Search Results (12)

This article introduces a novel approach for developing an electrical model of the lithium batteries used in an electric ultralight aircraft. Currently, no method exists in the technical literature for accurately modeling the electrical characteristics of batteries in an electric aircraft, making this study a valuable contribution to the field. The proposed method was validated with an all-electric ultralight aircraft designed and constructed at the Pascual Bravo University Institution. To build the detailed model, a kinematic analysis was first conducted through takeoff tests, where data on the speed, acceleration, time, and distance required for takeoff were collected, along with measurements of the current and power consumed by the batteries. The maximum speed and acceleration of the aircraft were also recorded. These kinematic results were obtained using two batteries made from Samsung INR-18650-35E lithium-ion cells, and different wing configurations of the aircraft were analyzed to assess their impacts on the battery energy consumption. Additionally, the discharge cycles of the batteries were evaluated. In the second phase, laboratory tests were performed on the individual battery cells, and the Peukert coefficient was estimated based on the experimental data. Finally, using the Peukert coefficient and the kinematic results from the takeoff tests, the electrical model of the battery was fine tuned. This model allows for the creation of charging and discharging equations for ultralight lithium batteries. With the final electrical model and energy consumption data during takeoff, it becomes possible to determine the energy usage and flight range of an electric aircraft. The model indicated that the aircraft did not require a long distance to takeoff, as it reached the necessary takeoff speed in a very short time. The equations used to simulate the discharge cycles of the batteries and lithium cells accurately described their energy capacities. Full article

In this paper, it is experimentally proven that the generalized Peukert equation C(i,T) = C_m(T)/(1 + (i/i₀(T))^n(T)) is applicable to nickel–metal hydride batteries at any discharge currents, while the classical Peukert equation can be used only in a limited range of the discharge currents (approximately from 0.3 C_n to 3 C_n). In addition, the classical Peikert equation does not take into account the influence of the temperature of a battery on its released capacity. It is also proven that for the nickel–metal hydride batteries, the generalized Peukert equation heavily depends on battery temperature (via the parameters C_m(T), i₀(T) and n(T)). The temperature dependencies of the parameters of the generalized Peukert equation and their physical meaning are also established. The obtained generalized Peukert equation, which considers the batteries’ temperature, can be used at any discharge current and temperature of the batteries. Full article

The Peukert equation is widely used in various analytical models of lithium-ion batteries. However, the classical Peukert equation is applicable to lithium-ion batteries only in a limited range of discharge currents. Additionally, it does not take into account the temperature impact on a battery’s released capacity. In this paper, the applicability of the generalized Peukert equation C = C_m/(1 + (i/i₀)ⁿ) is investigated for the residual capacity determination of lithium-ion batteries based on the Hausmann model. It is proved that all the parameters (C_m, i₀, and n) of this equation depend on a battery’s temperature. That is why, for a battery-released capacity calculation, it is necessary to take into account the battery’s temperature. The equations are found to describe the temperature dependence of all the parameters of the generalized Peukert equation. The physical meaning of all the parameters is established and it is shown that the generalized Peukert equation obtained with temperature consideration is applicable to any current and temperature of a battery. Full article

The design and operation of performant and safe electric vehicles depend on precise knowledge of the behavior of their electrochemical energy storage systems. The performance of the battery management systems often relies on the discrete-time battery models, which can correctly emulate the battery characteristics. Among the available methods, electric circuit-based equations have shown to be especially useful in describing the electrical characteristics of batteries. To overcome the existing drawbacks, such as discrete-time simulations for parameter estimation and the usage of look-up tables, a set of equations has been developed in this study that solely relies on the open-circuit voltage and the internal resistance of a battery. The parameters can be obtained from typical cell datasheets or can be easily extracted via standard measurements. The proposed equations allow for the direct analytical determination of available discharge capacity and the available energy content depending on the discharge current, as well as the Peukert exponent. The fidelity of the proposed system was validated experimentally using 18650 NMC and LFP lithium-ion cells, and the results are in close agreement with the datasheet. Full article

The accuracy of Peukert’s battery capacity equation may decrease under the conditions of variable current and variable temperatures. Some researchers have previously tried to overcome the lack of C-rate change. However, the dependence of battery capacity on temperature is still not included. In this paper, we mainly studied the capacity reduction effect of batteries under variable temperatures. The proposed method can calculate the battery’s available capacity according to the specific discharge conditions. The experimental method proposed in this paper provides a reasonable test method to generate the required coefficients in order to establish a state of charge prediction model with high accuracy. After establishing the method, we can make a real-time prediction of the available energy of battery including the remaining energy of battery. From the result, we can see that the result is of great precision and the method is valuable. Full article

In this paper, it is shown that the Peukert generalized equations C = C_m/(1 + (i/i₀)ⁿ), C = 0.522C_mtanh((i/i₀)ⁿ/0.522)/(i/i₀)ⁿ and C = C_merfc((i/i_k − 1)/(1/n))/erfc(−n) are applicable for capacity estimation of the automotive-grade lithium-ion batteries within the discharge current range, from 0 to 10 C_n. Additionally, it is shown here that all the parameters (C_m, n, i₀ and i_k) in the Peukert generalized equations under study have a clear physical meaning, unlike in the classical Peukert equation, in which all the parameters are just empirical constants. In addition, it is shown that, in the case of lithium-ion batteries, the dependence of their released capacity on the discharge current reflects the phase transition statistical pattern in the electrodes’ active substance, which follows the normal distribution law. As the Peukert equation is used in many analytical models, the better electrochemical and physical meaning and understanding of this equation and its clarification are of great practical importance. Full article

In this paper, the applicability of the Peukert equation and its generalizations were investigated for capacity evaluation of automotive-grade lithium-ion batteries. It is proved that the classical Peukert equation is applicable within the range of the discharge currents from 0.2C_n to 2C_n (C_n is the nominal battery capacity). As a rule, the operating currents of many automotive-grade lithium-ion batteries are exactly within this range of the discharge currents. That is why, successfully, the classical Peukert equation is used in many analytical models developed for these batteries. The generalized Peukert equation C = C_m/(1 + (i/i0)ⁿ) is applicable within the discharge currents range from zero to approximately 10C_n. All kinds of operating discharge currents (including both very small ones and powerful short-term bursts) fall into this discharge currents range. The modified Peukert equation C = C_m(1 − i/i1)/((1 − i/i1) + (i/i0)ⁿ) is applicable at any discharge currents. This equation takes into account the battery’s internal resistance and has the smallest error of experimental data approximation. That is why the discussed modified Peukert equation is most preferable for use in analytical models of automotive-grade lithium-ion batteries. The paper shows that all the parameters of the generalized Peukert equations have a clear electrochemical meaning in contrast to the classical Peukert equation, where all the parameters are just empirical constants. Full article

The Peukert and Liebenow equations were obtained from experimental studies of lead–acid batteries. Currently, they are used to evaluate capacity released by batteries of other electrochemical systems (alkaline, lithium-ion, etc.), as well. In this paper, it is experimentally proved that for lithium-ion batteries, the Peukert equation can be used in two intervals of the discharge currents. The first interval includes currents from 0.2C_n up to the first inflection point of the experimental function of the battery capacity dependence on the discharge currents C(i). The second interval covers currents from the second inflection point of the experimental function C(i) up to the maximum currents that were used in the experiments. For some lithium-ion batteries, the range of low discharge currents, where the Peukert equation is applicable, is quite large and often completely covers the range of the discharge currents used in practice for these batteries. Therefore, many authors, when estimating the capacity of lithium-ion batteries, use the Peukert equation. However, the research in this paper shows that for lithium-ion batteries, the use of the Peukert equation is limited to the two discharge current ranges indicated above. Unlike the Peukert equation, the Liebenow equation can be used only in the range of small discharge currents from zero to the first inflection point of the experimental function C(i). Full article

In many studies, for predicting the remaining capacity of batteries belonging to different electrochemical systems, various analytical models based on the Peukert equation are used. This paper evaluates the advantages and disadvantages of the most famous generalized Peukert equations. For lithium-ion batteries, the Peukert equation cannot be used for estimation of their remaining capacity over the entire range of discharge currents. However, this paper proves that the generalized Peukert equations enable estimation of the capacity released by lithium-ion batteries with high accuracy. Special attention is paid to two generalized Peukert equations: C = C_m/(1 + (i/i0)ⁿ) and C = C_merfc((i-i0)/n))/erfc(-i0/n). It is shown that they correspond to the experimental data the best. Full article

In many papers for forecasting remaining capacity of lithium-ion batteries, various analytical models are used based on the Peukert equation. In this paper, it is shown that the classic Peukert equation is applicable in two ranges of discharge currents. The first range isis the battery released capacity and ) to currents at which the discharge capacity of battery begins to rapidly decrease. The second range of discharge currents is from the inflection point of experimental curve to the highest currents used in the experiments. In the first range of discharge currents, both the classic Peukert equation and the Liebenow equation can be used. The operating range of the discharge currents for commercial automotive-grade lithium batteries is in the first range. Therefore, in many of the analytical models, the classic Peukert equation (taking into account the temperature) is successfully used to estimate the remaining capacity of these batteries. An analysis and evaluation of advantages and disadvantages of all the most popular generalized Peukert equations is presented. The generalized Peukert equation with allowance for temperature is established, which makes it possible to estimate the released capacity with high accuracy for lithium-ion batteries. Full article

In this paper, a comprehensive model for LiFePO₄ batteries is proposed to ensure high efficiency and safe operation. The proposed model has a direct correlation between its parameters and the electrochemical principles to estimate the state of charge (SoC) and the remaining capacity of the LiFePO₄ battery. This model was based on a modified Thévenin circuit, Butler–Volmer kinetics, the Arrhenius equation, Peukert’s law, and a back propagation neural network (BPNN), which can be divided into two parts. The first part can be represented by the dual exponential terms, responsive to the Coulomb efficiency; the second part can be described by the BPNN, estimating the remaining capacity. The model successfully estimates the SoC of the batteries that were tested with an error of 1.55%. The results suggest that the model is able to accurately estimate the SoC and the remaining capacity in various environments (discharging C rates and temperatures). Full article

To achieve accurate state-of-charge (SoC) estimation for LiFePO₄ (lithium iron phosphate) batteries under harsh conditions, this paper resorts to the Peukert’s law to accommodate different temperatures and load excitations. By analyzing battery heat generation and dissipation, a thermal evolution model (TEM) is elaborated and exploited for on-line parameter identification of the equivalent circuit model (ECM). Then, a SoC estimation framework is proposed based on the Adaptive Extended Kalman Filter (AEKF) algorithm. Experimental results on a LiFePO₄ pack subject to the Federal Urban Driving Schedule (FUDS) profile under different temperatures and initial states suggest that the proposed SoC estimator provides good robustness and accuracy against changing temperature and highly dynamic loads. Full article