmR) algorithm

Impact of participation ratios on the stability delay margins computed by direct method for multiple-area load frequency control systems with demand response

ABSTRACT This article studies the effect of dynamic demand response (DR) control on stability delay margins of load frequency control (LFC) systems including communication time delays. DR control is a significant tool to control the responsive loads and increase the reliability of LFC system. The DR control effort on the frequency regulation is provided to each control area of LFC system, called as LFC-DR system. Although the DR control provides some benefits to power grid, communication networks equipped in LFC systems cause communication time delays that degrade dynamic stability of the LFC systems resulting in exponential terms in the characteristic equation of LFC-DR system. This study utilizes an exact method to eliminate the exponential terms without any approximation and transform it into a regular polynomial. The method is utilized to identify stability delay margins for various proportional–integral gains and participation ratios of the secondary and DR control loops for the LFC-DR system. The delay margin values obtained are confirmed by time-domain simulations and a root finder algorithm based on quasi-polynomial mapping. Results indicate that the DR control significantly increases stability delay margins and improves the frequency response of the system as compared with conventional frequency regulation methods.

Determination of stability delay margins for multi-area load frequency control systems with incommensurate time delays through eigenvalue tracing method

This work presents delay-dependent stability analysis using eigenvalue tracing method for multi-area load frequency control (LFC) systems with incommensurate time delays. LFC systems face inevitable communication delays that adversely affect the frequency stability. Time delays exceeding the allowable limit lead to system instabilities. In this study, stability delay margins of a time-delayed LFC system are computed by a simple yet effective frequency-domain method for computing critical eigenvalues and the corresponding delay margins without using the characteristic equation of the system. By tracing eigenvalue loci of a transformation matrix, the method easily determines the critical eigenvalues on the imaginary axis and obtains stability delay margins. Both stability delay margins and the effectiveness of stability regions in the time delay space are confirmed by time-domain simulations and the quasi-polynomial mapping-based root finder (QPmR) algorithm. Results indicate that more accurate delay margin values are obtained as compared to ones with Lyapunov stability theory based algorithms.

The effect of demand response control on stability delay margins of load frequency control systems with communication time-delays

This paper studies the effect of dynamic demand response (DR) control on stability delay margins of load frequency control (LFC) systems including communication time-delays. A DR control loop is included in each control area, called as LFC-DR system and Rekasius substitution is utilized to identify stability margins for various proportionalintegral (PI) gains and participation ratios of the secondary and DR control loops. The purpose of Rekasius substitution technique is to obtain purely complex roots on the imaginary axis of the time-delayed LFC-DR system. This substitution first converts the characteristic equation of the LFC-DR system including delay-dependent exponential terms into an ordinary polynomial. Then the well-known Routh-Hurwitz stability method is applied to find those imaginary roots and the corresponding stability delay margin known as maximal time-delay. Delay margin results indicate that the inclusion of DR control loop significantly increases stability delay margin and improves the frequency dynamic behavior of the LFC system including time-delays. Theoretical stability margins are confirmed by a proven algorithm, quasi-polynomial mapping-based root finder (QPmR) algorithm and time-domain simulations

Impact of electric vehicles aggregators with communication delays on stability delay margins of two-area load frequency control system

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.

Impact of load sharing schemes on the stability delay margins computed by Rekasius substitution method in load frequency control system with electric vehicles aggregator

Impact of load sharing schemes on the stability delay margins computed by Rekasius substitution method in load frequency control system with electric vehicles aggregator

Stability Analysis of Grid-connected Inverter System Containing Virtual Synchronous Generator under Time Delay and Parameter Uncertainty

Virtual synchronous generator (VSG) control is an effective way to increase the equivalent inertia of grid connected inverter system and improve the stability of the power grid. However, the influence of this control on the stability of the whole system with time delay and parameter uncertainty should be researched further. In this paper, the state space model of the whole grid connected inverter system adopting VSG under control time-delay and parameter uncertainty is established. The Lyapunov functional with time-delay is constructed by employing time-delay dependent free weight matrix transformation. Furthermore, Lyapunov stability theorem is used to obtain the more conservative time-delay stability conditions with and without parameter uncertainty, linear matrix inequality is used to calculate the time-delay stability margin of the system under uncertainty, and the influence of the parameters of VSG control on the delay stability margin is analyzed. The validity of the proposed stability analysis and stability margin solution method are verified by simulation examples.

Impact of Electric Vehicle Aggregator with Communication Time Delay on Stability Regions and Stability Delay Margins in Load Frequency Control System

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.

Analysis and Mitigation of the Communication Delay Impacts on Wind Farm Central SSI Damping Controller

The use of supplementary controllers for mitigating subsynchronous interaction (SSI) in series compensated DFIG-based wind farms is quite promising due to high effectiveness and low cost. Implementation of such a controller requires effective communications between individual turbines and the wind farm controller, where the control performance is very much affected by the communication delays involved. This paper delivers the first detailed analysis on the impact of communication delays on SSI damping controller performance. A novel algorithm is proposed to calculate the stability delay margin (SDM) of the closed-loop system based on Rekasius Substitution and Guardian Map Theorem with the advantage of reduced computational burden particularly for high-order systems. Based on the proposed algorithm, the impacts of wind farm operating conditions and turbine control parameters on the SDM are investigated. To strengthen the SSI damping controller performance against communication delays, a Smith predictor scheme is also developed. The effectiveness of the proposed delay analysis framework and Smith predictor scheme based delay immune controller is validated through Electromagnetic Transient (EMT) simulations on a realistic test system with multiple series capacitor compensated lines considering various operation conditions.

Computation of Time Delay Stability Margin for the Automated Vehicular Platoon

Due to the limited band width and congestion of communication channels in the wireless vehicle-to-vehicle (V2V) communication, time delay inevitably arises and dramatically leads to the disturbances for the automated vehicular platoon. This paper focuses on computing the exact time delay stability margin. In this study, we treat this problem as a stability issue of a consensus system with time delay, where each vehicle in the platoon is recognized as a node, and the interconnected information flow is represented as a graph. Then, the distributed controller is designed by combining the states of the vehicle itself and its neighbouring vehicles. Furthermore, the stability of the entire platoon is analysed according to the characteristic equation of the closed-loop system, and a necessary and sufficient condition for the exact time delay stability margin is obtained. Especially, for the automated vehicular platoon with undirected topology, it is revealed that exact time delay stability margin is determined by the largest eigenvalue of the augmented Laplacian matrix. Furthermore, a rapid method for finding exact time delay stability margin is proposed. Finally, numerical simulations demonstrate that this work generates exact and satisfactory time delay stability margin for the automated vehicular platoon.

Gain-phase margins-based delay-dependent stability analysis of pitch control system of large wind turbines

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.

Gain and phase margins-based delay margin computation of load frequency control systems using Rekasius substitution

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.

Gain and phase margins based delay-dependent stability analysis of single-area load frequency control system with constant communication time delay

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.