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Two-level optimal load–frequency control for multi-area power systems
Abstract and Figures
In large-scale power systems, classical centralized control approaches may fail due to geographically distribution of information and decentralized controllers result in sub-optimal solution for load–frequency control (LFC) problems. In this paper, a two-level structure is presented to obtain optimal solution for LFC problems and also reduce the computational complexity of centralized controllers. In this approach, an interconnected multi-area power system is decomposed into several sub-systems (areas) at the first-level. Then an optimization problem in each area is solved separately, with respect to its local information and interaction signals coming from other areas. At the second-level, by updating the interaction signals and using an iterative procedure, the local controllers will converge to the overall optimal solution. By parallel solving of areas, the computational time of the algorithm is reduced in contrast to centralized controllers. This approach is applicable to any interconnected large-scale power system. However, for simulation purposes, a three-are power system is presented to show advantages and optimality of the proposed algorithm.
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... Various optimization methods have been employed for tuning the parameters of PI controllers to improve system performance under various disturbances [11]- [13]. To address the drawbacks of traditional PI controllers for LFC applications, a wide range of control strategies for the LFC problem have been extensively applied; these strategies include optimal control [14]- [18], adaptive control [19]- [23], fuzzy control [24]- [28], model-predictive control [29]- [32], H ∞ control [2], [33]- [36], and variable structure control [37]- [41]. A broad literature review on the effectiveness of various control strategies for the LFC can be found in [42]- [44]. ...
... The reachability of the sliding surface S i (t) = 0 is guaranteed in finite time by employing the controller (14) Proof: ...
... Fig. 5 illustrates the response curve of the disturbance estimations for all three areas; the curves show that the estimation errors asymptotically converge to zero. The sliding surface (13) and control effort (14) for all control areas are shown in Figs. 6 and 7, which show that the system trajectories are driven to the sliding surfaces in all control areas. ...
The load frequency control (LFC) problem in interconnected multiarea power systems is facing more challenges due to increasing uncertainties caused by the penetration of intermittent renewable energy resources, random changes in load patterns, uncertainties in system parameters and unmodeled system dynamics, leading to a compromised reliability of power systems and increasing the risk of power outages. In responding to this problem, this paper proposes a decentralized disturbance observer-based sliding mode LFC scheme for multiarea interlinked power systems with external disturbances. First, a reduced power system order is constructed by lumping disturbances from tie-line power deviations, load variations and the output power from renewable energy resources. The disturbance observer is then designed to estimate the lumped disturbance, which is further utilized to construct a novel integral-based sliding surface. The necessary and sufficient conditions to determine the tuning parameters of the sliding surface are then formulated in terms of linear matrix inequalities (LMIs), thus guaranteeing that the resultant sliding mode dynamics meet the H <sub>∞</sub> performance requirements. The sliding mode controller is then synthesized to drive the system trajectories onto the predesigned sliding surface in finite time in the presence of a lumped disturbance. From a practical perspective, the merit of the proposed control method minimizes the impact of the lumped disturbance on the system frequency, which has not been considered to date in sliding mode LFC design. Numerical simulations are illustrated to validate the effectiveness of the proposed LFC strategy and verify its advantages over other approaches.
... The main purpose of controlling the electrical power system, especially controlling the automatic generation of power(AGC), is to continue providing electrical power to the loads despite changes in the load and system disturbances that may occur in any area causing a change in frequency and thus directly affecting the performance operation of the electrical system and its reliability [1,2]. LFC is one of the most important control problems in the design and operation of an electrical power system. ...
... Fig. 8 represents the membership functions T2FL for the three fuzzy output variables (Kp, Kd, alpha). Two membership functions for the two outputs variables (Kp and Kd) are Gaussian (small and big) with a range (0,1) and four membership functions 'trimf'' for the output alpha with a range (2)(3)(4)(5). ...
In this study, based on the fuzzy logic type-2
(T2FL) technique, a new load frequency control (LFC) for
multi-area-power systems is proposed. The target of the T2FL
controller is to get back the frequency to its fundamental value
in the shortest potential time. The control structure ensures that
the frequency deviation (Delta f), output power generator
deviation (Delta Pg), and tie-line power deviation (Delta ti)
between areas are kept within certain limits. The prominent
feature of the suggested controller is not sensitive to significant
load changes even in the presence of nonlinearity. Thus, the
problem of traditional controllers that do not provide suitable
control performance under the above-mentioned non-linear
conditions has been overcome. LFCs and their controllers are
designed using simulation in Mat lab. Simulation results prove
of the suggested PID-T2FL controller is superior in
performance compared with both the PID controller and PIDgain
tuning by a type-1 fuzzy controller (PID-T1FL in reducing
settling time and peak overshoot to half approximately and gave
best response in the abrupt load disturbance.
... Two-level or multi-level control mechanisms are discussed in the literature to solve these limits. For an integrated power system, a two-level AGC regulator is suggested in [46]. Here, a multi-area interconnected power grid is disintegrated into many subsystems at the first stage and an optimization problem is solved in each region based on input from the local area and the other areas. ...
... Optimal control methods (OCM) fit in the calculus of variations and deal with the closed-set constrained variation problems. Several research articles on the optimal and sub-optimal controls are reported in the literature [43,46,54,55]. A detailed analysis of optimal control methods in the AGC system of an interconnected power system is presented in study [54]. ...
Automatic generation control (AGC) is primarily responsible for ensuring the smooth and efficient operation of an electric power system. The main goal of AGC is to keep the operating frequency under prescribed limits and maintain the interchange power at the intended level. Therefore , an AGC system must be supplemented with modern and intelligent control techniques to provide adequate power supply. This paper provides a comprehensive overview of various AGC models in diverse configurations of the power system. Initially, the history of power system AGC models is explored and the basic operation of AGC in a multi-area interconnected power system is presented. An in-depth analysis of various control methods used to mitigate the AGC issues is provided. Application of fast-acting energy storage devices, high voltage direct current (HVDC) inter-connections, and flexible AC transmission systems (FACTS) devices in the AGC systems are investigated. Furthermore, AGC systems employed in different renewable energy generation systems are overviewed and are summarized in tabulated form. AGC techniques in different configurations of microgrid and smart grid are also presented in detail. A thorough overview of various AGC issues in a deregulated power system is provided by considering the different contract scenarios. Moreover, AGC systems with an additional objective of economic dispatch is investigated and an overview of worldwide AGC practices is provided. Finally, the paper concludes with an emphasis on the prospective study in the field of AGC.
... In the recent years, great efforts have been paid to deal with the LFC problem [5]. In this regard, various control strategies including the adaptive neuro-fuzzy [6], variable structure control [7], robust control [8], non-integer control [9], state feedback control [10] are implemented to deal with LFC problem. On the other hand, some attentions have been concerned with the LFC for HlGS based on some conventional and meta-heuristic optimization algorithms. ...
This paper addresses a novel hunger games search (HGS) based on specular reflection-based learning (SRL) and dynamic quasi-opposition-based learning (DQOL), named HGS_RQ, for improving the optimization performance of the classical HGS while dealing with load frequency control task. By these learnings, a fitter solution can be generated whether by SRL or DQOL and therefore, the quality of the best solution can be refined. The effectiveness of the proposed HGS_RQ is demonstrated and validated on two-area interconnected power system with considering nonlinearity effect of governor dead band. Additional supplementary controller is proposed to reinforce frequency regulation through solid oxide fuel cell. The objective function is adapted to minimize the integral time absolute error in frequency deviations and tie line power. The efficacy and superiority are affirmed by the comparisons with some of prominent recent methods. It can be noted that the adequate response is proved, since the maximum frequency deviation is 0.088 Hz, the settling time is about 2 s, and the steady-state frequency change is zero in the two areas. On the other hand, there is a significant reduction in tie line power transient response with maximum deviation of 1.318% for the studied cases. Furthermore, the statistical measures and analysis of variance test are analyzed to exhibit the superior performance of the HGS_RQ in terms of accuracy and reliability.
The automatic generation control (AGC) is one of the core control systems in power grids that regulate frequency within the permissible range. However, its dependence on communication makes it highly vulnerable to cyber-attacks. An arbitrary false data injection attack (FDIA) on AGC frequency and tie-line flow measurements will likely be detectable by bad data detection methods; however, if an attack can be launched optimally, it often becomes stealthy. In this regard, we develop a framework of optimal FDIAs (OFDIAs) to demonstrate the feasibility of such attacks in the power system frequency control loop. We propose a linearized formulation of discretized power systems’ dynamics in an optimization framework to model OFDIAs that compromise the AGC system by corrupting tie-line flow and generators’ frequency measurements. Using the proposed formal modeling, we study the effects of two types of FDIAs, continuous and time-limited, on the frequency behavior in power grids. The results demonstrate that continuous OFDIAs can lead to severe consequences on a power grid’s performance, such as frequency instability. In contrast, the time-limited FDIAs can cause the frequency to fluctuate beyond the acceptable range, which may lead to the triggering of the frequency-based protection relays.
The automatic generation control (AGC) system is a crucial control system based on information and communication technology in interconnected power systems. However, the dependence on cyber systems has increased the risk of false data injection attacks (FDIAs) against AGC systems. Furthermore, as the penetration level of wind power increases, an AGC dynamic framework incorporating wind stochastic modeling should be developed, and the impact of FDIAs on AGC considering wind power penetrations should also be evaluated. This paper proposes an evaluation method of the impact of FDIAs on AGC considering wind power penetrations. First, a linearized analysis framework is developed, in which the network model is considered due to its geographical smoothing effects. Then, stochastic differential equations (SDEs) are employed to model wind power and load temporal uncertain behaviors, and the overall system dynamics under different FDIA types are also proposed. Finally, the proposed methodology is illustrated via a 4-area practical AGC system. The simulation results show the effects of different types of attacks on the AGC system considering wind power penetrations and demonstrate that the existing evaluation frameworks may overestimate FDIA effects and wind power fluctuation and corresponding system inertia reduction may help the attacker to cause system instability.
This paper presents a novel approach for designing a decentralized controller for load frequency control of interconnected power areas. The proposed fuzzy logic load frequency controller (FLFC) has been designed to improve the dynamic performance of the frequency and tie line power under a sudden load change in the power areas. The effect of generation rate constraint (GRC) for both areas has been considered in the controller design. The proposed FLFC consists of two internal fuzzy logic controllers namely, the PD-like fuzzy logic controller and the PI-like fuzzy logic controller. The FLFC has been co-coordinated with the conventional integral controller. Time-domain simulations using MATALB/SIMULINK program has been performed to demonstrate the effectiveness of the proposed FLFC. The simulation results show that the proposed FLFC can provide good damping and reduce the overshoot even in the presence of the GRC.
In this paper, a hierarchical optimal robust controller is presented for power system load-frequency control problem. In this approach, the multi-area power system is first decomposed into several subsystems (areas). Then by using a two-level control strategy, the overall optimal solution is obtained. At the first-level, the optimal control of each area is obtained with respect to local information and also considering interactions coming from other areas. At the second-level, by using a coordination strategy, the local controllers will converge to global solution and optimal robust controller is achieved. This
approach is applicable to both single-area and multi-area interconnected power systems. Simulation results show the effectiveness and optimality of the proposed robust controller in power systems.
An optimal decentralized load-frequency control of a multi-area intercon-nected power system is developed. It features the optimal design of decentralized load-frequency controller, the observer for unmeasurable local states and load disturbances, and ttie quadratic estimator for discrete tie-line power flow information. The optimal design of the decentralized controller is based on a modified application of the singular perturbation theory, and the decentralized Luenberger observer uses techniques of state augmentation for exponential disturbance functions and the representation of tie-line power flows as non-directly-controlled inputs.
Robust analysis for decentralized load frequency control (LFC) for multi-area power systems is studied in this paper. It is observed that such an analysis can be decomposed into two steps considering the inherent structure of a multi-area power system: robustness analysis against the parametric variations in local-area power systems and robustness analysis against the structure and/or magnitude variations in the tie-line power flow network. A detailed structured singular value method is proposed for local-area robustness analysis, and an eigenvalue method is derived for tie-line robustness analysis. The proposed method is then applied to a four-area power system and the results show that the method is convenient and useful for decentralized load frequency control of multi-area power systems.
An accessible text for the study of numerical methods for solving least squares problems remains an essential part of a scientific software foundation. Feedback that we have received from practicing engineers and scientists, as well as from educators and students in numerical analysis, indicates that this book has served this purpose. We were pleased when SIAM decided to republish the book in their Classics in Applied Mathematics series.
The main body of the book remains unchanged from the original book that was published by Prentice-Hall in 1974, with the exception of corrections to known errata. Appendix C has been edited to reflect changes in the associated software package and the software distribution method. A new Appendix D has been added, giving a brief survey of the many new developments in topics treated in the book during the period 1974–1995. Appendix D is organized into sections corresponding to the chapters of the main body of the book and includes a bibliography listing about 230 publications from 1974 to 1995.