Nonlinear Power Research Articles

Coordinate Transformation-Based Nonlinear Power Decoupling Control for Differential Buck Grid-Tied Inverter

Nonlinear time-varying systems complicate the analysis and controller design compared to nonlinear time-invariant systems. Single-phase differential grid-tied inverter is a classic nonlinear time-varying system. In this article, an input-output linearization (IOL) based coordinate transformation and a nonlinear power decoupling control scheme are proposed for the single-phase differential grid-tied inverter. Because of the transformation, the nonlinear periodic time-varying system is transformed into a nonlinear time-invariant one. Based on the nonlinear time-invariant model, a nonlinear power decoupling control scheme based on the idea similar to back-stepping control is designed, which realizes good grid current control and power decoupling. Furthermore, the small-signal stability of the inverter is proved by eigenvalue analysis method in the linear time-invariant (LTI) framework. Experiment results validate the effectiveness of the proposed control strategy and stability analysis.

A novel ANFIS-controlled customized UPQC device for power quality enhancement

Power quality is crucial for the reliable and efficient operation of domestic and industrial loads. Nonlinear power electronic converter loads have increased in usage, which has led to a decline in both voltage and current quality. To overcome these power quality issues, a universal power quality compensator (UPQC) has been developed and integrated into the power distribution network. The UPQC comprises dual active power filters which are equipped with a DC-link capacitor. The voltage of the DC-link capacitor is controlled by a DC-link voltage controller. However, the conventional PI controller is not suitable for regulating voltage at a defined level due to inappropriate gain values. In this work, we propose an intelligent adaptive neuro-fuzzy inference system-based DC voltage controller for customized UPQC devices. The proposed control scheme aims to mitigate the existing power quality challenges by reducing the issues in classical controllers and incorporating intelligence knowledge with subjective decisions. Using the MATLAB/Simulink software tool, we have tested a customized UPQC device controlled by ANFIS for critical operation and performance. The simulation results are presented along with valid comparisons.

An advanced multi-objective collaborative scheduling strategy for large scale EV charging and discharging connected to the predictable wind power grid

With the large-scale EV connected into the wind power grid, the intermittent, fluctuating and stability bring rigorous challenges for power quality and dispatch, thus wind curtailment becomes more serious. This paper proposes an advanced multi-objective collaborative scheduling strategy to improve the accuracy of the predictable wind grid and ensure the stable operation of the grid by optimizing wind power and EV synergistically. Firstly, a hybrid power prediction method is proposed based on density-based spatial clustering applied to noise (DBSCAN) and partial least squares regression (PLSR) combined with long and short-term memory neural network (LSTM). It establishes a linear component prediction mode to predict the nonlinear wind power efficiently. Secondly, a multi-objective optimization scheduling model is established according to the predicted wind power, considering the vehicle-to-grid (V2G) characteristics of EV, grid load fluctuations, wind curtailment capacity, EV charging costs, and grid losses. The global control aims to achieve overall energy balance and optimize the charging and discharging of EV in a time dimension under constrained conditions. Additionally, based on the total number of EV charging and discharging determined by the global level control, a spatial scheduling optimization is conducted for EV and wind power by the distribution network control, with the goal of minimizing network losses in the distribution network system. Finally, through simulation and comparison of four scenarios, the results demonstrate that the proposed method achieves synergistic optimization of wind power and EV. This paper provides an efficient solution for the optimized scheduling of large-scale EV connected to the predictable wind power grid.

Modeling and Control of a DC-DC Buck–Boost Converter with Non-Linear Power Inductor Operating in Saturation Region Considering Electrical Losses

The present work proposes a nonlinear model of a buck–boost DC-DC power converter considering the nonlinear magnetic characteristics of the power inductor and electrical losses of the system. The Euler–Lagrange formalism is used for formulating the proposed model. Previous research works have reported mathematical models to describe power inductor dynamics. However, a gap in the literature remains regarding modeling this kind of element when it operates within power converters. Also, a linear-based controller scheme is proposed to regulate a non-ideal buck–boost DC-DC power converter. A methodology for tuning the proposed controller is presented, which considers the nonlinear model structure of the power converter, the linearization procedure based on an identification process, and a frequency domain analysis based on the approximated linear model. Finally, the tuned control scheme is tested on the nonlinear model of the power converter under several operational conditions showing excellent performance by effectively regulating the output voltage. The results are compared with those derived from alternative control strategies, and a better performance is generally obtained.

Complementarity reformulations for the optimal design of distributed energy systems with multiphase optimal power flow

The optimal design of grid-connected distributed energy systems (DES) has been previously investigated, but most studies exclude nonlinear multiphase optimal power flow (MOPF) constraints which capture imbalances in alternating current (AC) distribution networks. Previous DES design studies considering AC power flow assume balanced loads and networks, which is an assumption that does not hold for distribution networks that are often inherently unbalanced. This is the first study to present an optimisation framework for designing grid-connected DES while simultaneously considering multiphase optimal power flow (MOPF) constraints to accurately represent unbalanced low-voltage distribution. This study proposes a new algorithm for obtaining DES designs subject to nonlinear multiphase power flow constraints with regularised complementarity reformulations for operational constraints containing binary variables. DES design models with either MOPF or OPF are tested using an unbalanced distribution network, where rooftop solar, gas boilers, and battery storage are considered as distributed resources. Despite the increased complexity, DES design with MOPF obtains the best solution, with 81% greater solar capacity and 6% lower total annualised cost when compared to DES with OPF. Designs from a commonly-used linear DES design framework based on direct current (DC) approximations produce the highest costs (8% more than initially predicted) when tested with MOPF. The proposed algorithm with complementarity reformulations achieves a 19% improvement in the objective value over a previous two-stage decomposition for DES with OPF, where the entire binary topology in the nonlinear model is fixed. The study therefore enables the acquisition of DES designs that can work symbiotically within unbalanced distribution networks.

Modeling of intelligent controllers for solar photovoltaic system under varying irradiation conditions

The increasing demand for solar renewable energy resources, driven by the global energy crisis and the depletion of conventional energy sources, has underscored the importance of harnessing solar energy. Solar photovoltaic (PV) systems, however, exhibit nonlinear output power due to their weather-dependent nature, impacting overall system efficiency. This study focuses on the development and comparative analysis of three intelligent Maximum Power Point Tracking (MPPT) controllers using the MATLAB Simulink. The controllers employ distinct methodologies, namely, Artificial Neural Networks (ANN), Adaptive Neural and Fuzzy Inference System (ANFIS), and Fuzzy Logic Controller (FLC). The results demonstrate that ANFIS achieved the highest accuracy at 99.50%, surpassing ANN and FLC with accuracies of 97.04% and 98.50%, respectively, thus establishing ANFIS as the superior MPPT controller. Additionally, the positives and negatives of all three MPPT-based algorithms are also compared in this work.

Direct active and reactive powers control of double-powered asynchronous generators in multi-rotor wind power systems using modified synergetic control

In the future, renewable energy sources will be of great importance in overcoming the problems of power generation using traditional sources, as their use contributes to protecting the environment from pollution and helps to raise human development. Therefore, it is necessary to search for a generation system that has high characteristics to raise the quality of energy and reduce the total cost of producing, transmitting, and consuming energy. This work proposes a new nonlinear direct reactive and active power control (DRAPC) for grid-connected double-powered asynchronous generators (DPAGs) in multi-rotor wind power (MRWP) systems. The designed DRAPC employs a modified synergetic control theory (MSCT) to regulate the DFPG-MRWP stator power. With out involving any synchronous coordinate transformations, the DRAPC-MSCT reduces the steady-state error (SSE), ripples and response time of stator powers while directly determining the required rotor control voltage. This technique fundamentally improves the transient performance compared to the DRAPC-SCT. Constant switching frequency is achieved as well by using pulse width modulation, which eases the designs of the power converters and AC harmonic filters.Through the use of three test cases (tracking test, robustness test, and variable-speed test using the Maximum Power Point Tracking), the potential of the DRAPC-MSCT to reduce system instability and uncertainty is evaluated. This comprises the ability of the controller to track DPAG powers references and improve performance during variations in system parameters and wind speed.Simulated results on a 1.5 MW grid-connected DPAG-MRWP are presented and compared with those of the DRAPC-SCT. The DRAPC-MSCT improves the reactive and active power ripples by 73.33% and 84.50%, respectively. Besides, improves the SSE of the reactive and active power by 51.61% and 69%, respectively compared to the DRAPC-SCT. The simulation results demonstrate the high performance and robustness of the DRAPC-MSCT for parametric variations of DPG-MRWP compared to the DRAPC-SCT.

Frequency control of power system with electric vehicles using hybrid african vultures optimization algorithm and pattern search tuned fuzzy PID controller

This work suggests a hybrid African Vultures Optimization Algorithm (AVOA) and Pattern search (hAVOA-PS) based Fuzzy PID (FPID) structure for frequency control of a nonlinear power system with Electric Vehicles (EVs). To illustrate the dominance of the projected hAVOA-PS algorithm, initially PI controllers are considered and results are compared with AVOA, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) methods. To further enhance the dynamic performance, PID and FPID controllers are considered. The dominance of FPID over PID and PI controllers is shown. In the next step, EVs are incorporated in the test system and a comparative analysis of hAVOA-PS based PI/PID/FPID and FPID+EV is presented. To exhibit the superiority of projected frequency control scheme in maintaining the stability of system under different disturbance conditions like load increase in area-1 only, load decrease/increase in all areas, and large load increase in all areas are considered. It is noticed that the suggested hAVOA-PS based FPID controller n presence of EV is able to maintain system stability for all the considered cases where as other compared approaches fail to maintain stability in some cases.

A nonlinear multi-period hydrothermal optimal power flow model for hydropower systems

Despite their social and climate benefits, renewable energy sources also present challenges such as intermittency, volatility and randomness, which may considerably reduce security and reliability of the system. Hydro units have the ability to provide flexible and rapid energy reserves, serving as an effective way of handling these challenges. Yet, many Hydrothermal Optimal Power Flow (HOPF) models in the literature often provide a simplified and sometimes inaccurate representation of the hydraulic aspects. In most HPOF models proposed in the literature, the representation of hydraulic aspects disregards important physical and operational hydro constraints. Such simplifications can curtail the potential benefits of hydro generation, especially concerning system security and reliability. In this paper, we investigate the impact of hydro constraints in the operation of hydrothermal systems by means of HOPF models. For such a purpose, we propose a nonlinear multi-period active–reactive HOPF model where hydro constraints are represented in detail, by means of a nonlinear framework. This model presents innovative formulations for hydro units, specifically designed to address pivotal non-differentiable constraints. The proposed multi-period HOPF model is used as a benchmark to assess inaccuracies present in linear or linearized HOPF model variants. The results using the IEEE 24-bus and 300-bus systems, adapted so they become hydropower systems, clearly identify significant impact of some hydro constraints which have been neglected in most models described in the literature, in the hydrothermal operational policy and scheduling.

Optimized hybrid ensemble learning approaches applied to very short-term load forecasting

The significance of accurate short-term load forecasting (STLF) for modern power systems’ efficient and secure operation is paramount. This task is intricate due to cyclicity, non-stationarity, seasonality, and nonlinear power consumption time series data characteristics. The rise of data accessibility in the power industry has paved the way for machine learning (ML) models, which show the potential to enhance STLF accuracy. This paper presents a novel hybrid ML model combining Gradient Boosting Regressor (GBR), Extreme Gradient Boosting (XGBoost), k-Nearest Neighbors (kNN), and Support Vector Regression (SVR), examining both standalone and integrated, coupled with signal decomposition techniques like STL, EMD, EEMD, CEEMDAN, and EWT. Through Automated Machine Learning (AutoML), these models are integrated and their hyperparameters optimized, predicting each load signal component using data from two sources: The National Operator of Electric System (ONS) and the Independent System Operators New England (ISO-NE), boosting prediction capacity. For the 2019 ONS dataset, combining EWT and XGBoost yielded the best results for very short-term load forecasting (VSTLF) with an RMSE of 1,931.8 MW, MAE of 1,564.9 MW, and MAPE of 2.54%. These findings highlight the necessity for diverse approaches to each VSTLF problem, emphasizing the adaptability and strength of ML models combined with signal decomposition techniques.

Discrete optimal designs for distributed energy systems with nonconvex multiphase optimal power flow

The optimal selection, sizing, and location of small-scale technologies within a grid-connected distributed energy system (DES) can contribute to reducing carbon emissions, consumer costs, and network imbalances. There is a significant lack of studies on how DES designs, especially those with electrified heating systems, impact unbalanced low-voltage distribution networks to which most DES are connected. This is the first study to present an optimisation framework for obtaining discrete technology sizing and selection for grid-connected DES design, while simultaneously considering multiphase optimal power flow (MOPF) constraints to accurately represent unbalanced low-voltage distribution networks. An algorithm is developed to solve the resulting Mixed-Integer Nonlinear Programming (MINLP) formulation. It employs a decomposition based on Mixed-Integer Linear Programming (MILP) and Nonlinear Programming (NLP) and uses integer cuts and complementarity reformulations to obtain discrete designs that are also feasible with respect to the network constraints. A heuristic modification to the original algorithm is also proposed to improve computational speed. Improved formulations for selecting feasible combinations of air source heat pumps (ASHPs) and hot water storage tanks are also presented. Two networks of varying size are used to test the optimisation methods. Designs with electrified heating (ASHPs and tanks) are compared to those with conventional gas boilers. The algorithms outperform one of the existing state-of-the-art commercial deterministic MINLP solvers, which fails to find any solutions in two instances within specified time limits. While feasible solutions were obtained for all cases, convergence was not achieved for all, especially for those involving the larger network. Where converged, the algorithm with the heuristic modification has achieved results up to 70% faster than the original algorithm. Results for case studies suggest that including ASHPs can support up to 16% higher renewable generation capacity compared to gas boilers, albeit with higher ASHP investment costs, as local generation and consumption minimises network violations associated with excess power export. The results also show the importance of including nonlinear power flow constraints in DES design problems. The optimisation framework and results can be used to inform stakeholders such as policymakers and network operators, to increase renewable energy capacity and aid the decarbonisation of domestic heating systems.

Kendiliğinden Kanal Oluşturmalı Karbon Tabanlı Memristörler İçin DC Dirençlerini Okuyarak Yapılan Bir Sağlamlık Testinin Güvenilirliğinin İncelenmesi

An ideal memristor that has been theoretically predicted almost a half-century ago is a nonlinear power dissipating circuit element. Nowadays, memristive systems such as thin films which are not ideal memristors are also called memristors. Such systems have current-dependent behavior and nonlinear charge-dependent electrical resistance. Self-directed channel Carbon-, Tungsten-, Chrome-, and Tin-based memristors have become commercially available nowadays and they are used for research purposes. All circuit components must be tested before their usage. It is expected that memristors will become commonly used in electronic circuits in the future. However, the literature has just a few memristor tests reported. To the best of our knowledge, there is not a suggested robustness test for the self-directed channel Carbon-based memristors in the literature. In this study, A recently suggested memristor robustness test which could be made using just a multimeter is modified using a series resistor. The test is tried on the Self-Directed Channel Carbon-Based memristors. Unfortunately, the test is found unreliable and invalid for the self-Directed Channel Carbon-Based memristors.

Hierarchical distributed MPC method for hybrid energy management: A case study of ship with variable operating conditions

The energy management (EM) strategy, power controller, and local controller of the EM system are coupled, and together affect hybrid power system performance. To achieve coordinated control and multi-objective optimisation of a hybrid power system, a hierarchical distributed control method was proposed, and a validation study was conducted based on model-in-the-loop simulations (MILs) and hardware-in-the-loop simulations (HILs). First, a real-time EM strategy based on a combination of forward dynamic programming (FDP) and model predictive control (MPC) methods was proposed to optimise the power allocation for multiple energy sources. Second, a distributed controller based on a consistency algorithm was proposed to coordinate the differences in the characteristics of multiple energy sources. A dynamic virtual impedance-based droop controller was designed for dynamic tracking of the reference power. The performance of the three-layer control structure was comprehensively validated through MILs and HILs. The results show that the dynamic virtual impedance-based droop control method can track the nonlinear reference power with control deviation within 5 %. The distributed controller is able to keep the bus voltage stable. The global control accuracy of the DC bus voltage is improved by 18.08 %, and the battery current global fluctuations is reduced by 17.4 %. The real-time FDP-MPC-based EM strategy can achieve 99.89 % energy savings and emissions reduction compared to the global DP-MPC-based method, with greater robustness, real-time performance. The results demonstrate that the proposed method is effective for real-time applications and can achieve hierarchical and multi-objective optimal control of the hybrid power system.

A class of fractional differential equations via power non-local and non-singular kernels: Existence, uniqueness and numerical approximations

We prove a useful formula and new properties for the recently introduced power fractional calculus with non-local and non-singular kernels. In particular, we prove a new version of Gronwall’s inequality involving the power fractional integral; and we establish existence and uniqueness results for nonlinear power fractional differential equations using fixed point techniques. Moreover, based on Lagrange polynomial interpolation, we develop a new explicit numerical method in order to approximate the solutions of a rich class of fractional differential equations. The approximation error of the proposed numerical scheme is analyzed. For illustrative purposes, we apply our method to a fractional differential equation for which the exact solution is computed, as well as to a nonlinear problem for which no exact solution is known. The numerical simulations show that the proposed method is very efficient, highly accurate and converges quickly.

Power quality improvement using rabbit optimization FOPID controlled photovoltaic- battery powered hybrid power filter

This paper presents the tuning of a fractional proportional controller (FOPI) using artificial rabbit optimization for the control of photovoltaic (PV) and battery power series active power filters along with a shunt passive filter which is known as a hybrid power filter. The PV power generation is combined into a series active filter to alleviate the problem of voltage sag and swell in the power system and also supply real power to the grid. Generally, the proportional controller is used to control the series active filter, but this is a linear controller and is not able to control the non-linear power system effectively. This problem is effectively controlled by non-linear control, i.e., a fractional-order proportional integral controller. Another problem in FOPI is finding the optimal value for proportional gain, integral gain, and fractional order. There are no standard rules for finding these values. This will make system design more complex. In this paper, artificial rabbit optimization is used to simplify the system design by finding optimal values of the FOPI controller for the series active filter and enhance the overall performance of the system. The MATLAB 2020b/Simulink environment is utilized to assess the recommended controller’s performance. According to the experimental findings, the suggested system has a total harmonic distortion (THD) value for load voltage of 0.10 % and a total harmonic distortion value for grid current of 1.87 %. The proposed artificial-rabbit optimized FOIPI controller effectively controls the system against voltage sag, swell, and non-linear loads and also obeys IEEE power quality standards.

Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and power–law of self–phase modulation by Lie symmetry

Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and power–law of self–phase modulation by Lie symmetry

Performance improvement through nonlinear control design and power management of a grid-connected wind-battery hybrid energy storage system

This paper presents a study on the application of nonlinear control and optimal power management techniques in a grid-connected wind energy conversion system with battery storage. The objective is to efficiently supply power to a load while considering performance constraints. The energy system under investigation comprises a wind turbine, battery, AC-grid, and load. Power is delivered to the load through various converters and a DC-link. However, the intermittent nature of wind energy and frequent load fluctuations can negatively impact the battery's lifetime and charging performance. To address these challenges, a nonlinear controller and a novel energy management system are designed. The energy management system generates multiple energy flow scenarios to achieve equilibrium in energy distribution between the load and energy sources. This equilibrium aims to minimize overall system costs, ensure DC-grid stability, and enhance power quality. Two distinct operation modes are identified: i) MPPT mode, which utilizes an optimizer to maximize power extraction, and ii) adaptive power point tracking (APPT) mode, which considers demand-driven production and the state of charge (SOC) of the storage system. The convergence of the closed-loop control is formally analyzed, and simulation results confirm the improved performance of the proposed multi-criteria design for energy management.

A self-stabilizing point absorber wave energy converter with a top-shaped buoy and non-linear power take-off for oceanographic applications

Point absorber wave energy converters (PA-WECs) are considered an independent renewable energy resource in oceanographic research to study wave climate data, ocean navigation and maritime security. Their performance enhancement through optimally designed floats and power take-off (PTO) is a crucial challenge. The proposed study investigates the combined PA-WEC model, including (i) the hydrodynamic of the optimally designed top-shaped buoy, (ii) non-linear characteristics of power take-off and (iii) self-stability of PA-WEC under the real-time wave climate of XiaoMaiDao wave station, Shandong, China. The proposed mechanical power take-off comprises a double-sided rack with gear transmission and three-phase DC generators. The components of the power take-off are symmetrically oriented on both sides of the rack to make it statically and dynamically balanced for the self-stability of the PA-WEC. The floating buoy absorbs kinetic energy from waves relative to a fixed point and transfers it to the PTO system. The PTO module alters the forward and reverted strokes of heaving motion into uni-directional rotations on the output shaft, employing a mechanical gearing mechanism with one-way bearings. Subsequently, supercapacitors store the rectified electrical energy in the power conversion and storage modules. The mechanical power take-off was initially modeled in MATLAB/Simscape and verified through experimental investigations using mechanical testing and sensing machine. Secondly, the hydrodynamics of the floating buoy was studied using frequency- and time-domain simulations in ANSYS AQWA. Thirdly, the wave tank tests were performed on a 1:25 scaled buoy in a wave tank, and the test results were validated against the time-domain simulations. Finally, the combined effects of power take-off and buoy were studied on the prototype scale, and it is concluded that at 1m significant wave height, the power take-off system integrated with the Cyl-AS buoy can generate 247.76W (RMS) with PTO efficiency of ηpto_rms = 76.37% at PA-WEC efficiency of ηwec_rms = 12.10%. Installing the proposed point absorber wave energy converter system along the offshore platforms can promote the UN-SDG-2030 Agenda, specifically the 7 and 14 goals, by supplying electricity for oceanographic applications.

Deep neural network based downlink power domain multi-user NOMA-OFDM signal detection

Non-orthogonal multiple access-based orthogonal frequency division multiplexing (NOMA-OFDM) is a promising waveform-based multiple access technology for future wireless networks for multiple-user symbol transmission (MUST) in the same time-frequency resource block. However, it differs in the power domain, enhancing its spectrum efficiency. This is essential to meet the high data rate required for ever-increasing connected devices and the Internet of Things (IoT). However, NOMA-OFDM systems suffer from impairments such as imperfect successive interference cancellation (SIC) caused by channel impairments like channel fading, carrier frequency offset, and non-linearity caused by non-linear power amplifiers. This paper identifies and addresses the key impairments mentioned in the NOMA-OFDM system and proposes DNN-based estimation in offline training and detection in online testing for downlink power domain multi-user NOMA-OFDM symbols. The reported 2 dB SNR gain compared to least square-SIC/minimum mean square error SIC-based methods is a significant finding and demonstrates the robustness of the proposed DNN-aided approach against various channel impairments.

Stability and multi-frequency dynamic characteristics of nonlinear grid-connected pumped storage-wind power interconnection system

Stability and multi-frequency dynamic characteristics of nonlinear grid-connected pumped storage-wind power interconnection system