Box Model Approach Research Articles

Experimental and analytical evaluation of exhaust air heat pumps in ventilation-based heating systems

The application of exhaust air heat pumps as an energy efficient heating technology to cover the heating and ventilation demand of highly efficient residential buildings is becoming popular. Available studies on exhaust air heat pumps tend mostly to focus only on comparing different technologies in efficient buildings. Most of the existing studies ignore the usual presence of the electrical heaters as backup. Moreover, the impact of varying boundary conditions on the heat pump's performance is often not considered in depth. In this sense, there is still a need for discussion on the influence of different buildings' standards and control strategies on heating performance. The present paper aims to consider the energy efficiency of exhaust air heat pumps under different operating conditions. In this study, the results of a long-term field monitoring are utilized to model the dynamic behavior of an exhaust air heat pump in MATLAB/Simulink using black box modeling approach. The impact of different boundary conditions such as outdoor and exhaust air conditions on the heat pump's efficiency is studied and additionally compared to other studies. Moreover, a physical approach to model the defrosting process of the evaporator was developed and integrated into the black-box model; to use annual simulations of ventilation-based heating systems in three different building standards. Finally, the influence of five different control strategies on system performance is investigated. The core findings of this study reveal that: (1) Due to the limited exhaust air volume flow rate the impact of the exhaust air moisture content with its condensation enthalpy on the HP performance is significant. (2) In designing ventilation-based heating systems with exhaust air heat pumps due to their limited power (e.g. 6 Wh/m³ at A-2), the control strategy of backup electrical heaters must be selected carefully. (3) Conventional heating control methods such as Nighttime Temperature Reduction (NTR) following a reference room are hardly suitable in ventilation-based heating systems. (4) However, employing the deployed control strategy, the electrical energy consumption of the system could be reduced up to 40% compared to the conventional heating control methods.

The slow and steady salinization of Sparkling Lake, Wisconsin

The concentrations of conservative solutes in seepage lakes are determined by the relative inputs of precipitation vs. groundwater. In areas of road salt application, seepage lakes may be at high risk of salinization depending on groundwater flow. Here, we revisit a 1992 analysis on the salinization of Sparkling Lake, a deep seepage lake in Northern Wisconsin. The original analysis predicted a rapid increase in chloride concentrations before reaching a steady steady of 8 mg L−1 by 2020. Forty years of monitoring Sparkling Lake show that rather than reaching a dynamic equilibrium, chloride concentrations have steadily increased. We update the original box model approach by adding a soil reservoir component that shows the slow steady rise in chloride is the result of terrestrial retention. For freshwater rivers and lakes, chloride retention on the landscape will both delay chloride impairment and prolong recovery and must be considered when modeling future chloride contamination risk.

Reproducing pyroclastic density current deposits of the 79 CE eruption of the Somma–Vesuvius volcano using the box-model approach

Abstract. We use PyBox, a new numerical implementation of the box-model approach, to reproduce pyroclastic density current (PDC) deposits from the Somma–Vesuvius volcano (Italy). Our simplified model assumes inertial flow front dynamics and mass deposition equations and axisymmetric conditions inside circular sectors. Tephra volume and density and total grain size distribution of EU3pf and EU4b/c, two well-studied PDC units from different phases of the 79 CE Pompeii eruption, are used as input parameters. Such units correspond to the deposits from variably dilute, turbulent PDCs. We perform a quantitative comparison and uncertainty quantification of numerical model outputs with respect to the observed data of unit thickness, inundation areas and grain size distribution as a function of the radial distance to the source. The simulations consider (i) polydisperse conditions, given by the total grain size distribution of the deposit, or monodisperse conditions, given by the mean Sauter diameter of the deposit; (ii) axisymmetric collapses either covering the whole 360∘ (round angle) or divided into two circular sectors. We obtain a range of plausible initial volume concentrations of solid particles from 2.5 % to 6 %, depending on the unit and the circular sector. Optimal modelling results of flow extent and deposit thickness are reached on the EU4b/c unit in a polydisperse and sectorialized situation, indicating that using total grain size distribution and particle densities as close as possible to the real conditions significantly improves the performance of the PyBox code. The study findings suggest that the simplified box-model approach has promise for applications in constraining the plausible range of the input parameters of more computationally expensive models. This could be done due to the relatively fast computational time of the PyBox code, which allows the exploration of the physical space of the input parameters.

Planning and implementation of a digital shadow for the friction factor quantification of the ECAP process using a grey box modeling approach and finite element analysis

This paper describes the possibility of analytical friction factor generation using a Grey Box modelling approach. A preprocessor is used, which automatically collects measured data via a Smart Production Network and calculates the effective friction coefficient as a function of all significant process parameters of the Equal-Channel-Angular-Pressing (ECAP) process using a data-driven evaluation algorithm. The results of this calculation are then automatically implemented in an efficiently programmed finite element analysis. This Digital Shadow then serves as the basis for the implementation of a Digital Twin, which is described shortly at the end.

Modeling and Validation of a Four‐Tank System for Level Control Process Using Black Box and White Box Model Approaches

Mathematical modeling of a system plays a vital role in controller design, tuning to meet the desired specifications and process parameter optimization. In this paper, different identification algorithms are implemented in the four‐tank system to demonstrate the superiority of the recommended subspace system identification method (Numeric Algorithms for Subspace State Space System Identification [N4SID]) for the different input design. A system identification method was utilized to identify the model of a dynamic system. It is modeled using the First‐Principle Method (FPM), Prediction Error Method (PEM) and Numeric Algorithms for N4SID method. The identification is performed through MATLAB. The plant input and output is acquired through LabVIEW. The developed models are validated with a new dataset based on the model performance specifications: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and Best Fit Rate (BFR). The results show that the proposed N4SID method with the amplitude‐modulated pseudorandom binary signal (APRBS) signal is better than the other methods with different inputs. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

On the concentration of SARS-CoV-2 in outdoor air and the interaction with pre-existing atmospheric particles

The spread of SARS-CoV-2 by contact (direct or indirect) is widely accepted, but the relative importance of airborne transmission is still controversial. Probability of outdoor airborne transmission depends on several parameters, still rather uncertain: virus-laden aerosol concentrations, viability and lifetime, minimum dose necessary to transmit the disease. In this work, an estimate of outdoor concentrations in northern Italy (region Lombardia) was performed using a simple box model approach, based on an estimate of respiratory emissions, with a specific focus for the cities of Milan and Bergamo (Italy). In addition, the probability of interaction of virus-laden aerosol with pre-existing particles of different sizes was investigated. Results indicate very low (<1 RNA copy/m3) average outdoor concentrations in public area, excluding crowded zones, even in the worst case scenario and assuming a number of infects up to 25% of population. On average, assuming a number of infects equal to 10% of the population, the time necessary to inspire a quantum (i.e. the dose of airborne droplet nuclei required to cause infection in 63% of susceptible persons) would be 31.5 days in Milan (range 2.7–91 days) and 51.2 days in Bergamo (range 4.4–149 days). Therefore, the probability of airborne transmission due to respiratory aerosol is very low in outdoor conditions, even if it could be more relevant for community indoor environments, in which further studies are necessary to investigate the potential risks. We theoretically examined if atmospheric particles can scavenge virus aerosol, through inertial impact, interception, and Brownian diffusion. The probability was very low. In addition, the probability of coagulation of virus-laden aerosol with pre-existing atmospheric particles resulted negligible for accumulation and coarse mode particles, but virus-laden aerosol could act as sink of ultrafine particles (around 0.01 μm in diameter). However, this will not change significantly the dynamics behaviour of the virus particle or its permanence time in atmosphere.

Evaluating 5 decades of atmospheric 85Kr measurements in the southern hemisphere to derive an input function for dating water and ice with implications for interhemispheric circulation and the global 85Kr emission inventory

In July 2015, the currently only active monitoring station for atmospheric 85Kr measurements in the southern hemisphere went operational at the Commonwealth Scientific and Industrial Research Organization (CSIRO) in Adelaide, Australia. Here, this new data is presented and combined with measurements from historic monitoring stations, to generate a85Kr input function for the southern hemisphere which is crucial for the application of 85Kr as a dating tracer for water and ice. After a linear increase in atmospheric 85Kr concentrations between 1980 and 2005, concentrations stabilized yielding mean 85Kr activity concentration during the Adelaide monitoring period of 1.3 ± 0.15 Bq/m³ air with slight variations indicating seasonal effects.Data from three northern hemispheric monitoring stations Schauinsland, Freiburg and Jungfraujoch of the German Federal Office for Radiation Protection (BfS), located in Central Europe are used to calculate an interhemispheric exchange time of 1.25 ± 0.24 years, using a simple box model approach. Furthermore, it is investigated whether a southern hemispheric 85Kr input function can be calculated from the baseline of the northern hemispheric data set. A comparison between the calculated and the fitted input function shows that analytical techniques can just resolve the concentration differences, emphasising the need of southern hemispheric monitoring stations for 85Kr. Analysing the decay-corrected input function and taking the current detection limit of low-level counting and Atom Trap Trace Analysis of 0.05 Bq/m³ air, a maximum apparent 85Kr tracer age of 40 years can be determined in the southern hemisphere. Finally, the 85Kr measurements are used to derive global 85Kr emission rates which are found to be in good agreement with published emissions from nuclear reprocessing plants.

Black box modeling approaches to judge the influence of a yeast extract on microbial growth and production

Black box modeling approaches to judge the influence of a yeast extract on microbial growth and production

Quantification of Po-210 and Pb-210 as tracer of sediment resuspension rate in a shallow riverine system: Case study from southeast Michigan, USA

Polonium-210 and Pb-210 were measured in surficial benthic sediments and particulate matter collected in sediment traps deployed at five different locations in the Clinton River, a dynamic system, in Lake St. Clair in Southeast Michigan to quantify the sediment resuspension rates and determine the particle residence time. The mean 210Poxs/210Pbxs activity ratio of suspended trap and surficial bottom sediments were 0.72 ± 0.12 (n = 16, range: 0.42–0.89) and 0.79 ± 0.15 (n = 15, range: 0.40–1.00) indicating that a major fraction of trapped material is from resuspended bottom sediments. Sediment resuspension rate calculated using a single box model approach yielded a resuspension rate of 0.1–1.0 g cm−2 yr−1 using 210Po and 0.2–1.4 g cm−2 yr−1using 210Pb. Particle residence time varied from 0.3 to 3.9 days using 210Pb and 0.9–13.4 days for 210Po. This present study indicates that sediment resuspension is considerably high in Clinton River and thus any decision on remedial action towards the restoration such as dredging, natural attenuation is challenging. This present study has direct relevance to the transport and resuspension of other sulfur group elements (Se, O, etc) and lithogenic elements (e.g., Th).

Estimation of submarine groundwater discharge and nutrient loading using radium isotopes quartet in Kuwait

The water resources in the arid region like Kuwait are a scarce commodity. With the increasing population, industry and urbanization have lead to the demand of water resources with respect to both in quantity and quality. Therefore, quantification of submarine groundwater discharge is essential for sustainable groundwater management. Moreover, submarine groundwater discharge plays a vital role in delivering nutrients, dissolved carbon, and trace elements to the sea. This study used the naturally occurring radioactive isotopes to identify and estimate the SGD in the coastal strip of Kuwait along the Arabian Gulf. The study gains its significance in determining the loss of brackish groundwater from inland, in the arid region. The groundwater samples were collected from wells along the coast. Seawater samples were collected from Kuwait bay and open sea in transects. Samples were analyzed for major ions, nutrients, and 223Ra, 224Ra, 226Ra, and 228Ra. Box model and offshore gradient model approaches were used to estimate the SGD. The variation of 223Ra, 224Ra, 226Ra, and 228Ra concentrations was studied in different transects, and it was inferred to be influenced by the Kuwait coastal jet in the territorial waters. The water mass residence time calculated for the Kuwait Bay and the open sea ranged from 10 to 58 and 12 to 64 days, respectively. The 223Ra-based horizontal eddy diffusion coefficients for the Kuwait Bay and the south Arabian Gulf were 205.1 and 827.5 m2/s, respectively. The estimation of SGD fluxes in the Kuwait Bay using box model approach based on the spatial distribution of 226Ra and 228Ra were 3.05 × 106 and 5.46 × 106 m3/day, respectively. Similarly, the estimated SGD fluxes for the south Arabian Gulf by offshore gradient model using 226Ra and 228Ra concentrations were 2.92 × 108 and 3.0 × 107 m3/day, respectively. The nutrient fluxes from groundwater to Kuwait Bay and open sea were estimated for PO43−-P, SiO2-Si, and NO3−-N using box model and offshore gradient model approach.

A Large-Eddy Simulation Study of Contrail Ice Number Formation

AbstractIce crystal number is a critical ingredient in the potential climate impact of persistent contrails and contrail-induced cirrus. We perform an extensive set of large-eddy simulations (LES) of ice nucleation and growth within aircraft exhaust jets with an emphasis on assessing the importance of detailed plume mixing on the effective ice-number emission index (EIiceno) produced for different conditions. Parameter variations considered include ambient temperature, pressure, and humidity; initial aerosol origin (exhaust or ambient), number, and properties; and aircraft engine size. The LES are performed in a temporal representation with binned microphysics including the basics of activation of underlying aerosol, droplet growth, and freezing. We find that a box-model approach reproduces EIiceno from LES well for sufficiently low aerosol numbers or when crystal production is predominantly on ambient aerosol. For larger exhaust aerosol number the box model generally overestimates EIiceno and can underestimate the fraction from ultrafine aerosol. The effects of different parameters on EIiceno can largely be understood with simpler analytic models that are formulated in low and high aerosol-number limits. The simulations highlight the potential importance of “cold” contrails, ambient ultrafine aerosols, crystal loss due to competition between different-sized crystals, and limitations on reducing EIiceno. We find EIiceno insensitive to engine size for lower aerosol numbers, but decreasing with increasing engine size for higher aerosol numbers. Temporal versus spatial representations for jet LES are compared in an appendix.

Classic and Reaction-Diffusion Models Used in Modified Atmosphere Packaging (MAP) of Fruit and Vegetables

Fruits and vegetables continue metabolic processes after being harvested. In some produce, mainly climacteric fruits, these processes cause deterioration of the produce during storage. To reduce the deterioration rate, several strategies have been implemented for postharvest handling. One of these preservation strategies is modified atmosphere packaging (MAP). In this technology, the respiration rate of the produce and the gas permeability of the storage film are the two fundamental kinetic processes accounted for in designing the packaging system. To understand the relationship of these two kinetic processes during packaging in modified atmospheres, two major techniques have been presented from the standpoint of mathematical modeling: the classic respiration rate models and the reaction-diffusion model. In the classic model of respiration rate, four types of black box model approaches have been proposed: linear, polynomial, exponential, and the Michaelis–Menten kinetic models. For the last black box model, four types of inhibition approaches are considered: competitive, uncompetitive, noncompetitive, and, finally, a combination of competitive and uncompetitive inhibition. In the reaction-diffusion model, it has been considered that the transport of a species in modified atmosphere packaging (mass transport in the headspace and the film used as packaging) obeys strictly diffusive transport models. For this reason, the main objective of this review is to show the advances in the two major techniques (classic respiration rate models and the reaction-diffusion model) implemented to describe the MAP of fruit and vegetables, as described in specialized literature.

Initiation of dilute and concentrated pyroclastic currents from collapsing mixtures and origin of their proximal deposits

Numerical solution of the time-dependent conservation equations for mass, momentum, specific internal energy, and granular temperature in flows involving gas-particle mixtures is used to explore the initiation of pyroclastic currents from collapsing mixtures such as during fountaining eruptions. One objective is to determine when a depth-averaged granular flow model or a box model for dilute currents is most applicable for hazards modeling of pyroclastic currents produced by column collapse; a second objective is to gain insight into the formation of proximal breccia facies of ignimbrites. Collapsing gas-particle mixtures impacting a flat surface are modeled with mixtures of coarse particles that are poorly coupled with the gas phase and well-coupled fine particles. Resulting lateral flows are sensitive to the impact speed, overall particle concentration, and proportions of fine and coarse particles. For total particle concentrations of around 1 vol.%, an impacting mixture consisting of at least ~ 50% coarse particles, relative to fines, will tend to form a concentrated lateral underflow, which can be approximated by a depth-averaged granular flow model for hazard assessment purposes starting from the impact zone. Low total particle concentrations (e.g., total concentrations of ~ 0.1 vol.%) tend to produce dilute lateral flows that could be simplified to box model approaches for dilute pyroclastic currents. Larger total particle concentrations in impacting mixtures (~ 10 vol.%) produce granular underflows if they have any coarse particles, but these can be complicated by Mach number effects. For intermediate concentrations of the impacting mixture, a rough threshold for development of a concentrated underflow versus a dilute-only current is based upon the flux per unit area of coarse particles to the impact and their Stokes numbers. In general, some knowledge of the eruption column (fountain) conditions is required in order to make an informed decision as to which hazards modeling approach is most applicable for a given scenario. Modeling indicates that proximal breccias are related to influxes of coarse wall-rock material into an eruptive mixture, which increase both the total particle concentration and the proportion of coarse, dense clasts in the mixture that subsequently collapses and impacts the ground. The breccias record concentration of dominantly coarse clasts immediately upon impact and formation of concentrated flows that propagate laterally while expelled fines and gas flow rapidly overhead as dilute currents. Lateral and vertical heterogeneity in proximal deposits likely record rapid time and space variations in avalanches of material into eruptive vents, and the occurrence of breccia hummocks might record the temporary positions of impact zones.

Zn Isotope Composition in the Water Column of the Northwestern Pacific Ocean: The Importance of External Sources

AbstractWe determined Zn isotope composition (δ66Zn) in the water column of the Northwestern Pacific Ocean (NWPO) and its marginal seas to investigate the processes driving vertical and spatial variations. Comparable to previous studies, dissolved δ66Zn was relatively low in the top 200 m, ranging from −0.91 to +0.24‰ and increased with depth toward an averaged value, +0.38±0.10‰, in deep water. We found that δ66Zn observed in the deep water of the NWPO was much lower than the Northeastern Pacific Ocean. Box model approaches suggest that spatial variations in the deep water may be attributed to isotopically light Zn originating from sedimentary input or anthropogenic aerosols. In the surface water, the fractionation factors derived from both closed or open system fractionation models are all less than one in the NWPO. However, both closed and open system models show a relatively poor fit to the measured data. We thus propose that external input is a major factor causing the variations of [Zn] and δ66Zn values in surface water, in addition to the effects of scavenging, physical mixing, and biological uptake. As elevated [Zn] and relatively light δ66Zn in the surface water were observed in high aerosol input regions, aerosol deposition may play a dominant role in regulating Zn elemental and isotopic composition in the surface ocean.

Exploration of Jute-HCP Composites Material for Building Environments

ABSTRACT Jute and hollow conjugated polyester fiber (HCP)-reinforced nonwoven composites were designed by Box and Behnken model approach. Its thermal properties such as thermal conductivity, thermal resistance, thermal transmittance, and thermal diffusivity were evaluated. From the test results of response surface method (RSM), the weight of composite material maintained as 3280 g/m2 with the proportion of jute/HCP fiber in the ratio of 50/50%, 60/40%, and 70/30% played a significant role in insulation and mechanical properties. Various needling density maintained on the composite material such as 300, 150, and 75 punches/cm2 contributes to the role of significant impacts on the research process. The optimum of 150 needling density with the proportion of 50/50 Jute and HCP fiber was selected to produce four kinds of composite structures. Its thermal, sound, electrical insulation values and limiting oxygen values were analyzed and suggested for building environments.

Fractional order neural networks for system identification

Abstract Neural networks and fractional order calculus have shown to be powerful tools for system identification. In this paper we combine both approaches to propose a fractional order neural network (FONN) for system identification. The learning algorithm was generalized considering the Grunwald-Letnikov fractional derivative. This new black box modeling approach is validated by the identification of three different systems (two benchmark systems and a real system). Comparisons vs others approaches showed that the proposed FONN model reached better accuracy with less number of parameters.

A box-model approach for reservoir operation during extreme rainfall events: A case study

Extreme rainfall events in an urban area pose various challenges to the water resource managers in terms of flood mitigation, inundation, water conservation and harvesting for drinking water supply. The objective of this study is to apply the box-model approach to evaluate reservoir operation during extreme rainfall events. A large water supply reservoir in Chennai was chosen to carry out this study. A box model, based on input–output parameters, is proposed to simulate the reservoir operation and hydraulic behaviour. Hydrologic Engineering Centre-Hydrologic Modelling System (HEC-HMS) has been used to simulate the reservoir inflow hydrograph and to understand the run-off characteristics of the basin. Three extreme rainfall events occurred in past have been selected for the analysis. Three different scenarios have been framed to assess the reservoir performance. Reducing the initial storage to 50% and releasing water at the beginning of the event gives a possible solution for flood mitigation in reducing the outflow volume by 9–37% and delaying the time to peak by 1–6 h. Though the reduced outflow volume from this reservoir is less, it can help to mitigate the flood inundation to a significant extent. Thus the box-model approach presented here can be utilised as a simple tool to generate the various combinations of outflow hydrographs for any reservoir.

High Emissions of Carbon Dioxide and Methane From the Coastal Baltic Sea at the End of a Summer Heat Wave

The summer heat wave in 2018 led to the highest recorded water temperatures since 1926 – up to 21 C – in bottom coastal waters of the Baltic Sea, with implications for the respiration patterns in these shallow coastal systems. We applied cavity ring-down spectrometer measurements to continuously monitor carbon dioxide (CO2) and methane (CH4) surface-water concentrations, covering the coastal archipelagos of Sweden and Finland and the open and deeper parts of the Northern Baltic Proper. This allowed us to i) follow an upwelling event near the Swedish coast leading to elevated CO2 and moderate CH4 outgassing, and ii) to estimate CH4 sources and fluxes along the coast by investigating water column inventories and air-sea fluxes during a storm and an associated downwelling event. At the end of the heat wave, before the storm event, we found elevated CO2 (1583 µatm) and CH4 (70 nmol/L) concentrations. During the storm, a massive CO2 sea-air flux of up to 274 mmol m-2 d-1 was observed. While water-column CO2 concentrations were depleted during several hours of the storm, CH4 concentrations remained elevated. Overall, we found a positive relationship between CO2 and CH4 wind-driven sea-air fluxes, however, the highest CH4 fluxes were observed at low winds whereas highest CO2 fluxes were during peak winds, suggesting different sources and processes controlling their fluxes besides wind. We applied a box-model approach to estimate the CH4 supply needed to sustain these elevated CH4 concentrations and the results suggest a large source flux of CH4 to the water column of 2.5 mmol m-2 d-1. These results are qualitatively supported by acoustic observations of vigorous and widespread outgassing from the sediments, with flares that could be traced throughout the water column penetrating the pycnocline and reaching the sea surface. The results suggest that the heat wave triggered CO2 and CH4 fluxes in the coastal zones that are comparable with maximum emission rates found in other hot spots, such as boreal and arctic lakes and wetlands. Further, the results suggest that heat waves are as important for CO2 and CH4 sea-air fluxes as the ice break up in spring.

New Insights Into Processes Controlling the δ30Si of Sinking Diatoms: A Seasonally Resolved Box Model Approach

AbstractIn the Southern Ocean, the silicon (Si) biogeochemical cycle is dominated by processes such as the supply of Si into the surface waters, Si uptake into diatom frustules, and their subsequent dissolution and export. Due to the incomplete assimilation of the silicic acid pool (DSi) and isotopic fractionation during silicification, the Si isotopic composition (δ30Si) of biogenic silica (BSi) is closely linked to the degree of Si utilization in the mixed layer (ML). In this study, we combined modelling approaches and seasonal sediment trap records of δ30Si of exported BSi to investigate the magnitude, timing, and isotopic composition of the flux of siliceous particles transferred from the surface to the deep ocean. We implemented a box model to describe the temporal evolution of DSi and BSi concentrations and δ30Si in the ML and at depth. The model allows us to quantify fluxes of Si in and out of the ML associated with export, dissolution, and mixing. It highlights that the time‐integrated δ30Si of exported BSi measured in the sediments reflects the extent of DSi consumption at the time when net BSi production and diatom accumulation are maximal in the ML and confirms that the δ30Si of diatoms is a reliable proxy for past Si utilization.

An Accurate and Precise Grey Box Model of a Low-Power Lithium-Ion Battery and Capacitor/Supercapacitor for Accurate Estimation of State-of-Charge

The fluctuating nature of power produced by renewable energy sources results in a substantial supply and demand mismatch. To curb the imbalance, energy storage systems comprising batteries and supercapacitors are widely employed. However, due to the variety of operational conditions, the performance prediction of the energy storage systems entails a substantial complexity that leads to capacity utilization issues. The current article attempts to precisely predict the performance of a lithium-ion battery and capacitor/supercapacitor under dynamic conditions to utilize the storage capacity to a fuller extent. The grey box modeling approach involving the chemical and electrical energy transfers/interactions governed by ordinary differential equations was developed in MATLAB. The model parameters were extracted from experimental data employing regression techniques. The state-of-charge (SoC) of the battery was predicted by employing the extended Kalman (EK) estimator and the unscented Kalman (UK) estimator. The model was eventually validated via loading profile tests. As a performance indicator, the extended Kalman estimator indicated the strong competitiveness of the developed model with regard to tracking of the internal states (e.g., SoC) which have first-order nonlinearities.