Hybrid cross entropy—cuckoo search algorithm for solving optimal power flow with renewable generators and controllable loads

The demand of energy is increasing due to the growing population of the world and improvements of technology. One of the best significant solution techniques to fulfill this energy demand is utilization of renewable energy sources (RESs). Modern power systems, which integrate RESs, such as wind, small hydro or solar energy sources need to carry out the uncertainty by the accessibility of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow (OPF) problems. This paper proposed a novel hybrid meta-heuristic algorithm entitled cross entropy—cuckoo search algorithm (CE-CSA). The application of levy flights in the cuckoo search algorithm (CSA) improves the local exploitation capability while the CE method is used in the initial stage for global exploration due to its fast convergence. The effectiveness of the proposed hybrid algorithm has been demonstrated in solving the OPF problem, considering RESs and controllable loads for different stochastic scenarios in a benchmark system to minimize the total operation cost. To verify its effectiveness, its performance is compared with the most advanced and recently proposed hybrid meta-heuristic techniques. Simulation results show that the proposed algorithm can solve the OPF problems with RESs and controllable loads efficiently and can give better solutions compared to different techniques. The conventional statistical method called analysis of variance (ANOVA) test, T ukey honestly significant difference test, and Wilcoxon sign rank test are performed for comparative analysis of different techniques. The results of this test show the validation of CE-CSA compared to different optimization techniques.     

A hybrid modified grey wolf optimization-sine cosine algorithm-based power system stabilizer parameter tuning in a multimachine power system

Damping of low-frequency oscillations due to the unpredictable perturbations of a power network has always been a challenging task. In an interconnected power network, power system stabilizers (PSSs) are in practice to damp out these low-frequency oscillations by providing a necessary control signal to the automatic voltage regulator unit based on the deviation in generator speed/power output. This article proposes a novel approach of hybrid modified grey wolf optimization-sine cosine algorithm for tuning the parameters of PSS of an interconnected multimachine power system. The optimal parameter tuning of PSS with the proposed algorithm is achieved by considering a multiobjective function comprises of improving the damping and eigenvalue characteristics of the consolidated multimachine system. A benchmark model of two area four machine system is adopted to investigate the performance achieved with the proposed algorithm in the simultaneous damping of the local and interarea mode of oscillations in a multimachine power system. The system study has been carried out under a self-clearing fault condition, and the detailed analysis is presented by analyzing the eigenvalues, and their corresponding natural frequencies, damping ratios. The damping nature achieved for the system states under system uncertainties with the proposed algorithm is also presented. The performance obtained from the proposed hybrid algorithm has been compared with the standalone and state-of-the-art optimization methods.     

Analysis of moth flame optimization optimized cascade proportional-integral-proportional-derivative controller with filter for automatic generation control system incorporating solar thermal power plant

In the fast developing electric power system network, ancillary services like automatic generation control (AGC) plays a vital and significant role to ensure good quality of power supply in the system. To distribute good quality of power, a hybrid AGC system along with an efficient and intelligent controller is compelled. So, in this article, a cascaded proportional-integral (PI)-proportional-derivative (PD) controller with filter (PI-PDF) is proposed as secondary controller for AGC system. A nature inspired optimization algorithm named as moth flame optimization (MFO) algorithm is employed for simultaneous optimization of controller gains. Initially, a two-area interconnected nonreheat thermal power system is investigated. Analysis revealed that MFO-tuned PI controller performs better than the different optimization techniques tuned PI controller for the same system and PI-PDF controller performs better than PI controller does. Then, the study is extended to a three-area interconnected hybrid system with proper generation rate constraint. Area-1 consists of solar thermal-thermal unit; area-2 consists of thermal-hydro unit and area-3 thermal-gas unit as generating sources. Performance of PI-PDF controller is compared with classical controllers such as PI, PID, PIDF, and PI-PD controller without filter. Result analysis divulges that MFO-tuned PI-PDF controller performs better than all other controllers considered in this article. Robustness of the PI-PDF controller is evaluated using parameter variations and random load variation.     

Modified whale optimization algorithm for fractional‐order multi‐input SSSC‐based controller design

In this paper, the design of a fractional‐order (FO) multi‐input–single‐output (MISO)–type static synchronous series compensator (SSSC) is proposed with a goal to improve the power system stability using modified whale optimization algorithm (MWOA). The proposed MWOA achieves an appropriate balance between exploitation and exploration stages of the original whale optimization algorithm. The performance of MWOA is validated by employing the benchmark test functions and further contrasted with whale optimization algorithm and other heuristic algorithms like gravitational search algorithm, particle swarm optimization, differential evolution, and fast evolutionary programming algorithms to demonstrate its strength. The proposed FO MISO SSSC controller is optimized by the MWOA technique and tested under single‐machine infinite bus system and further extended to a multi‐machine framework. To demonstrate the superiority of MISO‐type SSSC controller, the results obtained from it are compared with particle swarm optimization and differential evolution–based conventional single‐input–single‐output structured SSSC controllers. The comparison of results of MWOA with that of other methods validates its superiority in the present context.     

PI control based on parameter space approach supported metaheuristic optimization algorithms and ANFIS in a natural gas combined cycle power plant

In this article, proportional-integral (PI) control to ensure stable operation of a steam turbine in a natural gas combined cycle power plant is investigated, since active power control is very important due to the constantly changing power flow differences between supply and demand in power systems. For this purpose, an approach combining stability and optimization in PI control of a steam turbine in a natural gas combined cycle power plant is proposed. First, the regions of the PI controller, which will stabilize this power plant system in closed loop, are obtained by parameter space approach method. In the next step of this article, it is aimed to find the best parameter values of the PI controller, which stabilizes the system in the parameter space, with artificial intelligence-based control and metaheuristic optimization. Through parameter space approach, the proposed optimization algorithms limit the search space to a stable region. The controller parameters are examined with Particle Swarm Optimization based PI, artificial bee colony based PI, genetic algorithm based PI, gray wolf optimization based PI, equilibrium optimization based PI, atom search optimization based PI, coronavirus herd immunity optimization based PI, and adaptive neuro-fuzzy inference system based PI (ANFIS-PI) algorithms. The optimized PI controller parameters are applied to the system model, and the transient responses performances of the system output signals are compared. Comparison results of all these methods based on parameter space approach that guarantee stability for this power plant system are presented. According to the results, ANFIS- PI controller is better than other methods.     

Towards global solutions of optimal discrete‐valued control problems

This paper proposes a new heuristic approach for solving optimal discrete‐valued control problems. We illustrate the approach with an existing hybrid power system model. The problem of choosing an operating schedule to minimize generator, battery, and switching costs is first posed as a mixed discrete dynamic optimization problem. Then, a discrete filled function method is employed in conjunction with a computational optimal control technique to solve this problem. Computational results indicate that this approach is robust, efficient, and can successfully identify a near‐global solution for this complex applied optimization problem despite the presence of multiple local optima. Copyright © 2011 John Wiley & Sons, Ltd.     

Long-term optimization of hydro-thermal power systems by generalized Conjugate-Gradient Methods

The optimal management of hydro storage reservoirs is considered. The objective is to minimize thermal power station fuel costs, over a horizon of one or more years, in a mixed hydro-thermal power system. A model of the New Zealand system is developed that is simple enough for computational purposes but nevertheless accounts for all major factors including load diversity and transmission losses. A version of Powell's generalized conjugate-gradient algorithm with Beale restarts is used for the optimization. State and control constraints are enforced by penalty functions and transformations, respectively. Results are presented for a reduced-order model of the New Zealand system.     

Study of wind-solar based combined heat and power economic dispatch problem using quasi-oppositional-based whale optimization technique

Source of fossil fuel is impoverishing in the upcoming future. Renewable energy sources (RESs) are becoming challenging conventional energy substitutes in the present scenario. In this article, an attempt has been made to utilize RESs such as wind and solar energy with combined heat and power economic dispatch problems. The intention of this presentation is to minimize conflict objectives such as fuel cost accomplished with load demand along with transmission losses while satisfying all the constraints. A new optimization technique, namely a quasi-oppositionalbased whale optimization algorithm (QOWOA) is adopted to cope up with the non-linearities of the chosen systems. The proposed technique is tested on two different nonlinear realistic power systems to achieve the satisfactory performances. The superiority of the proposed QOWOA algorithm is judged by comparing it with some recently developed metaheuristic optimization techniques.     

A Comparison of optimal control algorithms for complex bioengineering studies

Two optimal control problems typically encountered in bioengineering studies are solved using five dynamic optimization algorithms carefully selected from among the most widely recognized gradient-based algorithms. All the problems are solved using a medium-sized mainframe computer. The convergence characteristics of each algorithm are tested by using them to solve each of the two problems. It is recognized that a number of difficulties arise with these larger problems. Some of these problems include prohibitive storage requirements and large computational times. The consequences of the choice of any specific algorithm for solving typical dynamic optimization problems in biomedicine are pointed out.     

A computational intelligence based maximum power point tracking for photovoltaic power generation system with small-signal analysis

There are multiple peak functions in its output power characteristic curve of a photovoltaic (PV) array under partial shading conditions (PSCs), the perturb and observe (P&O) may fail to track the global maximum power point (GMPP). Therefore, a reliable maximum power point tracking (MPPT) technique is essential to track the GMPP within an appropriate time. This article proposes a hybrid technique by combining an evolutionary optimization technique, namely the modified invasive weed optimization (MIWO) with the conventional P&O algorithm to enhance the search performance for the maximum power output of the PV system. MIWO executes in the initial stages of the tracking followed by the P&O at the final stages in the MPPT search process. The combined approach ensures faster convergence and better search to the GMPP under rapid climate change and PSCs. The search performance of the hybrid MIWO+P&O technique is examined on a standalone PV system through both MATLAB/Simulink environment and experimentally using dSPACE (DS1103)-based real-time microcontroller hardware setup. The performance of the proposed hybrid MPPT scheme is compared with the recent state-of-the-art MPPPT techniques. In addition, the small-signal analysis of the PV system is carried out to evaluate the loop robustness of the controller design. For a given set of system parameters, simulations for the small-signal model and robustness studies are analyzed to verify the results. The overall results justify the efficacy of the proposed hybrid MPPT algorithm.     

Meta-heuristics algorithms for optimization of gains for dynamic voltage restorers to improve power quality and dynamics

This article discusses metaheuristic algorithms for optimizing controller gains for dynamic voltage restorers (DVRs) that use an impedance control strategy to compensate for unbalance in source voltages, voltage harmonics, and sag/swell in source voltages. The gains of the proportional-integral (PI) controllers become critical for proper DVR load voltage extraction. Various techniques for optimization, such as whale optimization technique, gray wolf optimization technique, particle swarm optimization technique, and ant lion optimization technique, are used to obtain DC and AC PI controller gains for DVR. The impedance control strategy employs simple calculations to determine the resistance and reactance of a polluted source voltage, without the use of frame conversions as in synchronous reference theory, instantaneous reference power theory, and so on. The quick calculations of the impedance control scheme improve the power quality and dynamics. The Metaheuristic algorithms are used to calculate the number of iterations required to achieve the best possible controller gains, which further helps to improve power quality and dynamics. Among these optimization techniques, the antlion optimization technique provides fast convergence and the best possible controller gain values to improve the dynamics of the dc-link voltage of voltage source converter and terminal voltage, thereby improving power quality. The proposed antlion optimization technique-based DVR model is simulated in MATLAB R2019, and the results are validated with RT-LAB.     

Comparative performance analysis of 2DOF state feedback controller for automatic generation control using whale optimization algorithm

This paper presents the design of two‐degree‐of‐freedom state feedback controller (2DOFSFC) for automatic generation control problem. A recently developed new metaheuristic algorithm called whale optimization algorithm is employed to optimize the parameters of 2DOFSFC. The proposed 2DOFSFC is analyzed for a two‐area interconnected thermal power system including governor dead band nonlinearity and further extended to multiunit hydrothermal power system. The supremacy of the 2DOFSFC is established comparing with proportional‐integral, proportional‐integral‐derivative (PID), and 2DOFPID controllers optimized with different competitive algorithms for the concerned system. The sensitivity analysis of the optimal 2DOFSFC is performed with uncertainty condition made by varying bias coefficient B and regulation R parameters. Furthermore, the proposed controller is also verified against random load variations and step load perturbation at different locations of the system.     

Renewable energy management of an hybrid water pumping system (photovoltaic/wind/battery) based on Takagi–Sugeno fuzzy model

This research work presents an optimal energy management for a hybrid water pumping system driven by a photovoltaic generator (PVG) and a wind turbine. These two renewable energies are used as power generation sources, whereas a battery is added as an energy-storing system, for the purpose of controlling the power flow and providing a constant load supply. The proposed management system, serve to guarantee the pumping system autonomy in a rural region where's no access to the electrical network. As a result, a maximum power point tracking (MPPT) controller is created based on the fuzzy Takagi–Sugeno (TS) model, ensuring maximum power transfer to the moto-pump in spite of wind speed and insolation changes. The synthesis of MPPT control law involves TS fuzzy reference models which generate the desired trajectories to track. A supervisor has been developed for energy management and its major purpose is to effectively use the battery to satisfy the power load requirements, and that is by maintaining the state of charge (SOC) to extend the battery's life. Finally, simulation results have been done based on Matlab/Simulink with the aim of validating the efficiency of the proposed energy management supervisor.     

Optimal decentralized control of a wind turbine and diesel generator system

This article presents a decentralized optimal controller design technique for the frequency and power control of a coupled wind turbine and diesel generator. The decentralized controller consists of two proportional-integral (PI)-lead controllers which are designed and optimized simultaneously using a quasi-Newton based optimization technique, namely, Davidon–Fletcher–Powell algorithm. The optimal PI-lead controllers are designed in such a way that there are no communication links between them. Simulation results show the superior performance of the proposed controller with a lower order structure compared to the benchmark decentralized linear-quadratic Gaussian integral controllers of orders 4 and 11. It is also shown that the proposed controller demonstrates an effective performance in damping the disturbances from load and wind power, as well as a robust performance against the parameter changes of the power system.     

Optimal control of electrical vehicle incorporated hybrid power system with second order fractional-active disturbance rejection controller

This article proposes a novel control methodology employing a fractional-active-disturbance-rejection-controller for the combined operation of load frequency control and automatic voltage regulator of a hybrid power system. A two area hybrid power system with diverse energy sources like solar-thermal, conventional-thermal and wind sources equipped with appropriate system nonlinearities is investigated. In order to ascertain the role of modern-day electric-vehicle (EV), the hybrid power system is incorporated with EVs in both the areas. To establish an effective frequency, voltage and tie line power control of the hybrid power system, a second order fractional-active-disturbance-rejection-controller with fractional-extended state observer is modeled as secondary controller. Magnetotactic-bacteria-optimization (MBO) technique is applied to obtain optimal values of the controller gains and the hybrid system parameters. The robustness of the controller gains is tested under different system parameter changes from their nominal values. In addition, the effect of incorporating a power system stabilizer on the hybrid power system is evaluated. Further, the impact of integrating renewable sources and EVs in the hybrid power system is explored. Moreover, the stability of the hybrid power system is monitored with the inclusion of FACTS device. The developed controller operates encouragingly with reference to system stability, rapidity and accuracy in comparison to testified control strategies available in the literature. The robustness test under load-perturbation, solar-insolation, wind input variations also proves the efficiency of MBO optimized second order fractional-active-disturbance-rejection-controller gains.     

An elite hybrid strategy for solar photovoltaic system based optimized cascade controller under uniform and partial shading conditions

A hybrid technique for maximum power point tracking (MPPT) for a photovoltaic (PV) system is proposed in this paper. The proposed hybrid system is combination of Wing suit Flying Search (WFS) and modified Transient search optimization (MTSO), therefore it is called WFS-MTSO method. The proposed controller has three processes: (i) to identify the operating level of photovoltaic (uniform or in PSC), (ii) to estimate the maximal power point using WFS technique, and (iii) to ensure the photovoltaic system runs on the estimated maximum power point (MPP) by MTSO optimized cascade controller. This method begins with a sense of irradiance and temperature. The proposed photovoltaic system has two components. The first one is WFS maximal power point tracking algorithm attain maximal power point. The second one is MTSO optimized cascade controller to force the photovoltaic system to activate at maximal power point. Here, the proposed hybrid technique is utilized at MPPT to diminish tracking error and oscillation across MPP for optimizing power output. The proposed optimized cascade control improves the system efficiency by averting interruptions previously they propagate to the system. Finally, the performance of proposed hybrid system is executed on MATLAB/Simulink working platform and the performances are compared with various existing approaches. The statistical matrices, like mean, median, and standard deviation is analyzed the tracking efficiency of the proposed WFS-MTSO approach.     

An adaptive chaos particle swarm optimization for tuning parameters of PID controller

An adaptive chaos particle swarm optimization (ACPSO) is presented in this paper to tune the parameters of proportional‐integral‐derivative (PID) controller. To avoid the local minima, we introduced a constriction factor. Meanwhile, the chaotic searching is combined with the particle swarm optimization to improve the ability of the proposed algorithm. A series of experiment is performed on 6 benchmark functions to confirm its performance. It is found that the ACPSO can get better solution quality in solving the global optimization problems and avoiding the premature convergence. Based on it, the proposed algorithm is applied to tune the PID controller's parameters. The performances of the ACPSO are compared with different inspired algorithms, and these results show that the ACPSO is more robust and efficient when it is used to find the optimal parameters of PID controller.     

A second‐order optimization algorithm using quadric control updates for multistage optimal control problems

This paper describes a trajectory optimization algorithm that generates a quadric control update, which satisfies the constraints and necessary conditions to the second order. The algorithm is designed to solve multistage optimization problems. The algorithm is tested against a commercially available Sequential Quadratic Programming algorithm on problems with linear dynamics and linear and nonlinear constraints. This algorithm is a departure from previous methods because it explicitly satisfies the constraints to the second order. Copyright © 2009 John Wiley & Sons, Ltd.     

Load frequency predictive control for power systems concerning wind turbine and communication delay

This article addresses a model predictive control (MPC) technique for load frequency control (LFC) system in the presence of wind power, communication delay, and denial-of-service (DoS) attack. In this article, communication delay is incorporated into a single area control error transmission for simplicity, wind power and load disturbance are regarded as Lipschitz nonlinear terms, as for the randomly occurring DoS attack, it is modeled as Bernoulli processes with known conditional probability. Thinking all these adverse factors to stability and the limitation of input constraint synthetically, the stability of LFC system can be guaranteed by delay-dependent Lyapunov function lemma and a state feedback MPC controller is designed to solve the LFC problems by minimizing the infinite-horizon objective function. Although some scholars have studied the performance degradation and instability of LFC system caused by cyber attack and/or communication delay and some very nice results have been addressed, limited works have considered the MPC approach to deal with both the problems of cyber attack and communication delay which explicitly considers the physical constraints. In addition, the delay-dependent Lyapunov function is adopted to deal with the problem of communication delay, which results in less conservatism of the presented method. Finally, the optimization problem with input constraint is solved and proven to be recursive feasibility, and the closed-loop system turns out to be stable. The reasonability and validity of the provided strategy is verified through several groups of simulation experiments. It illustrates that the proposed control method can keep the system frequency steady in the standard range in spite of various attack conditions.     

Solar-wind-hydro-thermal scheduling using moth flame optimization

Ever increasing concern of environmental safeguard makes renewable energy sources (RES) useful for emission reduction as well as for production cost minimization. In this article, the multiobjective economic emission dispatch (EED) model with security constraints incorporating photovoltaic, nonconvex thermal, and wind units is introduced for hydro-thermal-solar-wind power scheduling arrangement. However, the significant reduction of emission is the foremost perspective for environmental sustainability and penetration of RESs into the electrical grid is being encouraged tremendously. To diminish the power generation expenditure and pollution generated by fossil fuels, renewable solar PV and wind power-oriented hydro-thermal scheduling have significant worth. Existing algorithms do not perform satisfactorily for unpredicted solar and wind-based nonlinear hydro-thermal-wind-solar scheduling problems and it may give local optimal solutions instead of global optimal solution. To overcome the shortcomings of the existing algorithms, an effective, and an intelligent robust algorithm, named moth flame optimization (MFO) has been proposed for solving the said nonlinear optimization problem. This article describes a scientific review on the application of the proposed method to obtain the scheduling of optimal generation for hydrothermal systems by incorporating RESs like solar PV and wind plant. Optimal solutions gained by the employment of different optimization methods for a variety of test instances are demonstrated and the projected methods are compared in terms of attained optimal solutions and convergence speed. The proposed MFO algorithm is competent for potential/hopeful outcomes, and it reduces the electrical power generation cost and emission significantly. The simulation outcomes reveal the usefulness and feasibility of the proposed method.