Christoph Unterrieder

Modeling, Control, and Implementation of DC–DC Converters for Variable Frequency Operation

In this paper, novel small-signal averaged models for dc-dc converters operating at variable switching frequency are derived. This is achieved by separately considering the on-time and the off-time of the switching period. The derivation is shown in detail for a synchronous buck converter and the model for a boost converter is also presented. The model for the buck converter is then used for the design of two digital feedback controllers, which exploit the additional insight in the converter dynamics. First, a digital multiloop PID controller is implemented, where the design is based on loop-shaping of the proposed frequency-domain transfer functions. And second, the design and the implementation of a digital LQG state-feedback controller, based on the proposed time-domain state-space model, is presented for the same converter topology. Experimental results are given for the digital multiloop PID controller integrated on an application-specified integrated circuit in a 0.13 μm CMOS technology, as well as for the state-feedback controller implemented on an FPGA. Tight output voltage regulation and an excellent dynamic performance is achieved, as the dynamics of the converter under variable frequency operation are considered during the design of both implementations.

Battery State Estimation Using Mixed Kalman/Hinfinity, Adaptive Luenberger and Sliding Mode Observer

For electric vehicles, the improvement of the range of miles and with it the utilization of the available cell/battery capacity has become an important research focus in the community. For optimization of the same, an accurate knowledge of internal cell parameters like the state-of-charge (SoC) or the impedance is indispensable. Compared to the state-of-the-art, in this paper discrete-time Kalman and H∞ filtering based SoC estimation schemes - up to now applied to linear battery models - are applied to the nonlinear model of a Li-Ion battery. For that, a linearization method is proposed, which utilizes a prior knowledge about the predominant nonlinearities in the model together with a coarse SOC estimate to obtain a linear state estimation problem. Based on that, a mixed Kalman/H∞ filter-, a discrete-time sliding mode observer-, and an adaptive Luenberger based estimation scheme is furthermore investigated for the nonlinear battery model under test. The above-mentioned methods are compared to the state-of-the-art reduced order SoC observer and the Coulomb counting method. In order to compare the performance, an appropriate battery simulation framework is used, which includes measurement and modeling uncertainties. The evaluation is done with respect to the ability to reduce the impact of error sources present in realistic scenarios. For the simulated load current pattern, best results are achieved by the mixed Kalman/H∞ filtering approach, which achieves an average SoC estimation error of less than 1%.

Comparative study and improvement of battery open-circuit voltage estimation methods

Due to the steadily-increasing demands on more powerful electronic devices, an accumulators operating lifetime plays an essential role for the usability of battery-powered devices. To avoid an insufficient utilization of a cells energy and/or lifetime, a reliable and reasonably accurate knowledge of its internal parameters like the state-of-charge (SoC) is indispensable. The determination of the SoC is often directly related to the estimation of a batterys open-circuit voltage (OCV). In this work, various OCV estimation methods are compared with respect to their inherent accuracy. Additionally, the observability-Gramian-based OCV estimation method is extended to deal with expanded kinds of cell currents. Moreover, interpolation-based methodologies are presented which considerably reduce the average OCV estimation error over the entire SoC range, compared to state-of-the-art implementations.

Approximate least squares

We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithms properties including its complexity, and we present theoretical results as well as simulation based performance results. We describe the analysis of its convergence behavior and show that in the noise free case the algorithm converges to the least squares solution.

Battery Internal State Estimation: A Comparative Study of Non-Linear State Estimation Algorithms

The tracking of the internal states of a battery such as the state-of-charge (SoC) is a substantive task in battery management systems. In general, batteries are represented as linear or non-linear mathematical models. The extended Kalman filter (EKF) and the unscented Kalman filter (UKF) are widely used for the non-linear battery state estimation but their efficiency is limited. Recently, more efficient non-linear state estimation methods such as the cubature Kalman filter (CKF) and the particle filters (PF) have been developed. In this paper, we compare the efficiency and the complexity of different non-linear battery internal state estimation methods based on the EKF, the UKF, the CKF, and the PF. In addition to the SoC, the transient response of the battery is also estimated. The experimental results show that the PF- and the CKF-based methods perform best. Under the chosen conditions, the PF-based method achieves the root mean square error of approximately 3% of the SoC. Although, the efficiency of the PF is slightly better than the CKF, it is computationally more complex.

Step-adaptive approximate least squares

Recently, we proposed approximate least squares (ALS), a low complexity approach to solve the linear least squares problem. In this work we present the step-adaptive linear least squares (SALS) algorithm, an extension of the ALS approach that significantly reduces its approximation error. We theoretically motivate the extension of the algorithm, and introduce a low complexity implementation scheme. Our performance simulations exhibit that SALS features a practically negligible error compared to the exact LS solution that is achieved with only a marginal complexity increase compared to ALS. This performance gain is achieved with about the same low computational complexity as the original ALS approach.

Battery state-of-charge estimation prototype using EMF voltage prediction

A reliable knowledge of cell parameters like the state-of-charge (SoC) is essential for the optimization of battery-powered applications. Usually, during relaxation (the phase of no or low loads) the SoC is determined based on the measurement of the batterys electro-motive force (EMF). To obtain a reliable measurment, it is required that the battery voltage transient is in a well-relaxed state, which is rarely reached in practice (e.g. due to periodic discharge activities). In this paper, a predictive methodology is presented which is able to forecast the EMF and therewith the SoC already during a not well-relaxed state of the voltage transient. A nonlinear relaxation voltage model is reformulated such that the problem can be treated as a linear least squares estimation problem. Based on this estimation, the performance is evaluated with respect to the following aspects: prediction time, current rate influence, SoC influence, cell-to-cell deviation, or rather aging and temperature effects. Experimental results are presented for a fixed-point implementation of the estimation scheme on a CY8CKIT-050 PSOC5 programmable system on chip. For validation, measurements of 2.25Ah Sanyo UR18650A lithium cells have been used. It is shown that the presented approach offers an improved re-initialization methodology for the Coulomb counting method, and that it clearly outperforms the usual EMF-measurement based SoC determination method.

Battery Internal State Estimation: Simulation Based Analysis on EKF and Auxiliary PF

In battery management systems, the estimation of internal cell parameters has become an important research focus in the recent years. Exemplarily, this includes the tracking of parameters such as the internal cell impedances, the cell capacity, or the state-of-charge (SoC) of a battery. In general, the battery is considered to be a non-linear dynamic system. Hence, this paper compares the accuracy and the complexity of the extended Kalman filter (EKF) and the particle filter (PF), which are applied for the estimation of internal cell states such as the SoC and the batterys transient response. The comparison shows that the PF yields better accuracy compared to the EKF under the given conditions. However, the EKF is computationally less complex compared to the PF.

Low-complexity, high frequency parametric system identification method for switched-mode power converters

Online system identification provides the possibility to track system changes and thus is the basis for successive adaption of control parameters. This paper introduces a concept for fast, efficient and accurate coefficient estimation of time-discrete transfer functions. The presented approach approximates least squares and, compared to well established algorithms, it drastically reduces the computational-complexity, while maintaining sufficient accuracy. In the experimental setup this technique has been applied to a dc-dc buck converter. For this application the proposed method is especially beneficial, since it significantly reduces the system excitation time compared to the state-of-the-art. This is achieved by using higher switching frequencies, while keeping the amount of used switching periods constant. Consequently, the proposed concept can be integrated into the start-up procedure of the converter module.

Computer-Aided Optimization for Predictive Battery State-of-Charge Determination

Optimizing the battery management of todays portable electronic applications goes hand in hand with the reliable and accurate knowledge of the batterys state-of-charge (SoC). During periods of low load, usually the SoC is determined based on the measurement of the corresponding open-circuit voltage (OCV). This requires a battery to be in a well-relaxed state, which can take more than 3 hours depending on influence factors like the SoC itself and the temperature. Unfortunately, a well-relaxed state is rarely reached in real world scenarios. As an alternative, predicted OCV values can be used to estimate the SoC. In this work, we use a polynomial-enhanced model description for the OCV prediction process. After identifying the critical model parameters, a computer-aided parameter optimization methodology is applied to optimize the OCV prediction process. As a major result, the proposed methodology enables the possibility to optimize the OCV prediction process with respect to a specified SoC estimation accuracy.