Nonlinear Power Research Articles

Low-Dimensional Post-Distortion for Nonlinear Power Amplifier in MIMO Systems

Low-Dimensional Post-Distortion for Nonlinear Power Amplifier in MIMO Systems

On a periodic problem for super-linear second-order ODEs

Abstract The present paper concerns the periodic problem u ″ = p ( t ) u − q ( t , u ) u + f ( t ) ; u ( 0 ) = u ( ω ) , u ′ ( 0 ) = u ′ ( ω ) , $$\begin{array}{} \displaystyle u''=p(t)u-q(t,u)u+f(t);\quad u(0)=u(\omega),\, u'(0)=u'(\omega), \end{array}$$ where p, f : [0, ω] → ℝ are Lebesgue integrable functions and q : [0, ω] × ℝ → ℝ is a Carathéodory function. We assume that the anti-maximum principle holds for the corresponding linear problem and provide sufficient conditions guaranteeing the existence and uniqueness of a positive solution to the given non-linear problem. The general results obtained are applied to the non-autonomous Duffing type equation with a super-linear power non-linearity.

Distributed control of DC microgrids: A relaxed upper bound for constant power loads

Motivated by the increasing interest in DC microgrids, we study the distributed secondary control problem of DC microgrids which aims to simultaneously guarantee load current sharing and DC bus voltage restoration. In particular, we analyze in-depth the effects of nonlinear constant power loads (CPLs), and successfully establish an upper bound for CPLs to guarantee the stability of DC microgrids. This established bound is less conservative than existing counterparts, allowing the connected power of CPLs to be much larger than that of linear resistive loads. Moreover, this bound explicitly reveals the connections between CPLs and droop gains, i.e., the upper bound of CPLs can be increased by decreasing droop gains, and vice versa. Three case studies are provided to verify the established results.

A novel structure adaptive new information priority grey Bernoulli model and its application in China's renewable energy production

At present, the global energy structure is undergoing major changes. China is in the transition period of energy structure. Accurately anticipating future energy trends is critical for China's energy structure and modernization. Considering the uncertainty and sparsity characteristics of China's energy system sequence, this study examines China's renewable energy scenario using the grey model with limited sample and uncertain system modelling features. Renewable energy is affected by a variety of uncertain factors, exhibiting a range of complicated traits including nonlinearity, periodicity and random volatility. The traditional grey model has been difficult to appropriately predict its future evolution. This paper focuses on the adaptability of the model, optimizes and improves the accumulation operator and model structure, and establishes a fractional-order structural self-adaptation grey Bernoulli model based on new information priority. Firstly, based on the new information priority accumulation operator, it is extended to the fractional order. In terms of model structure, combined with NGBM(1,1) model, SADGM(1,1) model and FPGM(1,1) model, periodic fluctuation term and nonlinear power term are included to improve the model's capacity to capture nonlinear, fluctuating and periodic features, and enhance the adaptability and flexibility of the model. The backward difference technique yields the model's parameter estimation and temporal response sequence. Based on the results of the algorithm comparison experiment, the Improved Grey Wolf Optimization Algorithm is chosen to optimize the structural parameters of the model in an effort to enhance its performance. The performance comparison experiment of the model was designed, and three cases of China's hydropower generation, China's renewable energy power generation installed capacity and China's solar energy quarterly power generation were selected to compare the performance with a variety of grey prediction models. Monte-Carlo simulation and probability density analysis were utilized to confirm the stability and accuracy of the proposed model. The results show that the proposed FSANGBM(1,1) model can handle data series of renewable energy with nonlinear, volatile, and periodic features with high prediction ability. Finally, the model is applied to forecast three cases' future development trends.

AC energy islands for the optimal integration of offshore wind energy resources: Operation strategies using multi-objective nonlinear programming

The increasing need for integrating offshore wind generation into power systems has highlighted energy islands as a promising solution. Such islands also could incorporate responsive infrastructure for improving grid flexibility such as energy storage and hydrogen production. AC energy islands could be particularly cost–benefit effective for short and medium distances between wind power parks and onshore grids. However, the implementation of AC energy islands presents challenges from the viewpoints of voltage stability, power dispatch and reliable operation. This paper develops optimal operation strategies for AC energy islands including: i) a nonlinear optimal power flow approach for controlling the reactive power compensation systems; ii) a finite horizon mathematical programming approach for the management of BESS and hydrogen production systems; and iii) a multi-objective programming approach for maximizing the active power delivered to the onshore power grid while minimizing the nodal voltage deviations simultaneously. Results show that the single-objective approach for real and reactive power dispatch reduces voltage deviations by around 20 % and line currents by over 70 % in the evaluated test system, compared to the non-optimal scenario. Moreover, the incorporation of energy storage in AC energy island test system increased the capacity for power dispatch over 10 %. Additionally, the multi-objective approach is effective in aligning the nodal voltages with nominal values and maximizing the power delivered to the onshore grid. Results show that with a small 1% reduction in power delivery, the proposed multi-objective approach achieved an approximate 50 % decrease in nodal voltage compared to the single-objective approach.

Array Optimization for a Wave Energy Converter with Adaptive Resonance Using Dual Bayesian Optimization

A novel Dual Bayesian optimization strategy is formed for an array of wave energy converters with adaptive resonance to maximize the annual performance through the energy conversion processes from irregular waves to electricity. A wave energy converter with adaptive resonance changes the natural frequency of power take-off dynamics for varying irregular waves, resulting in the maximum annual energy production. The first step of the two-step Dual Bayesian optimization determines the geometric layout of the array, which maximizes the first energy conversion to the total array excitation for irregular waves occurring annually. The second step optimizes the operational parameters of individual wave energy converters in the optimized array to maximize the power generation in varying sea states through simultaneous conversion to mechanical and electrical energy. The coupled hydrodynamics are solved in the frequency domain, and the power performance is evaluated by solving the Cummins’ equation in the time domain extended for multiple floating bodies, each strongly coupled with nonlinear power take-off dynamics. The proposed method is applied to a surface-riding wave energy converter, already optimized for single unit operation at individual sea states. Investigating two array layouts, linear and random, the optimized arrays after Step 1 increase the excitation spectral area by up to 40% relative to the single unit operation, indicating the synergy enhancing the first energy conversion. Subsequently, the dual-optimized linear layout attained a q-factor up to 1.13 in commonly occurring sea states, achieving improved average power generation in 60% of the evaluated sea states. The performance of the random layout exhibited the average power fluctuating along the wave spectra with a peak q-factor of 1.07. The individual adaptive resonance is confirmed in the optimized arrays, such that each surface-riding wave energy converter of both layouts adaptively resonates with the peak of the wave excitation spectra, maximizing the power generation for the different irregular waves.

Normalized ground states for Schrödinger equations on metric graphs with nonlinear point defects

We investigate the existence of normalized ground states for Schrödinger equations on noncompact metric graphs in presence of nonlinear point defects, described by nonlinear δ-interactions at some of the vertices of the graph. For graphs with finitely many vertices, we show that ground states exist for every mass and every L2-subcritical power. For graphs with infinitely many vertices, we focus on periodic graphs and, in particular, on Z-periodic graphs and on a prototypical Z2-periodic graph, the two–dimensional square grid. We provide a set of results unravelling nontrivial threshold phenomena both on the mass and on the nonlinearity power, showing the strong dependence of the ground state problem on the interplay between the degree of periodicity of the graph, the total number of point defects and their dislocation in the graph.

Data-driven dynamic state estimation in power systems via sparse regression unscented Kalman filter

This paper proposes a novel data-driven modeling and dynamic state-estimation approach for nonlinear power and energy systems, highlighting the critical role of a known dynamic model for accurate state estimation in the face of uncertainty and complex models. The proposed framework consists of a two-phase approach: data-driven model identification and state-estimation. During the model identification phase, which spans a relatively short time interval, state feedback is collected to identify the dynamics of the nonlinear systems in the power grid using a novel density-guided sparse identification algorithm. Unlike conventional sparse regression, which relies on a large library of linear and nonlinear functions to fit data, our proposed algorithm iteratively updates a relatively small initial library by adding higher-order nonlinear functions if the coefficients of the current functions are dense. Following the identification of the model’s dynamics, the estimation phase addresses the challenge of incomplete state measurements. By implementing an unscented Kalman filter, the state variables of the system are dynamically estimated by measuring the noisy output. Finally, simulation results on an IEEE 30-bus system are presented to illustrate the effectiveness of the density-guided sparse regression unscented Kalman filter compared to a physics-based unscented Kalman filter with model uncertainty. This study contributes to the fields of data-driven modeling techniques, machine learning for power systems, and computational intelligence in smart grids. It emphasizes the use of advanced sparse regression and unscented Kalman filter methods for state estimation, enhancing the robustness and accuracy of monitoring and control in electrical and energy systems.

A Novel development of soft computing based hybrid power point tracking controllers for hydrogen vehicle application with new wide source DC-DC converter

From the present power generation scenario, most of the power production companies are focusing on renewable energy systems because their merits are easy to install, more reliable power sources, free from atmospheric pollution, and better adaptable to all weather conditions. In this article, a Polymer Electrolyte Membrane Fuel Cell (PEMFC) module is selected in the first objective to produce constant and continuous power to the hydrogen-based electrical vehicle systems. This fuel module provides fast power production and gives good energy density. However, the demerits of this module are more current production and low-level voltage generation. A new single-switch DC-DC circuit is introduced in the second objective of this work for optimizing the current levels of the fuel module thereby reducing the source power loss of the proposed system. Here, another problem of the fuel module is nonlinear power production which is linearized by proposing the Cuckoo Search Optimization (CSO)-based Adaptive Network-based Fuzzy Inference System (ANFIS) in the third objective to extract the maximum voltage from the fuel module. The merits of this introduced Maximum Power Point Tracking (MPPT) Controller are better tracking speed, low-level disturbances in the consumer load power, high robustness, more sustainability, and easy operation. The entire proposed system is investigated by selecting the MATLAB Simulink tool. The introduced converter circuit is analyzed by selecting the programmed DC supply.

Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation. A direct integration approach is adopted to construct solutions in the beginning. This brings the emergence of interesting solutions like non‐topological solitons, trigonometric functions, exponential functions, elliptic functions, and Weierstrass functions in general structures. Besides, in a bid to secure more general exact solutions to the model, one adopts the extended Jacobi elliptic function expansion technique (for some specific cases of ). Thus, various cnoidal, snoidal, and dnoidal wave solutions to the understudied model are attained. The copolar trio explicated in a tabular form reveals that these solutions can be relapsed to various hyperbolic and trigonometric functions under certain criteria. Additionally, diverse graphical exhibitions of the dynamical attributes of the gained results are presented in a bid to have a sound understanding of the physical phenomena of the underlying model. Later, one gives the conserved vectors of the aforementioned equation by employing the standard multiplier approach.

Uncovering upconversion photoluminescence in layered PbI2 above room temperature.

As a van der Waals (vdW) layered semiconductor material, lead iodide (PbI2) possessing a direct bandgap with strong photoluminescence emission in visible range has gained wide attention in applications of photonic and optoelectronic devices. Here, upconversion photoluminescence (UPL) in exfoliated PbI2 flakes is demonstrated at room temperature and elevated temperatures. The linear power dependence of UPL emission with 532nm excitation suggests the one-photon involved multiphonon-assisted UPL emission process, which is revealed by the temperature-dependent UPL emission measurement. Meanwhile, the nonlinear power dependence of UPL emission with 561nm excitation indicates the transition of UPL emission mechanism from linear to nonlinear regime, and the temperature-dependent UPL emission study further shows that the upconversion is contributed by both the multiphonon-assisted UPL process and the two-photon absorption induced PL process. This study will provide an insight to the understanding of photon upconversion in vdW layered semiconductors and advancing applications in temperature-controlled photon upconversion, tunable photonics, photodetection and imaging.

Improved Bacterial Foraging Optimization Algorithm with Machine Learning-Driven Short-Term Electricity Load Forecasting: A Case Study in Peninsular Malaysia

Accurate electricity demand forecasting is crucial for ensuring the sustainability and reliability of power systems. Least square support vector machines (LSSVM) are well suited to handle complex non-linear power load series. However, the less optimal regularization parameter and the Gaussian kernel function in the LSSVM model have contributed to flawed forecasting accuracy and random generalization ability. Thus, these parameters of LSSVM need to be chosen appropriately using intelligent optimization algorithms. This study proposes a new hybrid model based on the LSSVM optimized by the improved bacterial foraging optimization algorithm (IBFOA) for forecasting the short-term daily electricity load in Peninsular Malaysia. The IBFOA based on the sine cosine equation addresses the limitations of fixed chemotaxis constants in the original bacterial foraging optimization algorithm (BFOA), enhancing its exploration and exploitation capabilities. Finally, the load forecasting model based on LSSVM-IBFOA is constructed using mean absolute percentage error (MAPE) as the objective function. The comparative analysis demonstrates the model, achieving the highest determination coefficient (R2) of 0.9880 and significantly reducing the average MAPE value by 28.36%, 27.72%, and 5.47% compared to the deep neural network (DNN), LSSVM, and LSSVM-BFOA, respectively. Additionally, IBFOA exhibits faster convergence times compared to BFOA, highlighting the practicality of LSSVM-IBFOA for short-term load forecasting.

Exact solitary wave solutions for a coupled gKdV–Schrödinger system by a new ODE reduction method

AbstractA new method is developed for finding exact solitary wave solutions of a generalized Korteweg–de Vries equation with ‐power nonlinearity coupled to a linear Schrödinger equation arising in many different physical applications. This method yields 22 solution families, with . No solutions for were known previously in the literature. For , four of the solution families contain bright/dark Davydov solitons of the 1st and 2nd kind, obtained in recent literature by basic ansatz applied to the ordinary differential equation (ODE) system for traveling waves. All of the new solution families have interesting features, including bright/dark peaks with (up to) symmetric pairs of side peaks in the amplitude and a kink profile for the nonlinear part in the phase. The present method is fully systematic and involves several novel steps that reduce the traveling wave ODE system to a single nonlinear base ODE for which all polynomial solutions are found by symbolic computation. It is applicable more generally to other coupled nonlinear dispersive wave equations as well as to nonlinear ODE systems of generalized Hénon–Heiles form.

Cosmological simulations of scale-dependent primordial non-Gaussianity

We present the results of a set of cosmological N-body simulations with standard ΛCDM cosmology but characterized by a scale-dependent primordial non-Gaussianity of the local type featuring a power-law dependence of the f NL loc(k) at large scales followed by a saturation to a constant value at smaller scales where non-linear growth leads to the formation of collapsed cosmic structures. Such models are built to ensure consistency with current Cosmic Microwave Background bounds on primordial non-Gaussianity yet allowing for large effects of the non-Gaussian statistics on the properties of non-linear structure formation. We show the impact of such scale-dependent non-Gaussian scenarios on a wide range of properties of the resulting cosmic structures, such as the non-linear matter power spectrum, the halo and sub-halo mass functions, the concentration-mass relation, the halo and void density profiles, and we highlight for the first time that some of these models might mimic the effects of Warm Dark Matter for several of such observables.

Integrating machine learning with causal inference for enhanced system dynamics modeling: A framework for predicting complex interactions

Approaches and methods like System Dynamics Modelling (SDM) have been significant for assessing the behavior of many systems. However, classical methodologies applied in traditional approaches to SDM fail to identify nonlinear feedback and power dependencies, revealing hidden temporal casual relationships. In this paper, I present a novel approach that combines ML and causal inference methods to improve the forecast capability and semantics of system dynamics models. Incorporating ML algorithms for predictions and Causal Inference techniques for explanation, this combined strategy presents a new era for understanding the system interaction and quantifying the hidden causes within various systems. We illustrate the advantages of the suggested framework over traditional SDM and purely ML approaches by employing it to analyze a genuine circumstance for both prognosis and discovering causal relationships. Our findings indicate that such integration is effective in enhancing the comprehension of system interactions and deriving a reliable method for estimating subsequent state conditions in complex contexts. The results are relevant for various disciplines, starting with economics and ending with environmental protection sciences, where interactions and changes vary. As a result, it will give a foundation for further studies of integrating future computerized methods in the dynamical system modeling of the next generation.

On solitary wave solutions to dispersive equations with double power nonlinearities

On solitary wave solutions to dispersive equations with double power nonlinearities

A mMSA-FOFPID controller for AGC of multi-area power system with multi-type generations

The exceptional growth in the penetration of renewable sources as well as complex and variable operating conditions of load demand in power system may jeopardize its operation without an appropriate automatic generation control (AGC) methodology. Hence, an intelligent resilient fractional order fuzzy PID (FOFPID) controlled AGC system is presented in this study. The parameters of controller are tuned utilizing a modified moth swarm algorithm (mMSA) inspired by the movement of moth towards moon light. At first, the effectiveness of the controller is verified on a nonlinear 5-area thermal power system. The simulation outcomes bring out that the suggested controller provides the best performance over the lately published strategies. In the subsequent step, the methodology is extended to a 5-area system having 10-units of power generations, namely thermal, hydro, wind, diesel, gas turbine with 2-units in each area. It is observed that mMSA based FOFPID is more effective related to other approaches. In order to establish the robustness of the controller, a sensitivity examination is executed. Then, experiments are conducted on OPAL-RT based real-time simulation to confirm the feasibility of the method. Finally, mMSA based FOFPID controller is observed superior than the recently published approaches for standard 2-area thermal and IEEE 10 generator 39 bus systems.

Non-linear cascade control with gain-scheduling and startup control strategy study for thermionic space reactor TOPAZ-II

The TOPAZ-II thermionic space reactor system, which was designed by the Soviet Union, is characterized by its high degree of nonlinearity and positive temperature reactivity feedback. The thermionic space reactor exhibits characteristics of high inertia and significant delay in controlling its electrical power and outlet temperature. The simple PID controller is difficult to achieve good performance. To carry out controller design for thermionic space reactor, the simulation platform for thermionic space reactor is developed based on coupling between reactor system thermal-hydraulic code RESYS and control system simulator in this study. After that, based on the cascade control strategy and gain-scheduling, the reactor thermal controller, electric power controller, outlet temperature controller applicable for the full power range is designed with transfer function model and frequency domain analysis method. To validate the nonlinear electric power controller performance, the continuous minor step disturbances, major step disturbances, and ramp variation of electric power setpoint is simulated. The performance of outlet temperature controller is verified with the simulation result of step and ramp variation of outlet temperature setpoint. Thereafter, the start-up process of the thermionic space reactor TOPAZ-II is simulated and analyzed. The simulation result reveals that the controller designed in this paper can overcome the nonlinearity of the thermionic space reactor system and has good performance throughout the entire power range. Compared to traditional simple PID controller, the cascade controller has better performance and can achieve good control performance even in situations where simple PID controllers cannot function properly.

The shape of dark matter halos: A new fundamental cosmological invariance

In this article, we focus on the complex relationship between the shape of dark matter (DM) halos and the cosmological models underlying their formation. We have used three realistic cosmological models from the DEUS numerical simulation project. These three models have very distinct cosmological parameters (Ωm, σ8, and w) but their cosmic matter fields beyond the scale of DM halos are quasi-indistinguishable, providing an exemplary framework to examine the cosmological dependence of DM halo morphology. First, we developed a robust method for measuring the halo shapes detected in numerical simulations. This method avoids numerical artifacts on DM halo shape measurements, induced by the presence of substructures depending on the numerical resolution or by any spherical prior that does not respect the triaxiality of DM halos. We then obtain a marked dependence of the halo’s shape both on their mass and the cosmological model underlying their formation. As it is well known, the more massive the DM halo, the less spherical it is and we find that the higher the σ8 of the cosmological model, the more spherical the DM halos. Then, by reexpressing the properties of the shape of the halos in terms of the nonlinear fluctuations of the total cosmic matter field or only of the cosmic matter field which is internal to the halos, we managed to make the cosmological dependence disappear completely. This new fundamental cosmological invariance is a direct consequence of the nonlinear dynamics of the cosmic matter field. As the universe evolves, the nonlinear fluctuations of the cosmic field increase, driving the dense matter halos toward sphericity. The deviation from sphericity, measured by the prolaticity, triaxiality, and ellipticity of the DM halos, is therefore entirely encapsulated in the nonlinear power spectrum of the cosmic field. From this fundamental invariant relation, we retrieve with remarkable accuracy the root-mean-square of the nonlinear fluctuations and, consequently, the power spectrum of the cosmic matter field in which the halos formed. We also recover the σ8 amplitude of the cosmological model that governs the cosmic matter field at the origin of the DM halos. Our results therefore highlight, not only the nuanced relationship between DM halo formation and the underlying cosmology but also the potential of DM halo shape analysis of being a powerful tool for probing the nonlinear dynamics of the cosmic matter field.

Non-linear matter power spectrum modeling in interacting dark energy cosmologies

Understanding the behavior of the matter power spectrum on non-linear scales beyond the ΛCDM model is crucial for accurately predicting the large-scale structure (LSS) of the Universe in non-standard cosmologies. In this work, we present an analysis of the non-linear matter power spectrum within the framework of interacting dark energy-dark matter cosmologies (IDE). We employ N-body simulations and theoretical models to investigate the impact of IDE on these non-linear scales. Beginning with N-body simulations characterized by a fixed parameter space delineated by prior observational research, we adeptly fit the simulated spectra with a simple parametric function, achieving accuracy within 5%. Subsequently, we refine a modified halo model tailored to the IDE cosmology, exhibiting exceptional precision in fitting the simulations down to scales of approximately 1 h/Mpc. To assess the model’s robustness, we conduct a forecast analysis for the Euclid survey, employing our refined model. We find that the coupling parameter ξ will be constrained to σ(ξ)=0.0110. This marks a significant improvement by an order of magnitude compared to any other current observational tests documented in the literature. These primary findings pave the way for a novel preliminary approach, enabling the utilization of IDE models for observational constraints concerning LSS data on non-linear scales.