Multi-area Load Frequency Control Research Articles

Security concern and fuzzy output sliding mode load frequency control of power systems

This research investigates the concern of security in multi-area load frequency control (LFC) power systems using fuzzy logic output sliding mode control approach. A motion-trends-based deception attack model is proposed to represent malicious threats from communication networks. The motion-trends-based deception attack model enhances the destructive effect of deception attacks by monitoring changes in system state. In terms of the security concerns, a fuzzy-based output sliding mode control (OSMC) is applied to protect the power system from potential cyber-attacks. We provide sufficient conditions for the power systems stability under motion-trends-based deception attack. An initial controller gain that will bring the power system to stability is calculated by linear matrix inequalities (LMIs). The obtained controller gain provides a design method for fuzzy logic member functions. Fuzzy logic is then used to adjust the resulting controller gain to improve power system performance. The simulation results validate the usefulness of the proposed strategy, and indicate the viability of fuzzy logic in fine-tuning controllers.

Delay-dependent stability analysis for load frequency control systems with time-varying delays

This paper introduces a delay-dependent criterion that addresses both computational accuracy and efficiency in dealing with delay-dependent stability challenges within multi-area load frequency control (LFC) systems. Firstly, the traditional power system LFC model is decomposed into delay-related and delay-independent parts using a model reconstruction technique. Subsequently, an augmented Lyapunov–Krasovskii functional (LKF) is formulated, focusing on the delay-related part of the model. The double integral component within the derivative of the LKF is constrained using the parameter-dependent slack matrices approach, resulting in a less conservative stability criterion. Finally, the proposed result is validated through case studies. Simulation results demonstrate that the proposed stability criterion significantly improves computational accuracy while maintaining better validity compared to existing approaches. Moreover, compared to the traditional LFC model, the reconstructed model offers substantial computational efficiency improvements, albeit with a slight decrease in computational precision.

Frequency regulation scheme in power system using an observer-based waiting event-triggered control with random features

Addressed in this paper is the observer-based waiting event-triggered control issue in multi-area load frequency control (LFC) power system subject to random communication delay and data packet dropout. In order to maintain the grid frequency stability of the multi-area LFC power system in an open communication network, an observer-based waiting event-triggered scheme (WETS) is proposed to deal with frequency fluctuation and extend the life of control equipments. Compared with the existing event-triggered mechanism, the proposed WETS has the merits of continuous event-triggered scheme and the periodic sampling event-triggered scheme in the both of theory and application. Then, by well considering the negative factors of data packet dropout and random time delay in data transmission, a stochastic delay-dependent multi-area LFC model is established, which involves the information of observer-based WETS, random communication delay and packet dropout in a unified structure. Further, an improved Lyapunov–Krasovskii functional (LKF) is constructed by dividing the interval of transmitted delay. Based on the constructed Lyapunov functional, Park’s theorem and Jensen’s integral inequality, some less conservative stabilization criteria are obtained. Finally, the validity of the proposed control method is verified via numerical examples.

Multivariate Spectral Analysis and Hypothesis Testing-Based Robust Attack Detection for Multiarea Frequency Control

Frequency control is one of the critical systems responsible for maintaining grid stability, making it a vulnerable and attractive choice for cyber-attacks. This article presents a multivariate singular spectrum analysis (MSSA) for extracting the system’s dynamics under normal operation and proposes a projection-based distance tracking and hypothesis testing method to detect multiarea load frequency control (MA-LFC) attacks. The proposed methodology is robust, adaptive, and computationally efficient, especially, when system and measurement noises are considered. The three main features of the proposed method are that: 1) it uses standard SCADA data and does not require attack data; 2) it can be integrated with the existing grid control system with minimal hardware; and 3) it is independent of system configuration and upgrades. The attack detection algorithm can successfully detect different types of false data injection attacks (FDIAs), including stealth attacks on multiple sensors. The algorithm is tested on an IEEE 39-bus New England test system, 300 bus test system, and 1888 bus RTE system. The attack detection algorithm was found to be reliable, fast, robust, and scalable under noisy measurements compared to the existing methods.

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.

Multi-Area Load Frequency Control in Power System Integrated With Wind Farms Using Fuzzy Generalized Predictive Control Method

Frequency security is critical for the power systems’ stability and reliability. The integration of renewable energy resources brings new challenges to the frequency security of power systems. To provide a more robust control method for controlling the frequency and tie-line power flow of an interconnected power system integrated with wind farms (IPSWF), a load frequency control (LFC) controller of generalized predictive control (GPC) based on the Takagi-Sugeno (T–S) fuzzy model (fuzzy-GPC) is proposed in this paper. First, the T–S fuzzy model of the IPSWF is constructed. Then, the GPC is used to design the controller. Lastly, to validate the proposed scheme, an LFC strategy is established for a two-area interconnected power system integrated with a wind farm in power systems computer aided design (PSCAD). The control performance of proportional-integral, GPC, and fuzzy-GPC controller are compared under two faulty operating conditions. The simulation results show that the performance indicators and the dynamic behavior when the fuzzy-GPC controller is used are better than the performance when the PI controller and GPC controller are used. The proposed fuzzy-GPC used in the LFC of the IPSWF can regulate the frequency deviation and tie-line power deviation adaptively and achieve minimum frequency deviation and tie-line power deviation in a multi-area IPSWF.

Dynamic memory event-triggered proportional-integral-based [formula omitted] load frequency control for multi-area wind power systems

Aiming at ensuring the stability of multi-area doubly fed induction generator (DFIG)-integrated wind power systems, a dynamic memory event-triggered H∞ load frequency control (LFC) scheme is presented in this article. Firstly, a unified LFC model of multi-area DFIG-integrated wind power systems is constructed considering the grid connection of the DFIG-based wind turbine. Secondly, a dynamic memory event-triggered scheme (DMETS) is proposed to reduce the utilization of communication bandwidth by introducing a dynamic threshold parameter and historical data. Furthermore, the designed multi-area LFC model is reconstructed as a time-delay system under DMETS and proportional-integral (PI) controller with transmission delays introduced by open communication network. Then, asymptotic stability criteria meeting the H∞ attenuation performance index and an H∞ controller design criterion are obtained according to a selected Lyapunov–Krasovskii functional. Finally, numerical examples are presented to demonstrate the availability of the designed control scheme and the advantages of the proposed DMETS in reducing communication burden.

Delay-Dependent Stability Analysis of Multi-Area LFC-EVs System

In this study, the delay-dependent stability of a multi-area Load Frequency Control (LFC) system with Electric Vehicle (EV) aggregators is investigated with the help of the Advanced Clustering with Frequency Sweeping (ACFS) method for incommensurate time delays. Both Integer-Order (IO) and Fractional-Order Proportional Integral (FOPI) controllers are utilized as a controller. The communication infrastructure used in LFC systems induces time delays resulting in deteriorations in the system stability. Even if the maximum allowable delay margin limits are not exceeded, these inevitable time delays could cause undesired frequency deviations and tie-line power fluctuations. The ACFS method is employed in this study to investigate impacts of time delays and to ensure better controller performance objectives taking into account the effects of time delays. Firstly, 2-dimensional (2D) stability delay maps are obtained for various LFC-EVs system parameters. The stability regions are then verified by the Quasi-Polynomial Mapping Root (QPmR) finder algorithm and MATLAB/Simulink-based time-domain simulations. The results clearly show that the participation of the EV aggregators in traditional LFC systems improves the frequency regulation and tie-line power-sharing in the system. Finally, it is concluded that the stability regions are enhanced as the fractional order of the FOPI decreases.

Bird Swarm Algorithm Optimized TIDD Controller for Multi-area Load Frequency Control Application

Bird Swarm Algorithm Optimized TIDD Controller for Multi-area Load Frequency Control Application

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.

Dynamic Response of Multi Area Load Frequency Control through Different Computational Techniques

Objective: To employ optimization technique (GA (Genetic Algorithm) Technique) to solve the problem of power generation, by means of mathematical approach to formulate the problem mathematically. Methods: Thermal units have been taken as a source of power generation. Transfer function model of thermal generating units has been developed and simulated through MATLAB Simulink software. The main issue of power generation is the continuous mismatching in the generation and consumption of electricity due to which continuous the change in frequency and corresponding power becomes a major issue, which need to be maintained in constancy for regular operation. For this purpose, optimization technique (GA Technique), PI (Proportional Plus Integral), PID (Proportional Plus Integral Plus Derivative) technique have been used to solve the issue of frequency and corresponding power. Findings: Solve the issues of change in frequency and corresponding tie line power, a table has been drawn for batter comparison. Novelty: The comparative results obtained from all technique have been put in table which shows that the optimization technique (GA Technique) gives very effective, efficient and dynamic results (8 Sec and 11 Sec in Frequency & Power Variation) compared to traditional technique (PI, PID) (28 Sec, 44 Sec & 27 Sec & 43 Sec in Frequency & Power Variation). Keywords: Traditional Technique; GA (Genetic Algorithm) Technique; Optimization Technique; Power Generation

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.

Spectral analysis based robust multi-level intrusion detection in wide area frequency control

Frequency control is one of the critical systems responsible for maintaining grid stability, making it an attractive choice for cyber-attacks. The paper presents a singular spectrum analysis for extracting the system’s dynamics under regular operation and proposes a projection-based distance tracking method to detect Multi-area Load Frequency Control (MA-LFC) attacks. Two variations of the algorithm, namely single-variate and multi-variate algorithms, are proposed for detection at different levels of the power system. The proposed methodology is robust, adaptive, and computationally efficient, especially when system and measurement noises are considered. The method’s main advantage is that it does not require attack data and can be integrated with the existing grid control system. The algorithm can be implemented within the RTUs/IEDs without the need for additional processors. The detection algorithm successfully detects different types of attacks, including stealth attacks on multiple sensors. By selecting proper set of signals, it is possible to obtain 99.85% accuracy and 2 cycles deduction speed. The algorithm is tested on an IEEE 39-bus New England test system in the MATLAB environment, and its performance under noisy measurements is better than existing methods.

Neural network based heuristic fractional order adaptive PID‐controller for eliminating communication time delay in multi‐area LFC

AbstractCommunication of interconnected power system components with each other and with control centers is provided by using various communication links. However, these links can cause significant time delays (TD) depending on the types, distance and conditions of the communication channel. In addition to temporary time delays caused by the time constants of the components due to system failures, this article draws attention to the negative effects that may be caused by permanent communication time delays in particular, as different from the literature. The communication time delays can disrupt the stable operation of power systems and even cause the whole system to breakdown by making it unstable, when combining with other delays. In the study, the fiber‐optic (F/O) links are assumed to commonly use in supervisory control and data acquisition (SCADA) systems and the communication time delays are calculated based on this scenario. However, it is no doubt that less used radio frequency (RF)‐links will create more time delays. Moreover, to eliminate the negative effects of these types of time delays, a novel neural network based‐heuristic fractional order hybrid adaptive proportional‐integral‐derivative (ML‐H‐PIλDμ) controller for multi area load frequency control (LFC) scheme is developed and analyzed.

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.