Finite-time economic model predictive control for optimal load dispatch and frequency regulation in interconnected power systems

This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.

Distributed Model Predictive Load Frequency Control of Multi-area Power System with DFIGs

Reliable load frequency control(LFC) is crucial to the operation and design of modern electric power systems. Considering the LFC problem of a four-area interconnected power system with wind turbines, this paper presents a distributed model predictive control(DMPC) based on coordination scheme.The proposed algorithm solves a series of local optimization problems to minimize a performance objective for each control area. The generation rate constraints(GRCs), load disturbance changes, and the wind speed constraints are considered. Furthermore, the DMPC algorithm may reduce the impact of the randomness and intermittence of wind turbine effectively. A performance comparison between the proposed controller with and without the participation of the wind turbines is carried out. Analysis and simulation results show possible improvements on closed–loop performance, and computational burden with the physical constraints.

Robust H_∞ Load Frequency Control of Multi-area Power System With Time Delay:A Sliding Mode Control Approach

This paper is devoted to investigate the robust H∞sliding mode load frequency control(SMLFC) of multi-area power system with time delay. By taking into account stochastic disturbances induced by the integration of renewable energies,a new sliding surface function is constructed to guarantee the fast response and robust performance, then the sliding mode control law is designed to guarantee the reach ability of the sliding surface in a finite-time interval. The sufficient robust frequency stabilization result for multi-area power system with time delay is presented in terms of linear matrix inequalities(LMIs). Finally,a two-area power system is provided to illustrate the usefulness and effectiveness of the obtained results.

Resilient Fixed-Order Distributed Dynamic Output Feedback Load Frequency Control Design for Interconnected Multi-Area Power Systems

The paper proposes a novel H∞ load frequency control(LFC) design method for multi-area power systems based on an integral-based non-fragile distributed fixed-order dynamic output feedback(DOF) tracking-regulator control scheme. To this end, we consider a nonlinear interconnected model for multiarea power systems which also include uncertainties and timevarying communication delays. The design procedure is formulated using semi-definite programming and linear matrix inequality(LMI) method. The solution of the proposed LMIs returns necessary parameters for the tracking controllers such that the impact of model uncertainty and load disturbances are minimized. The proposed controllers are capable of receiving all or part of subsystems information, whereas the outputs of each controller are local. These controllers are designed such that the resilient stability of the overall closed-loop system is guaranteed. Simulation results are provided to verify the effectiveness of the proposed scheme. Simulation results quantify that the distributed(and decentralized) controlled system behaves well in presence of large parameter perturbations and random disturbances on the power system.

Multi-objective optimization for voltage and frequency control of smart grids based on controllable loads

The output uncertainty of high-proportion distributed power generation severely affects the system voltage and frequency.Simultaneously,controllable loads have also annually increased,which markedly improve the capability for nodal-power control.To maintain the system frequency and voltage magnitude around rated values,a new multi-objective optimization model for both voltage and frequency control is proposed.Moreover,a great similarity between the multiobjective optimization and game problems appears.To reduce the strong subjectivity of the traditional methods,the idea and method of the game theory are introduced into the solution.According to the present situational data and analysis of the voltage and frequency sensitivities to nodal-power variations,the design variables involved in the voltage and frequency control are classified into two strategy spaces for players using hierarchical clustering.Finally,the effectiveness and rationality of the proposed control are verified in MATLAB.

Decentralized Resilient H_∞Load Frequency Control for Cyber-Physical Power Systems Under DoS Attacks

This paper designs a decentralized resilient H_(∞)load frequency control(LFC)scheme for multi-area cyber-physical power systems(CPPSs).Under the network-based control framework,the sampled measurements are transmitted through the communication networks,which may be attacked by energylimited denial-of-service(DoS)attacks with a characterization of the maximum count of continuous data losses(resilience index).Each area is controlled in a decentralized mode,and the impacts on one area from other areas via their interconnections are regarded as the additional load disturbance of this area.Then,the closed-loop LFC system of each area under DoS attacks is modeled as an aperiodic sampled-data control system with external disturbances.Under this modeling,a decentralized resilient H_(∞)scheme is presented to design the state-feedback controllers with guaranteed H∞performance and resilience index based on a novel transmission interval-dependent loop functional method.When given the controllers,the proposed scheme can obtain a less conservative H_(∞)performance and resilience index that the LFC system can tolerate.The effectiveness of the proposed LFC scheme is evaluated on a one-area CPPS and two three-area CPPSs under DoS attacks.

A New Design of Robust H∞Load-Frequency Controller for Optimal Coordination of Energy Generation in Power System Stability Using LMI Approach

This paper presents the problem of robust H∞?load frequency controller design and robust H￥ based approach called advanced frequency control (AFC). The objective is to split the task of balancing frequency deviations introduced by renewable energy source (RES) and load variations according to the capabilities of storage and generators. The problem we address is to design an output feedback controller such that, all admissible parameter uncertainties, the closed-loop system satisfies not only the prespecified H∞? norm constraint on the transfer function from the disturbance input to the system output. The conventional generators mainly balance the low-frequency components and load variations while the energy storage devices compensate the high- frequency components. In order to enable the controller design for storage devices located at buses with no generators, a model for the frequency at such a bus is developed. Then, AEC controllers are synthesized through decentralized static output feedback to reduce the complexity. The conditions for the existence of desired controllers are derived in terms of a linear matrix inequality (LMI) algorithm is improved. From the simulation results, the system responses with the proposed controller are the best transient responses.

Design of Nichols PID Controller for Load Frequency Control

为解决互联水电系统负荷频率控制（load frequencycontrol,LFC）问题,及保持互联电网系统频率、联络线功率及区域控制误差（area control error,ACE）的稳定,根据闭环系统谐振峰值与系统响应最大峰值之间的关系,构建一个与系统参数及控制器参数都相关的优化问题,通过该问题的求解获得控制器参数与系统参数之间的数学关系,针对水轮发电系统非最小相位特性,通过串加比例–微分（proportional-derivative,PD）控制方式降低系统阶次,设计尼科尔斯（Nichols）曲线的比例–积分–微分（proportional-integral-derivative,PID）控制器。基于模型参数扰动和负荷干扰的仿真结果表明：尼科尔斯PID控制器能快速调整系统频率偏差、联络线功率偏差及ACE为0,具有良好的鲁棒性能和抗负荷干扰性能,系统过渡过程性能明显优于传统PID调节器结果。

Load Frequency Control of Multi-interconnected Renewable Energy Plants Using Multi-Verse Optimizer

A reliable approach based on a multi-verse optimization algorithm(MVO)for designing load frequency control incorporated in multi-interconnected power system comprising wind power and photovoltaic(PV)plants is presented in this paper.It has been applied for optimizing the control parameters of the load frequency controller(LFC)of the multi-source power system(MSPS).The MSPS includes thermal,gas,and hydro power plants for energy generation.Moreover,the MSPS is integrated with renewable energy sources(RES).The MVO algorithm is applied to acquire the ideal parameters of the controller for controlling a single area and a multi-area MSPS integrated with RES.HVDC link is utilized in shunt with AC multi-areas interconnection tie line.The proposed scheme has achieved robust performance against the disturbance in loading conditions,variation of system parameters,and size of step load perturbation(SLP).Meanwhile,the simulation outcomes showed a good dynamic performance of the proposed controller.

Load Frequency Control of Small Hydropower Plants Using One-Input Fuzzy PI Controller with Linear and Non-Linear Plant Model

This study presents an intelligent approach for load frequency control (LFC) of small hydropower plants (SHPs). The approach which is based on fuzzy logic (FL), takes into account the non-linearity of SHPs—something which is not possible using traditional controllers. Most intelligent methods use two- input fuzzy controllers, but because such controllers are expensive, there is economic interest in the relatively cheaper single-input controllers. A non- linear control model based on one-input fuzzy logic PI (FLPI) controller was developed and applied to control the non-linear SHP. Using MATLAB/Si- mulink SimScape, the SHP was simulated with linear and non-linear plant models. The performance of the FLPI controller was investigated and compared with that of the conventional PI/PID controller. Results show that the settling time for the FLPI controller is about 8 times shorter;while the overshoot is about 15 times smaller compared to the conventional PI/PID controller. Therefore, the FLPI controller performs better than the conventional PI/PID controller not only in meeting the LFC control objective but also in ensuring increased dynamic stability of SHPs.

Coefficient Diagram Method Based Load Frequency Control for a Modern Power System

increasing penetration of renewable energy sources with a wide range of operating conditions causing power system uncertainties, conventional controllers are incapable of providing proper performance to keep the system stable. However, controllable or dispatchable loads such as electric vehicles （EVs） and heat pumps （HPs） can be utilized for supplementary frequency control. This paper shows the ability of plug-in hybrid EVs, HPs, and batteries （BTs） to contribute in the frequency control of an isolated power system. Moreover, we propose a new online intelligent approach by using a coefficient diagram method （CDM） to enhance the system performance and robustness against uncertainties. The performance of the proposed intelligent CDM control has been compared with the proportional-integral （PI） controller and the superiority of the proposed scheme has been verified in Matiab/Simulink programs.

Kautz Function Based Continuous-Time Model Predictive Controller for Load Frequency Control in a Multi-Area Power System

A continuous-time Model Predictive Controller was proposed using Kautz function in order to improve the performance of Load Frequency Control(LFC).A dynamic model of an interconnected power system was used for Model Predictive Controller(MPC)design.MPC predicts the future trajectory of the dynamic model by calculating the optimal closed loop feedback gain matrix.In this paper,the optimal closed loop feedback gain matrix was calculated using Kautz function.Being an Orthonormal Basis Function(OBF),Kautz function has an advantage of solving complex pole-based nonlinear system.Genetic Algorithm(GA)was applied to optimally tune the Kautz function-based MPC.A constraint based on phase plane analysis was implemented with the cost function in order to improve the robustness of the Kautz function-based MPC.The proposed method was simulated with three area interconnected power system and the efficiency of the proposed method was measured and exhibited by comparing with conventional Proportional and Integral(PI)controller and Linear Quadratic Regulation(LQR).

An Investigation of Scaled-FLC Using PSO for Multi-area Power System Load Frequency Control

Load Frequency Control (LFC) is one of power systems important requirements which maintain the zero steady-state errors in the frequency changing and restoring the natural frequency to its normal position. Many problems are subject to LFC such as suddenly large load or suddenly disconnecting generating unit by the protection device. In this paper, multi-area Frequency Control by using the combination of PSO and fuzzy logic control (FLC) technique. PSO optimization method is used to tuning the fuzzy controller input and output gains. Four of an interconnected electrical power system used as a testing the effectiveness of the proposed method compared to a conventional PI controller and scaled-fuzzy controller. The simulation result has been shown that the controller can generate the best dynamic response in multi-load conditions.

Bilateral Contract for Load Frequency and Renewable Energy Sources Using Advanced Controller

Reestablishment in power system brings in significant transformation in the power sector by extinguishing the possession of sound consolidated assistance.However,the collaboration of various manufacturing agencies,autonomous power manufacturers,and buyers have created complex installation processes.The regular active load and inefficiency of best measures among varied associates is a huge hazard.Any sudden load deviation will give rise to immediate amendment in frequency and tie-line power errors.It is essential to deal with every zone’s frequency and tie-line power within permitted confines followed by fluctuations within the load.Therefore,it can be proficient by implementing Load Frequency Control under the Bilateral case,stabilizing the power and frequency distinction within the interrelated power grid.Balancing the net deviation in multiple areas is possible by minimizing the unbalance of Bilateral Contracts with the help of proportional integral and advanced controllers like Harris Hawks Optimizer.We proposed the advanced controller Harris Hawk optimizer-based model and validated it on a test bench.The experiment results show that the delay time is 0.0029 s and the settling time of 20.86 s only.This model can also be leveraged to examine the decision boundaries of the Bilateral case.

Kalman-Filtering-Based Frequency Control Strategy Considering Electrolytic Aluminum Load

Traditional thermal power units are continuously replaced by renewable energies,of which fluctuations and intermittence impose pressure on the frequency stability of the power system.Electrolytic aluminum load(EAL)accounts for large amount of the local electric loads in some areas.The participation of EAL in local frequency control has huge application prospects.However,the controller design of EAL is difficult due to the measurement noise of the system frequency and the nonlinear dynamics of the EAL’s electric power consumption.Focusing on this problem,this paper proposes a control strategy for EAL to participate in the frequency control.For the controller design of the EAL system,the system frequency response model is established and the EAL transfer function model is developed based on the equivalent circuit of EAL.For the problem of load-side frequency measurement error,the frequency estimation method based on Kalman-filtering is designed.To improve the performance of EAL in the frequency control,a fuzzy EAL controller is designed.The testing examples show that the designed Kalman-filter has good performance in de-noising the measured frequency,and the designed fuzzy controller has better performance in stabilizing system frequency than traditional methods.

A Novel Technique for Detection of Time Delay Switch Attack on Load Frequency Control

In this paper, we focus on the estimation of time delays caused by adversaries in the sensing loop (SL). Based on the literature review, time delay switch (TDS) attacks could make any control system, in particular a power control system, unstable. Therefore, future smart grids will have to use advanced methods to provide better situational awareness of power grid states keeping smart grids reliable and safe from TDS attacks. Here, we introduce a simple method for preventing time delay switch attack on networked control systems. The method relies on an estimator that will estimate and track time delays introduced by an adversary. Knowing the maximum tolerable time delay of the plant’s optimal controller for which the plant remains stable, a time-delay detector issues an alarm signal when the estimated time delay is larger than the minimum one and directs the system to alarm state. In an alarm state, the plant operates under the control of an emergency controller that is local to the plant and remains in this mode until the networked control system state is restored. This method is an inexpensive and simple way to guarantee that an industrial control system remains stable and secure.

Integral Performance Criteria Based Analysis of Load Frequency Control in Bilateral Based Market

Performance index based analysis is made to examine and highlight the effective application of Particle Swarm Optimization (PSO) to optimize the Proportional Integral gains for Load Frequency Control (LFC) in a restructured power system that operates under Bilateral based policy scheme. Various Integral Performance Criteria measures are taken as fitness function in PSO and are compared using overshoot, settling time and frequency and tie-line power deviation following a step load perturbation (SLP). The motivation for using different fitness technique in PSO is to show the behavior of the controller for a wide range of system parameters and load changes. Error based analysis with parametric uncertainties and load changes are tested on a two-area restructured power system. The results of the proposed PSO based controller show the better performance compared to the classical Ziegler-Nichols (Z-N) tuned PI and Fuzzy Rule based PI controller.

A Novel Flower Pollination Algorithm to Solve Load Frequency Control for a Hydro-Thermal Deregulated Power System

Load frequency control plays a vital role in power system operation and control. LFC regulates the frequency of larger interconnected power systems and keeps the net interchange of power between the pool members at predetermined values for the corresponding changes in load demand. In this paper, the two-area, hydrothermal deregulated power system is considered with Redox Flow Batteries (RFB) in both the areas. RFB is an energy storage device, which converts electrical energy into chemical energy, that is used to meet the sudden requirement of real power load and hence very effective in reducing the peak shoots. With conventional proportional-integral (PI) controller, it is difficult to get the optimum solution. Hence, intelligent techniques are used to tune the PI controller of the LFC to improve the dynamic response. In the family of intelligent techniques, a recent nature inspired algorithm called the Flower Pollination Algorithm (FPA) gives the global minima solution. The optimal value of the controller is determined by minimizing the ISE. The results show that the proposed FPA tuned PI controller improves the dynamic response of the deregulated system faster than the PI controller for different cases. The simulation is implemented in MATLAB environment.

Ant Lion Optimization Approach for Load Frequency Control of Multi-Area Interconnected Power Systems

This work proposes a novel nature-inspired algorithm called Ant Lion Optimizer (ALO). The ALO algorithm mimics the search mechanism of antlions in nature. A time domain based objective function is established to tune the parameters of the PI controller based LFC, which is solved by the proposed ALO algorithm to reach the most convenient solutions. A three-area interconnected power system is investigated as a test system under various loading conditions to confirm the effectiveness of the suggested algorithm. Simulation results are given to show the enhanced performance of the developed ALO algorithm based controllers in comparison with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bat Algorithm (BAT) and conventional PI controller. These results represent that the proposed BAT algorithm tuned PI controller offers better performance over other soft computing algorithms in conditions of settling times and several performance indices.