Time-varying Power Research Articles

Time-varying predictability of financial stress on inequality in United Kingdom

PurposeExisting empirical evidence suggests that episodes of financial stress (crises) can act as driver of growth of inequality. Consequently, in this study, the authors explore the time-varying predictive power of an index of financial stress for growth in income (and consumption) inequality in the UK. The authors focus on the UK since income (and consumption) inequality data are available at a high frequency, i.e. on a quarterly basis for over 40 years (June, 1975 to March, 2016).Design/methodology/approachThe authors use Wang and Rossi's approach to analyze the time-varying impact of financial stress on inequality. Hence, the method provides a more appropriate inference of the effect rather than a constant parameter Granger causality method. Besides, understandably, the time-varying approach helps to depict the time-variation in the strength of predictability of financial stress on inequality.FindingsThis study’s findings point that financial distress correspond to subsequent increases in inequality, with the index of financial stress containing important information in predicting growth in income inequality for both in and out-of-sample periods. Interestingly, the strength of the in-sample predictive power is high post the period of the global financial crisis, as was observed in the early part of the sample. The authors believe these findings highlight an important role of financial stress for inequality – an area of investigation that has in general remained untouched.Originality/valueAccurate prediction of inequality at a higher frequency should be more relevant to policymakers in designing appropriate policies to circumvent the wide-ranging negative impacts of inequality, compared to when predictions are only available at the lower annual frequency.

Adaptive State-Feedback Stabilization for Stochastic Nonlinear Systems with Time-Varying Powers and Unknown Covariance

This paper investigates the adaptive state-feedback stabilization problem for stochastic nonlinear systems. Compared with the existing results, we consider more general and more practical systems, i.e., systems with time-varying powers and unknown covariance simultaneously. We propose a new adaptive state-feedback control method, which ensures that the closed-loop system is globally stable in probability and the states are regulated to the origin almost surely. Finally, the feasibility of the design method is verified by two examples.

Measurement-based prediction-correction online distributed optimal power flow algorithm for multi-phase active distribution networks

Online algorithms have shown great potential in solving time-varying optimal power flow (OPF) problems emerging in active distribution networks (ADNs) with numerous power-electronics-interfaced distributed energy resource (DER) integrations. However, existing online algorithms have the following limitations: 1) Correction-only algorithms ignore the time-varying characteristics of the optimization problem; 2) Prediction-correction algorithms cannot handle nonlinear OPF problems; 3) Most algorithms only consider the application of single-phase cases. This paper addresses the above limitations by proposing a novel measurement-based prediction-correction online distributed OPF algorithm for multi-phase ADNs. This algorithm is based on an improved multi-phase linearized alternating current (AC) power flow model that takes advantage of the voltage measurements to improve the approximation accuracy. In each sampling period, the proposed algorithm first performs a limited number of correction steps, iterating the incremental variable based on the current outputs of DERs and the voltage measurements to track the optimal solution. The DERs then execute the resultant incremental output powers. After forecasting the time-varying parameters, the proposed algorithm performs a few prediction steps to seek a better starting point for the correction steps before the next sampling. Numerical test results of the modified IEEE 37-bus and 123-bus distribution systems demonstrated that the proposed algorithm can track the optimal solution of the time-varying nonlinear OPF problem more accurately than existing online algorithms, even in extra-high penetration scenarios (≥200%).

Adaptive real-time grid operation via Online Feedback Optimization with sensitivity estimation

In this paper we propose an approach based on an Online Feedback Optimization (OFO) controller with grid input–output sensitivity estimation for real-time grid operation, e.g., at subsecond time scales. The OFO controller uses grid measurements as feedback to update the value of the controllable elements in the grid, and track the solution of a time-varying AC Optimal Power Flow (AC-OPF). Instead of relying on a full grid model, e.g., grid admittance matrix, OFO only requires the steady-state sensitivity relating a change in the controllable inputs, e.g., power injections set-points, to a change in the measured outputs, e.g., voltage magnitudes. Since an inaccurate sensitivity may lead to a model-mismatch and jeopardize the performance, we propose a recursive least-squares estimation that enables OFO to learn the sensitivity from measurements during real-time operation, turning OFO into a model-free approach. We analytically certify the convergence of the proposed OFO with sensitivity estimation, and validate its performance on a simulation using the IEEE 123-bus test feeder, and comparing it against a state-of-the-art OFO with constant sensitivity.

Cross-layer design for real-time grid operation: Estimation, optimization and power flow

In this paper, we propose a combined Online Feedback Optimization (OFO) and dynamic estimation approach for a real-time power grid operation under time-varying conditions. A dynamic estimation uses grid measurements to generate the information required by an OFO controller, that incrementally steers the controllable power injections set-points towards the solutions of a time-varying AC Optimal Power Flow (AC-OPF) problem. More concretely, we propose a quadratic programming-based OFO that guarantees satisfying the grid operational constraints, like admissible voltage limits. Within the estimation, we design an online power flow solver that efficiently computes power flow approximations in real time. Finally, we certify the stability and convergence of this combined approach under time-varying conditions, and we validate its effectiveness on a simulation with a test feeder and high resolution consumption data.

Governor controller improvement to enhance SSSG performance in presence of electrical arc furnace

Electrical Arc Furnaces (EAFs) consume time-varying power. This causes mechanical torque variations in the nearby small scale synchronous generators (SSSGs) and reduces their life expectancy. In this paper, an appropriate EAF model is implemented and verified by using field measurements. Moreover, an actual distribution system to which an SSSG is connected to supply industrial loads including an EAF is investigated based on time-domain simulation studies. To enhance dynamic performance of the SSSG adjacent to an EAF load, two novel approaches are presented in this paper. The first method is utilized for proper adjustment of governor controller parameters. Analytical and simulation-based studies are accomplished to determine proper parameters of the SSSG conventional governor controller to mitigate the mechanical oscillations caused by EAF. These comprehensive investigations reveal that the governor PI controller proportional parameter should be adjusted as small as possible to mitigate the SSSG oscillations; while, the oscillations are fairly independent of integrator parameter. Besides, the integrator parameter should be set as high as possible to improve the SSSG dynamic performance. Moreover, a new modified SSSG governor controller including steady-state and transient control loops is developed and a novel control strategy is proposed to enhance steady-state and transient performance of SSSG. Finally, robustness and effectiveness of the proposed controller and its parameters are investigated using field measured EAF current signals for various transients. It should be noted that the proposed strategies of this paper can be also applied to similar cases where a nonlinear time varying load is connected to an SSSG.

A 3-D Dynamic Non-WSS Cluster Geometrical-Based Stochastic Model for UAV MIMO Channels

The unmanned aerial vehicle (UAV) channel models are very important and useful for the design and evaluation of UAV communications. In existing works, the terrestrial scatterers are widely stationary or moving all the time, and the UAV is assumed to move at a constant speed. However, these modeling assumptions may not be appropriate in realistic scenarios. In this work, we propose a new 3-dimensional (3-D) dynamic non-wide-sense stationary (non-WSS) cluster-based geometric model for UAV multiple-input multiple-output (MIMO) channels. We assume that a few non-isotropic scatterers are distributed around the terrestrial receiver and have a probabilistic movement behavior. Meanwhile, we consider that the UAV flies at a varying speed, and we design a non-stationary mobility model with acceleration. The proposed channel model performs the birth-death evolutionary process of clusters based on a Markov model, and the time-variant multipath component (MPC) parameters (e.g., angle of arrival/departure (AoA/AoD), power, and delay) are obtained. In addition, we derive the space-time correlation function, mean Doppler spread, and root-mean-square doppler shift spread of the UAV MIMO channels, and provide the quasi-stationary interval. We also investigate the impact of some key model factors on the statistical properties by numerical simulations. Finally, we compare the space-time correlation functions and the second-order statistical properties between the proposed model and the UAV channel measurement results. The close agreements between the numerical simulations and field measurements have validated the proposed model.

Facilitating URLLC in UAV-Assisted Relay Systems With Multiple-Mobile Robots for 6G Networks: A Prospective of Agriculture 4.0

In the upcoming sixth-generation (6G) networks, ultra-reliable and low-latency communication (URLLC) is considered as an essential service that will empower real-time wireless systems, smart grids, and industrial applications. In this context, URLLC traffic relies on short blocklength packets to reduce the latency, which poses a daunting challenge for network operators and system designers since classical communication systems are designed based on the classical Shannon’s capacity formula. Therefore, to tackle this challenge, this article considers an unmanned aerial vehicle (UAV) acting as a decode-and-forward relay to communicate short URLLC control packets between a controller and multiple-mobile robots in a cell to enable a use-case of Agriculture 4.0. Moreover, this article employs perturbation theory and studies the quasi-optimization of the UAV’s location, height, beamwidth, and resource allocation, including time-varying power and blocklength for the two phases of transmission from the controller to UAV and from UAV to robots. In this regard, we propose an iterative optimization method to find the optimal UAV’s height and location, the antenna beamwidth, and the variable power and blocklength allocated to each robot inside the circular cell to minimize the average overall decoding error. It is demonstrated that the proposed algorithm outperforms other benchmark algorithms based on fixed parameters and performs nearly as well as the smart exhaustive search. Lastly, our results emphasize the need to jointly optimize all of the abovementioned UAV’s system parameters and resource allocation for the two phases of transmission to achieve URLLC for multiple-mobile robots.

A harmonic input method for computing time-varying response PSD of linear time-invariant structures subjected to nonstationary stochastic excitations

A number of stochastic response analysis methods have been successfully developed for computing the time-varying response power spectral density (PSD) of structures subjected to nonstationary stochastic excitations. However, how to compute the time-varying response PSD when transient response components have significant impacts on the stochastic responses remains largely unsolved. To this end, this paper proposes a harmonic input method (HIM) for accurately and efficiently computing time-varying response PSD of linear time-invariant structures subjected to nonstationary stochastic excitations, which can consider the transient response impact. The accuracy of the proposed HIM method is verified via comparison against the Monte Carlo simulations of an SDOF system and an MDOF system, which outperforms the classical methods if the transient response components are of significance. This study offers a high-efficient and high-accurate approach for response PSD estimation, particularly for a low-damping structural system subjected to short-duration nonstationary stochastic excitations.

A combinational transfer learning framework for online transient stability prediction

Data-driven methods have been intensively investigated in transient stability prediction due to the advantages on speed and accuracy. However, the variability of power systems disables the well-trained model when the contingencies or operation points are not covered in original training set. To address this issue, this paper proposes a combinational transfer learning framework to update transient stability prediction model in time-varying power systems, where convolutional neural network (CNN) is selected as the classifier. An innovative sample transfer algorithm is proposed to select applicable samples from source system, which decreases the time for time-domain simulation. Meanwhile, different model transfer schemes are compared for better accuracy and training efficiency of CNN. Test results on IEEE 39-bus system and an actual power grid verifies the efficiency and scalability of the proposed method. In addition, it performs well in the imbalanced training set and data with random noise.

Robust optimization approach with acceleration strategies to aggregate an active distribution system as a virtual power plant

An effective way to make full use of the flexibility of distributed generations in an active distribution system (ADS) is to aggregate ADS as a virtual power plant (VPP) to participate in the day-ahead energy market. This paper proposes a robust optimization model to obtain parameters of the VPP that do not depend on the information of day-ahead energy markets, such as time-varying power bounds and ramp rates. The robust model considers the uncertainty of dispatch orders from the transmission system operator (TSO) and outputs of renewable distributed generations. Furthermore, the column-and-constraint generation algorithm is applied to solve the robust model. To accelerate its solution, the period decomposition and connection method is first proposed to change the max–min sub-problem into small-scale independent linear programming problems. Second, the directional per-unit method is proposed to establish the linear relationship between uncertain dispatch orders from the TSO and the parameters of the VPP, and this relationship is substituted into the master problem to reduce iterations. Finally, the proposed method is evaluated on a modified IEEE 33-bus system and a practical 185-bus distribution system. The results verify the correctness and effectiveness of the proposed method.

Covert Rate Optimization of Millimeter Wave Full-Duplex Communications

In this paper, we consider the problem of full-duplex covert millimeter wave (mmWave) communications, where a mmWave transmitter (Alice) sends information signals to its intended receiver (Bob) covertly in the presence of a watchful warden (Willie). For covering the presence of Alice, Bob operates in the full-duplex mode and generates jamming signals with a time-varying power. We investigate the covert rate optimization for both the single data stream case and the multiple data streams case under the constraints of the detection error probability at Willie. Specifically, for the single data stream case, we analytically characterize the minimum detection error probability at Willie and establish a framework for optimizing the analog beamforming, transmit power, and analog jamming jointly. As for the case of multiple data streams, we derive a tractable lower bound of the minimum detection error probability at Willie and formulate a joint optimization of the hybrid precoder and analog jamming design problem for the maximization of the achievable covert rate. Although the joint design problem is nonconvex, we adopt the penalty decomposition technique to handle the effect of the coupling between the analog precoder and digital precoder paving the way for the development of an iterative algorithm to locate its Karush-Kuhn-Tucker (KKT) solution. Finally, we show that our proposed joint design algorithm can be adapted to handle the multi-antenna Willie scenario and simulation results show that our proposed joint design algorithms can achieve significantly better performance as compared with some benchmark schemes.

Optimization of time-variant laser power in a cladding process

Optimization of time-variant laser power in a cladding process

Explainable AI in Deep Reinforcement Learning Models for Power System Emergency Control

Artificial intelligence (AI) technology has become an important trend to support the analysis and control of complex and time-varying power systems. Although deep reinforcement learning (DRL) has been utilized in the power system field, most of these DRL models are regarded as black boxes, which are difficult to explain and cannot be used on occasions when human operators need to participate. Using the explainable AI (XAI) technology to explain why power system models make certain decisions is as important as the accuracy of the decisions themselves because it ensures trust and transparency in the model decision-making process. The interpretability issue in DRL models in power system emergency control is discussed in this article. The proposed interpretable method is a backpropagation deep explainer based on Shapley additive explanations (SHAPs), which is named the Deep-SHAP method. The Deep-SHAP method is adopted to provide a reasonable interpretable model for a DRL-based emergency control application. For the DRL model, the importance of input features has been quantified to obtain contributions for the outcome of the model. Further, feature classification of the inputs and probabilistic analysis of the outputs in the XAI model is added to interpretability results for better clarity.

Wind farm dynamic effect mitigation on power sharing and stability of MTDC grid through a supplementary controller

Effective and reliable integration of offshore wind farm to AC grid is easily achieved via multi-terminal HV direct current (MTDC) grid network. But the dynamics of wind power put stress on the converter terminals which may deteriorate its performance and life span. Therefore, a suitable control scheme is needed which minimizes the dynamic effect of wind farm power on the MTDC grid. This paper presents a supplementary linear quadratic regression (LQR) based control strategy to minimize the effect of wind farm power variability on dynamic power sharing capability of voltage source converter (VSC) terminals. The feedback gains with penalty weights of LQR control strategy optimizes the performance using linear matrix inequality (LMI) approach. The asymptotic convergence of LQR based controller is derived using the Lyapunov stability theorem. In addition to control design to achieve optimal power sharing in MTDC grid, an independent control is also applied on wind farm to exploit maximum power. This is achievable using sliding mode controller (SMC) on wind farm side. The active power sharing capability and DC voltage regulation with proposed control strategy follows smoothly with negligible oscillations against the dynamics of wind farm power variability and changes in converter terminal reference power. The proposed control approach remains effective to distribute the power flow among un-faulted converters against outage of converter terminals. This control strategy is able to share proportionate power according to converter rating, maintain minimum DC voltage deviation, even with time-varying power flow from the wind farm side. The performance of proposed control strategy is validated on five terminal MTDC system through MATLAB® simulations.

Wind-Farm Power Tracking Via Preview-Based Robust Reinforcement Learning

This article aims to address the wind-farm power tracking problem, which requires the farm's total power generation to track time-varying power references and, therefore, allows the wind farm to participate in ancillary services such as frequency regulation. A novel preview-based robust deep reinforcement learning (PR-DRL) method is proposed to handle such tasks which are subject to uncertain environmental conditions and strong aerodynamic interactions among wind turbines. To our knowledge, this is for the first time that a data-driven model-free solution is developed for wind-farm power tracking. Particularly, reference signals are treated as preview information and embedded in the system as specially designed augmented states. The control problem is then transformed into a zero-sum game to quantify the influence of unknown wind conditions and future reference signals. Built upon the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> control theory, the proposed PR-DRL method can successfully approximate the resulting zero-sum game's solution and achieve wind-farm power tracking. Time-series measurements and long short-term memory networks are employed in our DRL structure to handle the non-Markovian property induced by the time-delayed feature of aerodynamic interactions. Tests based on a dynamic wind-farm simulator demonstrate the effectiveness of the proposed PR-DRL wind-farm control strategy.

A data-driven linear formulation of the optimal demand response scheduling problem for an industrial air separation unit

Demand response (DR) has become a key element in balancing the power grid as the contribution of time-varying renewable power generation increases. Chemical plants are appealing candidates for DR programs as they offer large, concentrated and flexible loads. DR participation calls for frequent production rate changes over time scales that overlap with the dominant dynamics of the plant. Production scheduling should therefore consider the process dynamics explicitly. We present a data-driven approach for modelling the scheduling-relevant dynamics based on historical closed-loop operating data using autoregressive with extra inputs (ARX) models. We introduce a new, linear scheduling problem formulation based on the ARX representation, and demonstrate its implementation on an industrial air separation unit.

Discrete/continuous-time online algorithm application for time-varying optimal power flow in active distribution networks

This paper discusses and analyzes the latest online algorithm applications for time-varying optimal power flow problems in active distribution networks with numerous power-electronics-interfaced distributed energy resources, which bring significant time-varying characteristics to the optimal operation of active distribution networks. Conventional offline optimization algorithms are time-consuming and unable to track time-varying optimal solutions in highly variable environments. In contrast, online algorithms are characterized by fast calculation speeds and the ability to continuously track optimal solutions, thus having great potential in solving optimization problems that vary rapidly over time. In this paper, we design online time-varying optimal power flow algorithms based on the latest online algorithms, including three discrete-time algorithms (i.e., correction-only, prediction-correction, and correction-extra correction algorithms) and one continuous-time algorithm (i.e., prediction-correction interior-point method). According to our survey of the current applications of online algorithms, this study represents the first time that discrete-time prediction-correction and correction-extra correction algorithms have been applied in solving time-varying optimal power flow problems in active distribution networks. Detailed case studies, including correctness, validity, and sensitivity analysis, are carried out on a modified IEEE 33-node system. The numerical results reveal the advantages, disadvantages, and applicability of the proposed algorithms. Moreover, the characteristics of the discrete-time and continuous-time algorithms are compared intuitively. Finally, based on the numerical results, a guide for how to select an appropriate online time-varying optimal power flow algorithm for active distribution network optimization is provided, wherein the discrete-time prediction-correction optimal power flow algorithm is the most frequently recommended choice.

Analytical RS-GBSM-Based Nonstationary Low-Altitude Air-to-Air Channel Modeling over Open Area

Aerial communication is very flexible due to almost no restrictions on geographical conditions. In recent years, with the development and application of the unmanned aerial vehicle, the air-to-air communication attracts dense interests from the researchers. More accurate and precise channel modeling for air-to-air communication is a new hot topic because of its essential role in the performance evaluation of the systems. This paper presents an analytical nonstationary regular-shaped geometry-based statistical model for low-altitude air-to-air communication over an open area with considerations on ground scattering. Analytical expressions of the channel impulse response and the autocorrelation functions based on the three-ray model are derived. Based on the assumption of uniform distribution of the ground scatterers, the distributions of the channel coefficients such as time delay and path attenuation are derived, simulated, compared, and fitted. The nonstationary characteristics of the channel are observed through the time-variant distributions of the channel coefficients as well as the time-variant autocorrelated functions and time-variant Doppler power spectrum density.

Design and partial load operation optimization of integrated ship energy system based on supercritical CO2 waste heat recovery cycle

In the present work, a supercritical CO2 cycle, designed for recovering waste heat originating specifically from heavy-duty turbocharged diesel engines, constitutes the basis of an integrated energy system. The purpose of this system is to cover the time-varying power loads required during the operation of ships, appearing in diverse forms of energy (propulsive/mechanical, electrical, thermal). Optimization procedures are applied for the determination of the optimal design and of the optimal operational characteristics of the CO2 cycle during partial loading conditions. Appropriate techno-economic criteria are used for evaluating the optimality of the proposed engineering solutions. The effects of the added capital costs of the CO2 cycle on its useful power output are investigated, while the temporal variations of the energy loads are appropriately taken into account in the determination of the optimum CO2 cycle design characteristics. The inclusion of the CO2 cycle is economically justified, while a reduction of operational fuel costs from 5.8% to 6.3 % is achieved for a typical yearly energy profile, according to the optimal allocation of the useful power produced by the CO2 waste heat recovery cycle towards the propulsive or electric loads.