Nonlinear Thermal Model Research Articles

PV-EV Integrated Home Energy Management Considering Residential Occupant Behaviors

Rooftop photovoltaics (PV) and electrical vehicles (EV) have become more economically viable to residential customers. Most existing home energy management systems (HEMS) only focus on the residential occupants’ thermal comfort in terms of indoor temperature and humidity while neglecting their other behaviors or concerns. This paper aims to integrate residential PV and EVs into the HEMS in an occupant-centric manner while taking into account the occupants’ thermal comfort, clothing behaviors, and concerns on the state-of-charge (SOC) of EVs. A stochastic adaptive dynamic programming (ADP) model was proposed to optimally determine the setpoints of heating, ventilation, air conditioning (HVAC), occupant’s clothing decisions, and the EV’s charge/discharge schedule while considering uncertainties in the outside temperature, PV generation, and EV’s arrival SOC. The nonlinear and nonconvex thermal comfort model, EV SOC concern model, and clothing behavior model were holistically embedded in the ADP-HEMS model. A model predictive control framework was further proposed to simulate a residential house under the time of use tariff, such that it continually updates with optimal appliance schedules decisions passed to the house model. Cosimulations were carried out to compare the proposed HEMS with a baseline model that represents the current operational practice. The result shows that the proposed HEMS can reduce the energy cost by 68.5% while retaining the most comfortable thermal level and negligible EV SOC concerns considering the occupant’s behaviors.

Germination response of black nightshade (Solanum nigrum) to temperature and the establishment of a thermal time model

AbstractBlack nightshade (Solanum nigrum L.) is one of the worst weeds in crop fields, and it spreads mainly by the dispersal of seeds. Temperature is one of the key environmental factors affecting seed germination. We investigated the seed germination response to temperature in six populations of S. nigrum from mid- to northern China and derived mathematical models from germination data. The results showed that S. nigrum seeds exhibit distinct germination responses to temperature within the range of 15 to 35 C. The optimum temperature for populations XJ1600, JL1697, and HLJ2134 was 30 C, and those for populations NMG1704, HN2160, and LN2209 were 25, 20, and 15 C, respectively. Based on the nonlinear fitting and thermal time models, the predicted base temperatures of the six populations ranged from 2.3 to 6.4 C, and the required accumulated growing degree days (GDD) ranged from 50.3 to 106.0 C·d. The base temperatures and the accumulated GDD for germination differed among populations, and there was a significant negative correlation. HLJ2134 population required a high base temperature and accumulated GDD for germination, indicating that it might be highly adapted to a warmer and moister environment. Based on the different germination responses of S. nigrum populations to temperature, the thermal time model reflects an innate relationship between base temperature and accumulated GDD required for initiation of seed germination, which provides a better basis for predicting seedling emergence and the timing for optimal control of S. nigrum under field conditions.

Numerical simulation for melting heat transport in nanofluids due to quadratic stretching plate with nonlinear thermal radiation

The purpose of this investigation is to examine the effect of MHD on steady 2D transport of C6H9NaO7(SA)MWCNT&C6H9NaO7(SA)SWCNT nanofluids over a quadratic stretching surface with velocity slip conditions. Non-linear thermal radiation, melting phenomenon and CCHF model are also employed. Carbon nanotubes (CNTs) are taken as nanomaterials in this study which are then submerged in the base-fluid. Carbon nanotubes can effectively increase the thermal efficiency and the mechanical characteristics of the working liquid. The CNTs used in the presented research are thus studied with considerable potential for thermal applications. The mathematical expressions of the nano-fluid problem in state of PDEs are overset in the dimensionless ODEs by utilizing suitable variables. The numerical and graphical outcomes of the flow and thermal transport are investigated by utilizing the proficiency of the bvp4c technique (Labotto IIIA formula) in MATLAB. Furthermore, the rheological behavior of pertinent parameters is analyzed against the flow and thermal fields.

Non-linear thermal resistance model for the simulation of high power GaN-based devices

We report on the modeling of self-heating in GaN-based devices. While a constant thermal resistance is able to account for the self-heating effects at low power, the decrease of the thermal conductance of semiconductors when the lattice temperature increases, makes necessary the use of temperature dependent thermal resistance models. Moreover, in order to correctly account for the steep increase of the thermal resistance of GaN devices at high temperature, where commonly used models fail, we propose a non-linear model which, included in an electro-thermal Monte Carlo simulator, is able to reproduce the strongly non-linear behavior of the thermal resistance observed in experiments at high DC power levels. The accuracy of the proposed non-linear thermal resistance model has been confirmed by means of the comparison with pulsed and DC measurements made in devices specifically fabricated on doped GaN, able to reach DC power levels above 150 W mm−1 at biases below 30 V.

Demand Response Coupled with Dynamic Thermal Rating for Increased Transformer Reserve and Lifetime

(1) Background: This paper proposes a strategy coupling Demand Response Program with Dynamic Thermal Rating to ensure a transformer reserve for the load connection. This solution is an alternative to expensive grid reinforcements. (2) Methods: The proposed methodology firstly considers the N-1 mode under strict assumptions on load and ambient temperature and then identifies critical periods of the year when transformer constraints are violated. For each critical period, the integrated management/sizing problem is solved in YALMIP to find the minimal Demand Response needed to ensure a load connection. However, due to the nonlinear thermal model of transformers, the optimization problem becomes intractable at long periods. To overcome this problem, a validated piece-wise linearization is applied here. (3) Results: It is possible to increase reserve margins significantly compared to conventional approaches. These high reserve margins could be achieved for relatively small Demand Response volumes. For instance, a reserve margin of 75% (of transformer nominal rating) can be ensured if only 1% of the annual energy is curtailed. Moreover, the maximal amplitude of Demand Response (in kW) should be activated only 2–3 h during a year. (4) Conclusions: Improvements for combining Demand Response with Dynamic Thermal Rating are suggested. Results could be used to develop consumer connection agreements with variable network access.

Measurements and Computations of Internal Temperatures of the IGBT and the Diode Situated in the Common Case

This article proposes effective methods of measurements and computations of internal temperature of the dies of the Insulted Gate Bipolar Transistor (IGBT) and the diode mounted in the common case. The nonlinear compact thermal model of the considered device is proposed. This model takes into account both self-heating phenomena in both dies and mutual thermal couplings between them. In the proposed model, the influence of the device internal temperature on self and transfer thermal resistances is taken into account. Methods of measurements of each self and transfer transient thermal impedances occurring in this model are described and factors influencing the measurement error of these methods are analysed. Some results illustrating thermal properties of the investigated devices including the IGBT and the antiparallel diode in the common case are shown and discussed. Computations illustrating the usefulness of the proposed compact thermal model are presented and compared to the results of measurements. It is proved that differences between internal temperature of both dies included in the TO-247 case can exceed even 15 K.

Robust Nonlinear Economic MPC Based Management of a Multi Energy Microgrid

In this paper, the nonlinear economic model predictive control based energy management of a multi-energy microgrid is presented. The microgrid is composed of the district heating system with a cogeneration power plant supplying both the heat and the electricity demand of residential buildings with photovoltaic sources. Furthermore, access to liberalized heat and electricity market is assumed. This kind of environment requires consideration of the economical aspects, the technical aspects, the safety/quality of supply, and consumer preferences. The major contributions introduced in the presented approach are the following. A nonlinear formulation is adopted to capture the nonlinear thermal models and the nonlinear algebraic model of the heat supply network. The second major contribution is the economic character of the objective following the assumption of a liberalized market environment. Such formulation accounts for the specifics of the energy market organization. Finally, the stochastic nature of the planning problem is introduced through a practical robust formulation. The results obtained on a representative case study clearly show the benefits of the proposed approach compared to the traditional energy management approach.

Numerical study on magneto-acoustic thermal characteristics of micro-speaker for mobile phones

The numerical study was conducted on 1.2 W micro-speaker module of yoke thickness 0.40 mm without center air hole used in mobile phones and experimentally validated for sound pressure level and temperature distribution within ± 5.9% and ± 3.6%, respectively for frequency ranging from 100 Hz to 20 kHz. The sound pressure level, magnetic flux density, magnetic excitation force and temperature distribution of three different micro-speaker designs were evaluated. The micro-speaker module design with yoke thickness of 0.45 mm without center air hole showed superior acoustic, magnetic and thermal performance as compared to other module designs with the lowest voice coil temperature of 126.02 °C and the maximum sound pressure level of 118.6 dB around resonant frequency of 1100 Hz. The proposed nonlinear thermal model predicted the voice coil temperature accurately. In addition, the present study demonstrated the complete 3-dimensional thermal distribution of micro-speaker components and the detailed heat flow pattern.

Accurate Computation of IGBT Junction Temperature in PLECS

In the article, a new method to improve the accuracy of the insulated-gate bipolar transistor (IGBT) junction temperature computations in the piecewise linear electrical circuit simulation (PLECS) software is proposed and described in detail. This method allows computing the IGBT junction temperature using a nonlinear compact thermal model of this device in PLECS. In the method, a nonlinear compact thermal model of the IGBT is used, which considers the dependence of thermal resistance on the junction temperature. The usefulness of the method is experimentally verified, and it is confirmed that it increases the accuracy of the computations and shortens their time. The differences between the measured and computed characteristics are discussed. The application of the developed method for computations resulted in a significant reduction of their error to only a few percent. The developed method can be applied in the system-level simulations of the power electronics converters.

Optimal Solar Panel Area Computation and Temperature Tracking for a CubeSat System using Model Predictive Control

Recently, there has been a rising interest in small satellites such as CubeSats in the aerospace community due to their small size and cost-effective operation. It is challenging to ensure precision performance for satellites with minimum cost and energy consumption. To support maneuverability, the CubeSat is equipped with a propellant tank, in which the fuel must be maintained in the appropriate temperature range. Simultaneously, the energy production should be maximized, such that the other components of the satellite are not overheated. To meet the technological requirements, we propose a multicriteria optimal control design using a nonlinear dynamical thermal model of the CubeSat system. First, a PID control scheme with an anti-windup compensation is employed to evaluate the minimum heat flux necessary to keep the propellant tank at a given reference temperature. Secondly, a linearization-based controller is designed for temperature control. Thirdly, the optimization of the solar cell area and constrained temperature control is solved as an integrated nonlinear model predictive control problem using the quasilinear parameter varying form of the state equations. Several simulation scenarios for different power limits and solar cell coverage cases are shown to illustrate the trade-offs in control design and to show the applicability of the approach.

Compact Thermal Model of the Pulse Transformer Taking into Account Nonlinearity of Heat Transfer

This paper presents a compact nonlinear thermal model of pulse transformers. The proposed model takes into account differentiation in values of the temperatures of a ferromagnetic core and each winding. The model is formulated in the form of an electric network realising electrothermal analogy. It consists of current sources representing power dissipated in the core and in each of the windings, capacitors representing thermal capacitances and controlled current sources modelling the influence of dissipated power on the thermal resistances in the proposed model. Both self-heating phenomena in each component of the transformer and mutual thermal couplings between each pair of these components are taken into account. A description of the elaborated model is presented, and the process to estimate the model parameters is proposed. The proposed model was verified experimentally for different transformers. Good agreement between the calculated and measured waveforms of each component temperature of the tested pulse transformers was obtained. Differences between the results of measurements and calculations did not exceed 9% for transformers with a toroidal core and 13% for planar transformers.

Nonlinear Compact Thermal Model of the IGBT Dedicated to SPICE

In this article, the problem of modeling the thermal properties of the IGBT using a nonlinear compact thermal model is considered. This model has the form of an electrical network. In the proposed model, the influence of the internal temperature of this transistor on the efficiency of heat dissipation is taken into account. The elaborated model form is presented and the estimation method of this model parameters is described. The correctness of the new model is verified experimentally for different cooling conditions and different values of ambient temperature. Additionally, some results of calculations are compared to the results of calculations performed using selected models given in the literature.

Real-Time Prediction of Curing Processes using Model Order Reduction

Manifold engineering applications are directly affected by temperature. For rubber or composite curing processes, temperature distributions over time inside the compounds are crucial for chemical cross-linking reactions. Most of these reactions occur subsequently to a heating process during product cool down. Online prediction of cooling phases is performed during the actual heating process and hence, final cure status can be estimated before the actual process finishes. Therefore, mold temperatures and heating duration can be adapted in regard to current ambient conditions, and hence product quality is increased. In order to achieve longterm thermal predictions for complex product geometries, simulating nonlinear thermal finite element models is unfeasible, due to high computational effort. Hence, a prediction-model is derived from finite element analysis using matrix export, linearization, model order reduction algorithms such as rational Krylov or iterative rational Krylov and correction of operating point deviation. A special remark is given to temperature dependent boundary conditions, choice of time discretization and choice of solving algorithm, to address arising conflicting goals between execution time and simulation accuracy. Eventually, a complete process simulation is performed during the task-cycle time on a PLC control with a sufficiently high accuracy.

Optimal Retail Pricing for Demand Response of HVAC Systems in Commercial Buildings Considering Distribution Network Voltages

Retail pricing can be well deployed with support of distribution companies (DISCOs) to promote demand response (DR) programs using heating, ventilating, and air-conditioning (HVAC) systems as thermal energy storage resources. This paper proposes a retail pricing strategy to assist a DISCO and end-users in achieving optimal price-based DR for HVAC systems while considering operational aspects of distribution network. The pricing strategy is developed using a bi-level decision model. In the upper level, the DISCO optimizes the retail price to maximize its profit. In the lower level, the end-users schedule HVAC loads to minimize their electricity bills. The nonlinear thermal response model of an experimental building room is integrated with a data-driven model of an HVAC system and incorporated into the pricing strategy using piecewise linear approximation. The proposed strategy also employs time-of-use rates as retail price caps, leading to low-level price volatility. Case studies are presented for various ranges of bus voltage deviation and penetration levels of HVAC systems. The results demonstrate that the proposed strategy is effective for determining the optimal balancing point between the DISCO’s profit and end-users’ electricity bills while enabling the DISCO to reliably regulate the network voltages via the price-sensitive HVAC units.

Leakage-Aware Predictive Thermal Management for Multicore Systems Using Echo State Network

Leakage power is becoming significant in new generation IC chips. As leakage power is nonlinearly related to temperature, it is challenging to manage the thermal behavior of today’s multicore systems, since thermal management becomes a nonlinear control problem. In this paper, a new predictive dynamic thermal management (DTM) method with neural network thermal model is proposed to naturally consider the inherent nonlinearity between leakage and temperature. We start with analyzing the problems of using recurrent neural network (RNN) to build the nonlinear thermal model, and point out that there is exploding gradient induced long-term dependencies problem, leading to large model prediction errors. Based on this analysis, we further propose to use echo state network (ESN), which is a special type of RNN, as the leakage-aware nonlinear thermal model. We theoretically and experimentally show that ESN achieves much higher accuracy by completely avoiding the long-term dependencies problem. On top of this nonlinear ESN thermal model, we propose a novel model predictive control (MPC) scheme called ESN MPC, which uses iterative steps to find the optimal future power recommendations for thermal management. Being able to consider the leakage-temperature nonlinear effects and equipped with advanced control technique, the new method achieves an overall high quality temperature management with smooth and accurate temperature tracking. The experimental results show the new method outperforms the state-of-the-art leakage-aware multicore DTM method in both temperature management quality and computing overhead.

A 3-D nonlinear thermal circuit model of underground MV power cables and their joints

A 3D thermal model of underground power cable is presented in this paper. A detailed representation of the cable and its joints, the laying condition, the soil and the heat exchanges between soil upper surface and air, considering different weather conditions, is given. The model solves the thermal problem by means of an equivalent electric circuit and has been validated against field measurements, showing its applicability both for steady state and transient studies.In order to verify if any correlation between the occurrence of overheatings and the anomalous increase of failures, observed by Italian Distribution System Operators (DSOs) during summer 2015, exists, the model has been applied to simulate one-year operation of an existing underground cable. The cable is located in the MV distribution network owned by A.S.M. Terni S.p.A., the DSO in Terni, a city placed in the Central Italy. Ambient temperature and relative humidity trends have been taken from registrations made by a weather station, whereas the current profile along the cable has been assumed equal to that measured in 2015 by A.S.M., sampled every ten minutes. A second current profile has been also used, derived from the measured one in order to have the cable loaded at ampacity for a considerable time span during the year. In all cases, results show that no overheating occurred and, moreover, that the joint is the coldest part of the underground power cable.

Nonlinear Transient Thermal Modeling and Analysis of a Convective-Radiative Fin with Functionally Graded Material in a Magnetic Environment

Nonlinear transient thermal analysis of a convective-radiative fin with functionally graded materials (FGMs) under the influence of magnetic field is presented in this study. The developed nonlinear thermal models of linear, quadratic, and exponential variation of thermal conductivity are solved approximately and analytically using the differential transformation method (DTM). In order to verify the accuracies of the nonlinear solutions, exact analytical solutions are also developed with the aids of Bessel, Legendre, and modified Bessel functions. Good agreements are established between the exact and the approximate analytical solutions. In the parametric studies, effects of heat enhancement capacity of fin with functionally graded material as compared to fin with homogeneous material are investigated. Also, influence of the Lorentz force and radiative heat transfer on the thermal performance of the fin are analyzed. From the results, it is shown that increase in radiative and magnetic field parameters as well as the in-homogeneity index improve the thermal performance of the fin. Also, the transient responses reveal that the FGM fin with quadratic-law and exponential-law function shows the slowest and fasted thermal responses, respectively. This study will provide a very good platform for the design and optimization of an improved heat transfer enhancement in thermal systems, where the surrounding fluid is influenced by a magnetic field.

A Novel Optimal Combined Fuzzy PID Controller Employing Dragonfly Algorithm for Solving Automatic Generation Control Problem

In this paper, a novel optimal combined fuzzy PID controller employing Dragonfly Algorithm (DA) was proposed for solving Automatic Generation Control (AGC) problem in interconnected power systems. The DA algorithm was employed in this work to optimize the controller parameters including the scaling factors of fuzzy logic and the PID gains. To show the potential of the proposed approach, initially, a two equal areas non-reheat thermal power system was investigated, and then the proposed approach was extended to a typical AC/DC two-area multisource power system connected via an AC tie-line as well as High Voltage Direct Current (HVDC) transmission link. The superiority of the proposed controller was proven by comparing the obtained results with the previous AGC techniques reported in the literature. Moreover, sensitivity analysis was done. Further, the proposed control strategy was also extended to a nonlinear three-area thermal power system model by considering the effect of appropriate Generation Rate Constraint (GRC) with nonlinearity in each area. Finally, the results were tabulated in terms of settling time and peak overshoot. The comparative study demonstrates the effectiveness of the proposed control strategy and shows its robustness to enhance frequency regulation loop of linear and nonlinear interconnected power systems.

An analytical circuit based nonlinear thermal model for capacitor banks

The thermal couplings among capacitors in a bank could significantly alter the reliability performance compared to a single capacitor. The impact of thermal coupling is becoming stronger for high power density systems due to more stringent constraint in volume. Prior-art studies take into account the thermal coupling effects of a capacitor bank by either Finite Element Method (FEM) or experimental characterization, which are case dependent and time-consuming. This paper proposes a nonlinear mathematical model for capacitor banks based on physics of thermal conduction, convection, and radiation. A simplified version of the model is also obtained and represented by an RC circuit network, which enables computational-efficient thermal stress modeling. The proposed models are convenient to use to support model based sizing of capacitor banks and is scalable for multi-cell rectangle layout. A case study with experimental testing is discussed to verify the accuracy of the models.

Thermal aspects in friction stir process of AISI 316L: Numerical and experimental investigation

ABSTRACTFriction stir processing (FSP) is an innovative surface engineering method, considered as a green processing technique. A good physical understanding of the process can be reached by the combined efforts of experimental examination and numerical modeling. In this paper, numerical and experimental investigations of heat generation during FSP of AISI 316L were performed. A 3D nonlinear thermal model was developed to simulate the thermal history. The simulated temperature distributions were compared with experimental values.