Co-simulation Methodologies for Hybrid and Electric Vehicle Dynamics

In recent decades, full electric and hybrid electric vehicles have emerged as an alternative to conventional cars due to a range of factors, including environmental and economic aspects. These vehicles are the result of considerable efforts to seek ways of reducing the use of fossil fuel for vehicle propulsion. Sophisticated technologies such as hybrid and electric powertrains require careful study and optimization. Mathematical models play a key role at this point. Currently, many advanced mathematical analysis tools, as well as computer applications have been built for vehicle simulation purposes. Given the great interest of hybrid and electric powertrains, along with the increasing importance of reliable computer-based models, the author decided to integrate both aspects in the research purpose of this work. Furthermore, this is one of the first final degree projects held at the ETSII (Higher Technical School of Industrial Engineers) that covers the study of hybrid and electric propulsion systems. The present project is based on MBS3D 2.0, a specialized software for the dynamic simulation of multibody systems developed at the UPM Institute of Automobile Research (INSIA). Automobiles are a clear example of complex multibody systems, which are present in nearly every field of engineering. The work presented here benefits from the availability of MBS3D software. This program has proven to be a very efficient tool, with a highly developed underlying mathematical formulation. On this basis, the focus of this project is the extension of MBS3D features in order to be able to perform dynamic simulations of hybrid and electric vehicle models. This requires the joint simulation of the mechanical model of the vehicle, together with the model of the hybrid or electric powertrain. These sub-models belong to completely different physical domains. In fact the powertrain consists of energy storage systems, electrical machines and power electronics, connected to purely mechanical components (wheels, suspension, transmission, clutch…). The challenge today is to create a global vehicle model that is valid for computer simulation. Therefore, the main goal of this project is to apply co-simulation methodologies to a comprehensive model of an electric vehicle, where sub-models from different areas of engineering are coupled. The created electric vehicle (EV) model consists of a separately excited DC electric motor, a Li-ion battery pack, a DC/DC chopper converter and a multibody vehicle model. Co-simulation techniques allow car designers to simulate complex vehicle architectures and behaviors, which are usually difficult to implement in a real environment due to safety and/or economic reasons. In addition, multi-domain computational models help to detect the effects of different driving patterns and parameters and improve the models in a fast and effective way. Automotive designers can greatly benefit from a multidisciplinary approach of new hybrid and electric vehicles. In this case, the global electric vehicle model includes an electrical subsystem and a mechanical subsystem. The electrical subsystem consists of three basic components: electric motor, battery pack and power converter. A modular representation is used for building the dynamic model of the vehicle drivetrain. This means that every component of the drivetrain (submodule) is modeled separately and has its own general dynamic model, with clearly defined inputs and outputs. Then, all the particular submodules are assembled according to the drivetrain configuration and, in this way, the power flow across the components is completely determined. Dynamic models of electrical components are often based on equivalent circuits, where Kirchhoff’s voltage and current laws are applied to draw the algebraic and differential equations. Here, Randles circuit is used for dynamic modeling of the battery and the electric motor is modeled through the analysis of the equivalent circuit of a separately excited DC motor, where the power converter is included. The mechanical subsystem is defined by MBS3D equations. These equations consider the position, velocity and acceleration of all the bodies comprising the vehicle multibody system. MBS3D 2.0 is entirely written in MATLAB and the structure of the program has been thoroughly studied and understood by the author. MBS3D software is adapted according to the requirements of the applied co-simulation method. Some of the core functions are modified, such as integrator and graphics, and several auxiliary functions are added in order to compute the mathematical model of the electrical components. By coupling and co-simulating both subsystems, it is possible to evaluate the dynamic interaction among all the components of the drivetrain. ‘Tight-coupling’ method is used to cosimulate the sub-models. This approach integrates all subsystems simultaneously and the results of the integration are exchanged by function-call. This means that the integration is done jointly for the mechanical and the electrical subsystem, under a single integrator and then, the speed of integration is determined by the slower subsystem. Simulations are then used to show the performance of the developed EV model. However, this project focuses more on the validation of the computational and mathematical tool for electric and hybrid vehicle simulation. For this purpose, a detailed study and comparison of different integrators within the MATLAB environment is done. Consequently, the main efforts are directed towards the implementation of co-simulation techniques in MBS3D software. In this regard, it is not intended to create an extremely precise EV model in terms of real vehicle performance, although an acceptable level of accuracy is achieved. The gap between the EV model and the real system is filled, in a way, by introducing the gas and brake pedals input, which reflects the actual driver behavior. This input is included directly in the differential equations of the model, and determines the amount of current provided to the electric motor. For a separately excited DC motor, the rotor current is proportional to the traction torque delivered to the car wheels. Therefore, as it occurs in the case of real vehicle models, the propulsion torque in the mathematical model is controlled through acceleration and brake pedal commands. The designed transmission system also includes a reduction gear that adapts the torque coming for the motor drive and transfers it. The main contribution of this project is, therefore, the implementation of a new calculation path for the wheel torques, based on performance characteristics and outputs of the electric powertrain model. Originally, the wheel traction and braking torques were input to MBS3D through a vector directly computed by the user in a MATLAB script. Now, they are calculated as a function of the motor current which, in turn, depends on the current provided by the battery pack across the DC/DC chopper converter. The motor and battery currents and voltages are the solutions of the electrical ODE (Ordinary Differential Equation) system coupled to the multibody system. Simultaneously, the outputs of MBS3D model are the position, velocity and acceleration of the vehicle at all times. The motor shaft speed is computed from the output vehicle speed considering the wheel radius, the gear reduction ratio and the transmission efficiency. This motor shaft speed, somehow available from MBS3D model, is then introduced in the differential equations corresponding to the electrical subsystem. In this way, MBS3D and the electrical powertrain model are interconnected and both subsystems exchange values resulting as expected with tight-coupling approach.When programming mathematical models of complex systems, code optimization is a key step in the process. A way to improve the overall performance of the integration, making use of C/C++ as an alternative programming language, is described and implemented. Although this entails a higher computational burden, it leads to important advantages regarding cosimulation speed and stability. In order to do this, it is necessary to integrate MATLAB with another integrated development environment (IDE), where C/C++ code can be generated and executed. In this project, C/C++ files are programmed in Microsoft Visual Studio and the interface between both IDEs is created by building C/C++ MEX file functions. These programs contain functions or subroutines that can be dynamically linked and executed from MATLAB. This process achieves reductions in simulation time up to two orders of magnitude. The tests performed with different integrators, also reveal the stiff character of the differential equations corresponding to the electrical subsystem, and allow the improvement of the cosimulation process. When varying the parameters of the integration and/or the initial conditions of the problem, the solutions of the system of equations show better dynamic response and stability, depending on the integrator used. Several integrators, with variable and non-variable step-size, and for stiff and non-stiff problems are applied to the coupled ODE system. Then, the results are analyzed, compared and discussed. From all the above, the project can be divided into four main parts: 1. Creation of the equation-based electric vehicle model; 2. Programming, simulation and adjustment of the electric vehicle model; 3. Application of co-simulation methodologies to MBS3D and the electric powertrain subsystem; and 4. Code optimization and study of different integrators. Additionally, in order to deeply understand the context of the project, the first chapters include an introduction to basic vehicle dynamics, current classification of hybrid and electric vehicles and an explanation of the involved technologies such as brake energy regeneration, electric and non-electric propulsion systems for EVs and HEVs (hybrid electric vehicles) and their control strategies. Later, the problem of dynamic modeling of hybrid and electric vehicles is discussed. The integrated development environment and the simulation tool are also briefly described. The core chapters include an explanation of the major co-simulation methodologies and how they have been programmed and applied to the electric powertrain model together with the multibody system dynamic model. Finally, the last chapters summarize the main results and conclusions of the project and propose further research topics. In conclusion, co-simulation methodologies are applicable within the integrated development environments MATLAB and Visual Studio, and the simulation tool MBS3D 2.0, where equation-based models of multidisciplinary subsystems, consisting of mechanical and electrical components, are coupled and integrated in a very efficient way.

R-type Ca2+ currents evoke transmitter release at a rat central synapse

Voltage-dependent Ca2+ currents evoke synaptic transmitter release. Of six types of Ca2+ channels, L-, N-, P-, Q-, R-, and T-type, only N- and P/Q-type channels have been pharmacologically identified to mediate action-potential-evoked transmitter release in the mammalian central nervous system. We tested whether Ca2+ channels other than N- and P/Q-type control transmitter release in a calyx-type synapse of the rat medial nucleus of the trapezoid body. Simultaneous recordings of presynaptic Ca2+ influx and the excitatory postsynaptic current evoked by a single action potential were made at single synapses. The R-type channel, a high-voltage-activated Ca2+ channel resistant to L-, N-, and P/Q-type channel blockers, contributed 26% of the total Ca2+ influx during a presynaptic action potential. This Ca2+ current evoked transmitter release sufficiently large to initiate an action potential in the postsynaptic neuron. The R-type current controlled release with a lower efficacy than other types of Ca2+ currents. Activation of metabotropic glutamate receptors and γ-aminobutyric acid type B receptors inhibited the R-type current. Because a significant fraction of presynaptic Ca2+ channels remains unidentified in many other central synapses, the R-type current also could contribute to evoked transmitter release in these synapses.

Antisense oligonucleotides against α1E reduce R-type calcium currents in cerebellar granule cells

Many neurons of the central nervous system display multiple high voltage-activated Ca2+ currents, pharmacologically classified as L-, N-, P-, Q-, and R-type. Of these current types, the R-type is the least understood. The leading candidate for the molecular correlate of R-type currents in cerebellar granule cells is the α1E subunit, which yields Ca2+ currents very similar to the R-type when expressed in heterologous systems. As a complementary approach, we tested whether antisense oligonucleotides against α1E could decrease the expression of R-type current in rat cerebellar granule neurons in culture. Cells were supplemented with either antisense or sense oligonucleotides and whole-cell patch clamp recordings were obtained after 6–8 days in vitro. Incubation with α1E antisense oligonucleotide caused a 52.5% decrease in the peak R-type current density, from −10 ± 0.6 picoamperes/picofarad (pA/pF) (n = 6) in the untreated controls to −4.8 ± 0.8 pA/pF (n = 11) (P < 0.01). In contrast, no significant changes in the current expression were seen in sense oligonucleotide-treated cells (−11.3 ± 3.2 pA/pF). The specificity of the α1E antisense oligonucleotides was supported by the lack of change in estimates of the P/Q current amplitude. Furthermore, antisense and sense oligonucleotides against α1A did not affect R-type current expression (−11.5 ± 1.7 and −11.7 ± 1.7 pA/pF, respectively), whereas the α1A antisense oligonucleotide significantly reduced whole cell currents under conditions in which P/Q current is dominant. Our results support the hypothesis that members of the E class of α1 subunits support the high voltage-activated R-type current in cerebellar granule cells.

Activation and inhibition of K-ATP currents by guanine nucleotides is mediated by different channel subunits

The ATP-sensitive potassium channel (K-ATP channel) plays a key role in insulin secretion from pancreatic β-cells. It is closed by glucose metabolism, which stimulates secretion, and opened by the drug diazoxide, which inhibits insulin release. Metabolic regulation is mediated by changes in ATP and MgADP concentration, which inhibit and potentiate channel activity, respectively. The β-cell K-ATP channel consists of a pore-forming subunit, Kir6.2, and a regulatory subunit, SUR1. The site at which ATP mediates channel inhibition lies on Kir6.2, while the potentiatory action of MgADP involves the nucleotide-binding domains of SUR1. K-ATP channels are also activated by MgGTP and MgGDP. Furthermore, both nucleotides support the stimulatory actions of diazoxide. It is not known, however, whether guanine nucleotides mediate their effects by direct interaction with one or more of the K-ATP channel subunits or indirectly via a GTP-binding protein. We used a truncated form of Kir6.2, which expresses independently of SUR1, to show that GTP blocks K-ATP currents by interaction with Kir6.2 and that the potentiatory effects of GTP are endowed by SUR1. We also showed that mutation of the lysine residue in the Walker A motif of either the first (K719A) or second (K1384M) nucleotide-binding domain of SUR1 abolished both the potentiatory effects of GTP and GDP on K-ATP currents and their ability to support stimulation by diazoxide. This argues that the stimulatory effects of guanine nucleotides require the presence of both Walker A lysines.

Combined Recording of Mechanically Stimulated Afferent Output and Nerve Terminal Labelling in Mouse Hair Follicle Lanceolate Endings

Acknowledgements The work was in part funded by UK Medical Research Council project grant G0601253 to G.S.B. and R.W.B.

Defective γ-aminobutyric acid type B receptor-activated inwardly rectifying K+ currents in cerebellar granule cells isolated from weaver and Girk2 null mutant mice

Stimulation of inhibitory neurotransmitter receptors, such as γ-aminobutyric acid type B (GABAB) receptors, activates G protein-gated inwardly rectifying K+ channels (GIRK) which, in turn, influence membrane excitability. Seizure activity has been reported in a Girk2 null mutant mouse lacking GIRK2 channels but showing normal cerebellar development as well as in the weaver mouse, which has mutated GIRK2 channels and shows abnormal development. To understand how the function of GIRK2 channels differs in these two mutant mice, we compared the G protein-activated inwardly rectifying K+ currents in cerebellar granule cells isolated from Girk2 null mutant and weaver mutant mice with those from wild-type mice. Activation of GABAB receptors in wild-type granule cells induced an inwardly rectifying K+ current, which was sensitive to pertussis toxin and inhibited by external Ba2+ ions. The amplitude of the GABAB receptor-activated current was severely attenuated in granule cells isolated from both weaver and Girk2 null mutant mice. By contrast, the G protein-gated inwardly rectifying current and possibly the agonist-independent basal current appeared to be less selective for K+ ions in weaver but not Girk2 null mutant granule cells. Our results support the hypothesis that a nonselective current leads to the weaver phenotype. The loss of GABAB receptor-activated GIRK current appears coincident with the absence of GIRK2 channel protein and the reduction of GIRK1 channel protein in the Girk2 null mutant mouse, suggesting that GABAB receptors couple to heteromultimers composed of GIRK1 and GIRK2 channel subunits.

Ca2+-induced rebound potentiation of γ-aminobutyric acid-mediated currents requires activation of Ca2+/calmodulin-dependent kinase II

In cerebellar Purkinje neurons, γ-aminobutyric acid (GABA)-mediated inhibitory synaptic transmission undergoes a long-lasting “rebound potentiation” after the activation of excitatory climbing fiber inputs. Rebound potentiation is triggered by the climbing-fiber-induced transient elevation of intracellular Ca2+ concentration and is expressed as a long-lasting increase of postsynaptic GABAA receptor sensitivity. Herein we show that inhibitors of the Ca2+/calmodulin-dependent protein kinase II (CaM-KII) signal transduction pathway effectively block the induction of rebound potentiation. These inhibitors have no effect on the once established rebound potentiation, on voltage-gated Ca2+ channel currents, or on the basal inhibitory transmission itself. Futhermore, a protein phosphatase inhibitor and the intracellularly applied CaM-KII markedly enhanced GABA-mediated currents in Purkinje neurons. Our results demonstrate that CaM-KII activation and the following phosphorylation are key steps for rebound potentiation.

Ablation of P/Q-type Ca2+ channel currents, altered synaptic transmission, and progressive ataxia in mice lacking the α1A-subunit

The Ca2+ channel α1A-subunit is a voltage-gated, pore-forming membrane protein positioned at the intersection of two important lines of research: one exploring the diversity of Ca2+ channels and their physiological roles, and the other pursuing mechanisms of ataxia, dystonia, epilepsy, and migraine. α1A-Subunits are thought to support both P- and Q-type Ca2+ channel currents, but the most direct test, a null mutant, has not been described, nor is it known which changes in neurotransmission might arise from elimination of the predominant Ca2+ delivery system at excitatory nerve terminals. We generated α1A-deficient mice (α1A−/−) and found that they developed a rapidly progressive neurological deficit with specific characteristics of ataxia and dystonia before dying ≈3–4 weeks after birth. P-type currents in Purkinje neurons and P- and Q-type currents in cerebellar granule cells were eliminated completely whereas other Ca2+ channel types, including those involved in triggering transmitter release, also underwent concomitant changes in density. Synaptic transmission in α1A−/− hippocampal slices persisted despite the lack of P/Q-type channels but showed enhanced reliance on N-type and R-type Ca2+ entry. The α1A−/− mice provide a starting point for unraveling neuropathological mechanisms of human diseases generated by mutations in α1A.

Glutamate transporter currents in Bergmann glial cells follow the time course of extrasynaptic glutamate

Glutamate transporters in the central nervous system are expressed in both neurons and glia, they mediate high affinity, electrogenic uptake of glutamate, and they are associated with an anion conductance that is stoichiometrically uncoupled from glutamate flux. Although a complete cycle of transport may require 50–100 ms, previous studies suggest that transporters can alter synaptic currents on a much faster time scale. We find that application of l-glutamate to outside-out patches from cerebellar Bergmann glia activates anion-potentiated glutamate transporter currents that activate in <1 ms, suggesting an efficient mechanism for the capture of extrasynaptic glutamate. Stimulation in the granule cell layer in cerebellar slices elicits all or none α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptor and glutamate transporter currents in Bergmann glia that have a rapid onset, suggesting that glutamate released from climbing fiber terminals escapes synaptic clefts and reaches glial membranes shortly after release. Comparison of the concentration dependence of both α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptor and glutamate transporter kinetics in patches with the time course of climbing fiber-evoked responses indicates that the glutamate transient at Bergmann glial membranes reaches a lower concentration than attained in the synaptic cleft and remains elevated in the extrasynaptic space for many milliseconds.

Nitric oxide-related species inhibit evoked neurotransmission but enhance spontaneous miniature synaptic currents in central neuronal cultures

Nitric oxide (NO·) does not react significantly with thiol groups under physiological conditions, whereas a variety of endogenous NO donor molecules facilitate rapid transfer to thiol of nitrosonium ion (NO+, with one less electron than NO·). Here, nitrosonium donors are shown to decrease the efficacy of evoked neurotransmission while increasing the frequency of spontaneous miniature excitatory postsynaptic currents (mEPSCs). In contrast, pure NO· donors have little effect (displaying at most only a slight increase) on the amplitude of evoked EPSCs and frequency of spontaneous mEPSCs in our preparations. These findings may help explain heretofore paradoxical observations that the NO moiety can either increase, decrease, or have no net effect on synaptic activity in various preparations.

Stretch-activated single K+ channels account for whole-cell currents elicited by swelling

Functionally significant stretch-activated ion channels have been clearly identified in excitable cells. Although single-channel studies suggest their expression in other cell types, their activity in the whole-cell configuration has not been shown. This discrepancy makes their physiological significance doubtful and suggests that their mechanical activation is artifactual. Possible roles for these molecules in nonexcitable cells are acute cell-volume regulation and, in epithelial cells, the complex adjustment of ion fluxes across individual cell membranes when the rate of transepithelial transport changes. We report the results of experiments on isolated epithelial cells expressing in the basolateral membrane stretch-activated K+ channels demonstrable by the cell-attached patch-clamp technique. In these cells, reversible whole-cell currents were elicited by both isosmotic and hyposmotic cell swelling. Cation selectivity and block by inorganic agents were the same for single-channel and whole-cell currents, indicating that the same entity underlies single-channel and whole-cell currents and that the single-channel events are not artifactual. In these cells, when the rate of apical-membrane NaCl entry increases, the cell Na+ content and volume also increase, stimulating the Na+,K+-ATPase at the basolateral membrane, i.e., both Na+ extrusion and K+ uptake increase. We speculate that, under these conditions, the parallel activation of basolateral K+ channels (by the swelling) elevates conductive K+ loss, tending to maintain the cell K+ content constant (“pump-leak parallelism”). This study describes a physiologically relevant stretch-activated channel, at both the single-channel and whole-cell levels, in a nonneural cell type.

β subunits influence the biophysical and pharmacological differences between P- and Q-type calcium currents expressed in a mammalian cell line

Human epithelial kidney cells (HEK) were prepared to coexpress α1A, α2δ with different β calcium channel subunits and green fluorescence protein. To compare the calcium currents observed in these cells with the native neuronal currents, electrophysiological and pharmacological tools were used conjointly. Whole-cell current recordings of human epithelial kidney α1A-transfected cells showed small inactivating currents in 80 mM Ba2+ that were relatively insensitive to calcium blockers. Coexpression of α1A, βIb, and α2δ produced a robust inactivating current detected in 10 mM Ba2+, reversibly blockable with low concentration of ω-agatoxin IVA (ω-Aga IVA) or synthetic funnel-web spider toxin (sFTX). Barium currents were also supported by α1A, β2a, α2δ subunits, which demonstrated the slowest inactivation and were relatively insensitive to ω-Aga IVA and sFTX. Coexpression of β3 with the same combination as above produced inactivating currents also insensitive to low concentration of ω-Aga IVA and sFTX. These data indicate that the combination α1A, βIb, α2δ best resembles P-type channels given the rate of inactivation and the high sensitivity to ω-Aga IVA and sFTX. More importantly, the specificity of the channel blocker is highly influenced by the β subunit associated with the α1A subunit.