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.     

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.     

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.     

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.     

Improving the grid frequency by optimal design of model predictive control with energy storage devices

This paper proposes the optimal design of model predictive control (MPC) with energy storage devices by the bat‐inspired algorithm (BIA) as a new artificial intelligence technique. Bat‐inspired algorithm‐based coordinated design of MPCs with superconducting magnetic energy storage (SMES) and capacitive energy storage (CES) is proposed for load frequency control. Three‐area hydrothermal interconnected power system installed with MPC and SMES is considered to carry out this study. The proposed design procedure can account for generation rate constraints and governor dead bands. Transport time delays imposed by governors, thermodynamic processes, and communication telemetry can be captured as well. In recent papers, the parameters of MPC with SMES and CES units are typically set by trial and error or by the designer's expertise. This problem is solved here by applying BIA to tune the parameters of MPC with SMES and CES units simultaneously to minimize the deviations of frequency and tie line powers against load perturbations. Simulation results are carried out to emphasize the superiority of the proposed coordinated design as compared with conventional proportional‐integral controller and with BIA‐based MPC without SMES and CES units.     

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.     

Application of chaos assisted sine cosine algorithm on wind–solar integrated hydrothermal scheduling problem

In recent times, renewable energy sources are essential for generating low-cost, pollution-free power. Since the last two decades, hydrothermal coordination system has been used to fulfill the demand power. The traditional generating model's two biggest flaws are high generation cost and excessive fossil fuel emission. In the proposed work, generation process of traditional hydrothermal scheduling (HTS) has been improved by integrating wind–solar energy. To overcome current issues of HTS, that is, excessive emission and generation cost, hydrothermal–solar–wind scheduling (HTSWS) problem has been introduced where two wind and two solar power generating units have been considered with four hydro and three thermal power generating units. Here, effective performance of low cost-emission based proposed HTSWS has been examined by using chaos-based sine cosine algorithm (SCA) (CSCA). Chaos has been used in sine cosine function of SCA to improve searching process for finding global optimal results. The proposed CSCA has been used to investigate three separate situations of standard HTS and recommended HTSWS problems including generation cost, emission, and combined cost-emission. The cost of generation and emissions from conventional HTS can be reduced by 11% and 68%, respectively, by the suggested renewable energy source-based generation model. The results of several case studies of proposed HTSWS and standard HTS reveal that wind–solar energy is effective in the HTS issue, and chaos assists in the SCA to improve its optimization process. In this study, effectiveness and robustness of the CSCA have been demonstrated by comparing the CSCA-based results to existing methods for the challenges under consideration.     

Development of MADB of P-I controller using LMI technique in a renewable energy based AGC system and study its application in a deregulated environment including energy storage device

In recent decades, inclusion of renewable resources is considered as one of the most promising options for the long run uninterrupted power supply without depending on conventional resources. Thus, the renewable energy generation will get more attention and massive growing, so that the goal of 40% share of electricity in the worldwide energy portfolio in 2050 would be realized. But during replacement of renewable energy by conventional energy, engineers are facing a lot of problem due to solar generation, wind generation change their characteristic rapidly with weather condition, which may cause large synchronizing imbalance between different units and generate large system delay or communication delay in large interconnected grid. In this article, the authors propose linear matrix inequalities techniques to developed margin of allowable delay for delay dependent stable hybrid system. Initially, to judge the efficacy of proposed chaotic atomic search optimization (CASO) algorithm over other evolutionary algorithms with PID controller, a thermal-hydro gas system is considered. The second part of this article is motivated by the fact that proposed CASO algorithm with P-I controller is superior in contrast to bacterial foraging algorithm technique. In addition to this, some energy storage devices such as fuel cell, aqua electrolyzer, and ultra-capacitor are used to achieve a better dynamic response within specified delay margin. Moreover, to study the impact of communication delays (delay margin) due to the loss of synchronism between solar-wind (for their unpredicted environmental features) and thermal unit (nonlinearities like generation rate constraints, boiler dynamics, and governor with the dead band) are considered in thermal unit and the simulation results verify with the effectiveness of the proposed approach on providing a balance between the delay margin and the damping performances is evaluated under deregulated environment. The simulation results help to make an inter-relation between the delay margin and the controller gain (P-I) which help the system operator in designing controllers gain for stable operation of the proposed hybrid system.     

Hybrid BOA-GWO-PSO algorithm for mitigation of congestion by optimal reactive power management

The generation of power with load optimization, particularly in the current deregulated electricity market conditions, is a very important process for improved planning and operation of the grid. In addition, it is very important for the system not to experience problems due to congestion, have tensile stability, and protection to increase the share of electricity from renewable sources with the current supply system. This article presents load balancing with the butterfly optimization algorithm (BOA) in a hybridized form to minimize and maximize loads when used in pool and hybrid markets. The methods have been designed to prevent the drawbacks of BOA and generate a better trade-off between exploration and exploitation abilities by hybridizing it with particle swarm optimization (PSO) and gray wolf optimizer (GWO). Empirical research on other algorithms shows that proposed hybrid BOA-GWO-PSO algorithm performs better and shows potential in diverse problems. These studies give it a significant advantage over BOA in general, and when it is employed to solve complex optimization problems validated on benchmark IEEE 30 bus system. A comparative analysis has been conducted to validate the potency of the hybrid BOA-GWO-PSO approach with some conventional meta-heuristic algorithms. Analysis of results by mathematical validation on 23 benchmark functions and application in congestion management by optimal reactive power management (RPM) reveal that the proposed technique has the potent to solve real world optimization problems and is competitive with recent methods reported in state-of- art literature.     

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.     

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.     

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.     

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.     

High‐order observers‐based LQ control scheme for wind speed and uncertainties estimation in WECSs

Tip speed ratio control is a popular method in wind energy conversion systems in order to capture the maximum power. This method, however, requires wind speed information, which is difficult in practice to accurately measure it. Therefore, estimation methods are usually applied, where a high‐precision estimate leads to a high‐efficient system. Based on the fact that the wind speed varies in a random way, this paper proposes a generalized high‐order observer to estimate the aerodynamic torque and the wind speed accordingly. This observer algorithm releases the assumption that the wind speed should be slowly varying, which is required in previous observer designs. Moreover, two other generalized high‐order observers are also applied to estimate the uncertainties, which depend on state variables and cannot be considered as slow‐varying disturbances. Using the outputs of these observers, a robust high‐performance optimal control system is developed for the rotor speed to keep the optimal tip speed ratio. The stability analysis of the designed control system is fully presented. The effectiveness of the proposed technique is validated via simulation studies.     

Randomized optimal consensus of multiagent systems based on a novel intermittent projected subgradient algorithm

In this article, a novel intermittent projected subgradient algorithm is presented to solve the randomized optimal consensus problem for heterogeneous multiagent systems with time-varying communication topologies. The multiagent systems achieve the consensus meanwhile minimizing the global objective function via the proposed algorithm, where f_i(x) is the convex objective function of agent i itself. Due to the common Bernoulli distribution adopted in the existing random optimization algorithm without considering the different computing capability of each agent. An individual projection probability is assigned for each agent based on computing capabilities so that either making projection or taking average is chosen according to the above probability which can effectively avoid overload for some agents with lower computing capabilities and improve the reliability of the overall systems. A new sufficient step-size condition is given to ensure all agents converge to the optimal solution with probability one. Finally, a numerical example is also given to validate the proposed method.     

Accelerated Molecular Statics Based on Atomic Inertia Effect

Molecular statics (MS) based on energy minimization serves as a useful simulation technique to study mechanical behaviors and structures at atomic level. The efficiency of MS, however, still remains a challenge due to the complexity of mathematical optimization in large dimensions. In this paper, the Inertia Accelerated Molecular Statics (IAMS) method is proposed to improve computational efficiency in MS simulations. The core idea of IAMS is to let atoms move to meta positions very close to their final equilibrium positions before minimization starts at a specific loading step. It is done by self-learning from historical movements (atomic inertia effect) without knowledge of external loadings. Examples with various configurations and loading conditions indicate that IAMS can effectively improve efficiency without loss of fidelity. In the simulation of three-point bending of nanopillar, IAMS shows efficiency improvement of up to 23 times in comparison with original MS. Particularly, the size-independent efficiency improvement makes IAMS more attractive for large-scale simulations. As a simple yet efficient method, IAMS also sheds light on improving the efficiency of other energy minimization-based methods.     

Control vector parameterization approach in optimization of alternating aerobic–anoxic systems

Determination of the optimal aeration profile for an activated sludge system in which nitrification and denitrification take place sequentially in a single reactor (alternating aerobic–anoxic) is an attractive optimization problem because of complexities involved in, and high computational times required for solution. The rigorous dynamic modeling and start‐up simulation of such a system, together with aeration profile optimization by an evolutionary algorithm (EA), were tackled in a previous study. In this paper an easy‐to‐implement dynamic optimization technique based on sequential quadratic programming method and control vector parameterization approach is provided. In comparison with EA, the proposed algorithm gives better results in shorter computation times. Copyright © 2009 John Wiley & Sons, Ltd.     

Solving chiller loading optimization problems using an improved teaching‐learning‐based optimization algorithm

In this study, we present a novel teaching‐learning‐based optimization (TLBO) algorithm for solving the optimal chiller loading problem. The proposed algorithm uses a novel integer‐based encoding and decoding mechanism that is efficient and easy to implement. The teaching phase can improve the quality of learning process and thus enhance the exploitation ability. In addition, a well‐designed learning phase procedure is developed to enhance the learning process between one another in the population. A novel exploration and self‐learning procedures are embedded in the proposed TLBO algorithm, which can enhance the exploitation and exploration capabilities. The proposed algorithm is tested on several well‐known case studies and compared with several efficient algorithms. From the experimental comparisons, the efficient performance of the proposed TLBO is verified.     

Design and performance analysis of elephant herding optimization based controller for load frequency control in thermal interconnected power system

In this present contribution, an attempt has been taken to design and analyze the performance of elephant herding optimization (EHO) based controller for load frequency control (LFC) applications of interconnected power system. The studied system is a two‐area nonreheat thermal interconnected system which is widely used in literature. A proportional‐integral‐differential controller is utilized for LFC of the studied system. EHO technique is applied to obtain the tuned set of controller parameters. The objectives considered for design of the controller are the minimization of settling times and integral‐time‐multiplied‐absolute‐error of frequency deviations (FDs) and tie‐line power deviation (TPD). The design objectives are integrated together to form a function with single objective by assigning equal weights after normalization. Several test cases of diverse set of disturbances are taken into account to test the performance of the proposed controller and the obtained results are compared with other controllers designed with differential evolution, gray wolf optimization, particle swarm optimization, teacher‐learner‐based optimization, and whale optimization algorithm. Furthermore, the time‐domain simulations of FDs and TPD are illustrated to support the tabulated results. In addition, comparative statistical analysis is presented to validate the robust behavior of the proposed controller.     

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.