Load Frequency Control Of Multi-area System Research Articles

Formula omitted] Load frequency control of power systems with multiple time-varying delays via improved reciprocally convex inequality

This paper focuses on the stability problem and the design method of PI-type H∞ controller for load frequency control (LFC) of power systems with multiple time-varying delays (MTD). In the existing researches, the model of LFC system with time delays is not accurate enough since it is established based on the assumption that the time delays are all the same. This paper proposes a novel model of multi-area LFC system with MTD. Both the stability analysis and controller design in this paper are based on the improved model to ensure the applicability of the proposed method in general. First, a novel Lyapunov-Krasovskii functional (LKF) containing delay-product-type term (DPT) is constructed and auxiliary function-based integral inequality (AFBII) is utilized to handle the integral term of the derivative of LKF. Then, an improved reciprocally convex inequality is proposed to obtain the less conservative stability criteria in terms of linear matrix inequalities (LMIs). Next, an effective H∞ controller design method is developed based on the proposed stability criteria. Finally, simulation experiments are done to illustrate the superiority of proposed criteria and effectiveness of proposed design method.

Stabilization of Load Frequency Control System via Event-Triggered Intermittent Control

This brief studies the stabilization of load frequency control (LFC) system. The event-triggered intermittent control (ETIC) is designed for the multi-area LFC system. The stabilization of the LFC system is achieved under the designed ETIC. Moreover, the scheme of ETIC is improved via state-based control width (SCW) and an ETIC-SCW is proposed. Two performance indices: the rate of control and the cost of control, are defined for comparisons. Specific cases are studied to verify the effectiveness of the proposed ETIC schemes. From the numerical simulations, it is shown that the designed ETIC, especially ETIC-SCW, achieves clearly lower rate of control and cost of control than the time-based intermittent control and the event-triggered control for LFC system in the literature.

Delay-Dependent Optimal Load Frequency Control for Sampling Systems With Demand Response

The continuous-time model is widely used to design load frequency control (LFC) schemes for power systems with delays and demand response (DR). In practice, however, the LFC system works in a sampled-data manner. The plant operates continuously while the control updates every few seconds. This paper focuses on the sampled-data LFC system with DR and the delay. Based on the linear quadratic regulator (LQR) theory, an optimal control scheme is designed to regulate the DR and generation units in a sampled-data manner. The LQR controller can be applied to the LFC system with constant and time-varying delays, regardless of DR. An observer is also designed to make the state-feedback control law feasible. The observer is efficient in that its gain is delay independent. Case studies on the one-area and multi-area LFC systems are conducted to verify the effectiveness of the proposed LFC controller. Simulation results also demonstrate the excellent stability and performance of the proposed LQR controller in the sampled-data LFC-DR 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.

Inserting of heuristic techniques into the stability regions for multiarea load frequency control systems with time delays

The design and optimization of robust controller parameters are required to improve the controller performances and to keep the stability of load frequency control (LFC) system. In addition, reducing the number of iterations and computational time is very important for swiftly tuning of the controller parameters and the system to reach stability rapidly. For this purpose, this study presents the inserting of heuristic optimization techniques into stability regions method identified in proportional-integral (PI) controllers space for multiarea LFC systems with communication time delays (CTDs). This method consists of two steps: determination of stability region for the system and application of heuristics. Stability region for the system is found via stability boundary locus (SBL) and moth-flame optimization (MFO), particle swarm optimization (PSO), sine cosine algorithm (SCA), slime mould algorithm (SMA) and whale optimization algorithm (WOA) are inserted and applied to this region. In addition, a cost function having time domain specifications is developed for improving the performances of LFC and it is compared with the well-known integral error functions. Also, the robust stability region, which tolerates any system parameter and any time delay variation, is identified and the significance of this region is given for robustness analysis. It is observed from the analyses that better system outputs have been obtained with developed cost function. Steady state errors are minimized and transient state performances are improved with the proposed method. Moreover, desired system performances have been achieved with lower computational time and iteration number (approximately more than about 89% reduced according to classical approach) without deteriorating the stable structure of the system by the proposed method.

Delay-Dependent Stability for Load Frequency Control System via Linear Operator Inequality

The stability analysis problem is considered for multiarea load frequency control (LFC) systems with electric vehicles (EVs) and time delays. The novel linear operator inequality approach is proposed and a less conservative delay-dependent stability condition is achieved. First, the model of the multiarea LFC system with EVs and delays is expressed by the partial integral equation (PIE) at the first time. Then, a complete quadratic Lyapunov-Krasovskii functional is built in the form of an inner product of the linear partial integral (PI) operator. The novel stability criteria with less conservatism are proposed in the form of linear operator inequality. Moreover, the relationships between the delay margins and the controller parameters are shown. Finally, the simulations are conducted on both one-area and two-area LFC systems to show the effectiveness of the proposed approach.

Event-triggering load frequency control for multi-area power system based on random dynamic triggering mechanism and two-side closed functional

By taking into account sampled-data mechanism and transmission delay, the novel event-triggering load frequency control (LFC) strategy involving random dynamic triggering algorithm (RDTA) is developed for multi-area power systems in this paper. Firstly, an improved multi-area LFC model considering sampling and transmission delay (STD) simultaneously is addressed. Secondly, a modified event-triggering mechanism (ETM) with RDTA is proposed, considering parameter disturbances and a dynamic adjustment mechanism of the triggering threshold. Thirdly, a more advanced Lyapunov–Krasovskii functional (LKF) is constructed, introducing the delay-dependent matrices, more variable cross terms and the two-sided closed functional. Furthermore, two less conservative stability criteria are obtained according to the designed approach. Finally, two multi-area LFC systems are presented to verify the progressiveness of the proposed approach.

An Accurate Method for Computing the Delay Margin in Load Frequency Control System with Gain and Phase Margins

In traditional power systems, a dedicated communication channel is utilized to transfer the frequency measurements. With the deregulation and reconstruction of power systems, the information is sent through a shared communication network that makes time delays unavoidable in load frequency control (LFC) systems. With the existence of time delays, the LFC system becomes a standard time delay system that complicates the stability analysis and controller synthesis. In this paper, we present a new approach for analyzing the stability and determining the delay margin of the LFC system. By introducing a new variable, the transcendental equation is converted to nonlinear equations. To find the crossing frequencies, the nonlinear equations are solved, which is simpler than solving a set of linear matrix inequalities. A single-area and a multi-area LFC system are selected as case studies. The new method accurately determines the delay margin of the LFC system with phase and gain margin. The effect of the PI controller gains on the delay margin is also considered. A sensitivity analysis is conducted to discover the effects of the system parameters on the delay margin, and it is found that the primary loop parameters have a powerful influence on the delay margin. The stability region of the LFC system is also clearly identified through the proposed method. The influence of the system parameters on the stability region is studied. Compared to the published methods in the literature, the proposed method has a simpler structure while giving more accurate results.

Co-Estimation of State and FDI Attacks and Attack Compensation Control for Multi-Area Load Frequency Control Systems Under FDI and DoS Attacks

This paper proposes a co-estimation and resilient compensation control framework for multi-area load frequency control (LFC) systems in the presence of false data injection (FDI) attacks and denial-of-service (DoS) attacks. To relax the requirement on existing DoS attack models, which are usually considered under the assumption that both its frequency and duration are constrained, a new DoS model within a known bounds of the sleeping and active period of the attack signal is proposed. The injected FDI attack signal is generated by an external dynamic systems. A switching impulsive observer and a switching state observer are constructed to estimate the unknown FDI attack signal and the system state, respectively. Moreover, a new exponential stability criteria of the output feedback multi-area LFC systems under DoS and FDI attacks is first derived by using attack parameter dependent time varying Lyapunov function method. Then, a co-design method of a resilient attack compensation controller, state estimator, and attack estimator is developed. Finally, case studies are considered for verification of the effectiveness of the proposed theoretical results.

Detection of False Data Injection Attacks on Load Frequency Control System with Renewable Energy Based on Fuzzy Logic and Neural Networks

Load frequency control (LFC) system may be destroyed by false data injection attacks (FDIAs) and consequently the security of the power system will be impacted. High-efficiency FDIA detection can reduce the damage and power loss to the power system. This paper defines various typical and hybrid FDIAs, and the influence of several FDIAs with different characteristics on the multi-area LFC system is analyzed. To detect various attacks, we introduce an improved data-driven method, which consists of fuzzy logic and neural networks. Fuzzy logic has the features of high applicability, robustness, and agility, which can make full use of samples. Further, we construct the LFC system on MATLAB/Simulink platform, and systematically simulate the experiments that FDIAs affect the LFC system by tampering with measurement data. Among them, considering the large-scale penetration of renewable energy with intermittency and volatility, we generate three simulation scenarios with or without renewable energy generation. Then, the performance for detecting FDIAs of the improved method is verified by simulation data samples.

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.

False Data Injection Attacks on Hybrid AC/HVDC Interconnected Systems With Virtual Inertia—Vulnerability, Impact and Detection

Power systems are moving towards hybrid AC/DC grids with the integration of HVDC links, renewable resources and energy storage modules. The load frequency control (LFC) of tomorrow has to consider the complex interactions between these components. Meanwhile, more attention should be paid to cyber security concerns as the LFC loop highly depends on data communications which may be exposed to cyber attacks. In this regard, this article aims to analyze the false data injection (FDI) attacks on the AC/DC interconnected LFC system with inertia emulation and develop advanced diagnosis tools to reveal their occurrence. We build an optimization-based framework for the purpose of vulnerability analysis. Considering the attack impact on frequency stability, it is shown that the multi-area LFC system with parallel AC/DC links and emulated inertia by storage devices is more vulnerable to FDI attacks, compared to the one without inertia emulation and the normal AC system. We then propose a detection approach to detect and isolate each FDI intrusion with a sufficient fast response, and even recover the attack value. In addition to theoretical results, the effectiveness of the proposed method is validated through simulations on the two-area AC/DC interconnected LFC system with inertia emulation capabilities.

Robust exponential load frequency control for time delay power system considering wind power

The injection of intermittent wind power reduces the equivalent inertia of power systems, and therefore, the change rate of frequency deviation for the load frequency control (LFC) schemes is increased. LFC schemes employ communication channels to transmit signals, which introduces time delays resulting in badly dynamic performance. This paper presents a delay-dependent approach to obtain the robust load frequency controllers based on decay rate for a multi-area LFC scheme integrated with wind power. An index of decay rate related to settling time is introduced. For a preset delay upper bound, controller gains are optimized by maximizing the decay rate. Also, the controller gains can be designed under the desired decay rate while obtaining the allowable maximum delay margins. Case studies are based on the deregulated multi-area LFC system to verify the robustness of developed controller against inertia reduction. Moreover, the proposed method enables the frequency deviation to be restrained and eliminated within a few seconds.

Computation of stability regions for load frequency control systems including incommensurate time delays

This article studies the impact of incommensurate communication time delays on stability regions defined in proportional-integral (PI) controller parameter space for a two-area load frequency control (LFC) system. Distributed power generations and large power plants increase the complexity and control issues of interconnected power systems. In interconnected power systems, LFC systems need to have complex communication networks to exchange data between control center and geographically dispersed generations. The receiving/transmitting of remote measuring data through communication infrastructures causes inevitable time delays, which adversely affect controller performance and stability of the LFC system. Time delays introducing feedback control loops of a multiarea LFC system could exhibit incommensurate characteristics. In this study, a simple graphical method based on extracting a stability boundary locus is implemented to get PI controller parameters responsible for stabilizing the LFC system having incommensurate delay values. The boundaries of the stability regions in the PI controller parameter space are confirmed by time-domain simulations and a numerical algorithm known as the quasipolynomial mapping-based root finder algorithm. Results illustrate that incommensurate delays have remarkable effects on the stability region.

Further Improvement on Delay-Dependent Load Frequency Control of Power Systems via Truncated B–L Inequality

In this paper, a new method is put forward for the closed-loop stability analysis of PI-type load frequency control (LFC) scheme with interval time-varying delay. Improved delay-dependent conditions in terms of linear matrix inequalities for single-area and multi-area LFC systems are deduced by the proposed augmented Lyapunov–Krasovski (L-K) functional. Less conservativeness of our main results is due to an integral inequality called truncated second-order Bessel–Legendre (B-L) inequality, which can produce tighter bounds than Wirtinger-based inequality that encompasses Jensen inequality. Finally, the two-area interconnected power system based on Matlab/Simulink is provided to show the effectiveness and superiority of the obtained results.

Optimal Decentralized LQR Control to Enhance Multi-Area LFC System Stability

Many studies have been made in the field of load frequency control (LFC) through the last few decades because of its importance to healthy power system. It is important to maintain frequency deviation at zero level after a load perturbation. In decentralized control, the multi-area power system is decomposed into many single input single output (SISO) subsystems and a local controller is designed for each subsystem. The controlled subsystems may have slow poles; these undesired poles may drive the aggregated overall system into the instability region. Thus, it is required to relocate these poles to much more stable places to avoid their effect upon the overall system stability. This study aims to design a new load frequency controller based on the powerful optimal linear quadratic regulator (LQR) technique. This technique can be applied over subsystem level to shift each subsystem undesired poles one by one into a prespecified stable location which in turn shift the overall system slow poles and reduce the effect of the interaction between the interconnected subsystems among each other. This procedure must be applied many times as the number of undesired poles (pairs) until all the desired poles are achieved. The main objective is considered to get a robust design when the system is affected by a physical disturbance and ±40% model uncertainties. LQR can be applied again over the aggregated system to enhance the stability degree. Simulation results are used to evaluate the effectiveness of the proposed method and compared to other research results.

The Effect of EV Aggregators With Time-Varying Delays on the Stability of a Load Frequency Control System

Participation of electric vehicles (EVs) aggregators in frequency regulation service may cause time-varying delays in load frequency control (LFC) systems. These time-varying delays affect the performance and even cause instability of power systems. In this paper, we investigate a single and multiple time-varying delays-dependent stability of an LFC system with participation of EV aggregators. Based on the Lyapunov theory and linear matrix inequality approach, we propose delay-dependent stability criteria for a single and multiple time-varying delays using the Wirtinger-based improved integral inequality. With the stability criteria, we obtain delay margins for LFC with a single and two EV aggregators and investigate the interaction among the delay margins, PI controller gains, and participation ratios of EV aggregators. In addition, we investigate the significance of time-varying delays in fast-response resources by comparing the delay margin obtained in EV aggregator model with that obtained in delayed conventional generators. We discuss an extension to multiarea LFC systems and guidelines on how to improve performance of LFC systems under time-varying delays. We expect that the proposed criteria can help to guide the determination of delay requirements for EV aggregators participating in frequency regulation service.

A New Load Frequency Control Method of Multi-Area Power System via the Viewpoints of Port-Hamiltonian System and Cascade System

The existed control methods of the multi-area load frequency control (LFC) system fail to decouple the total tie-line power flow. This defect can be addressed as a problem on how to effectively utilize the total tie-line power flow. To improve that defect, the energy and structure of multi-area LFC system have been carefully studied, such that, the energy goes through the systemic cascade parts and the systemic structure matrix is partially skew symmetry. Namely, the energy and structural properties of the multi-area LFC system are similar to the properties of Port-Hamiltonian (PH) system and cascade system. Inspired by the above properties, a new method based on the PH system and cascade system that is proposed to design some PID control laws for the multi-area LFC system successfully works out the aforementioned problem. Compared with the existed PID methods for the multi-area LFC system, the proposed method has two advantages, which are the decoupling of total tie-line power flow and the robust disturbance rejection. At last, simulations results demonstrate the validity and advantages of the proposed method.