Offering a new perspective, this textbook demystifies the operation of electric machines by providing an integrated understanding of electromagnetic fields, electric circuits, numerical analysis, and computer programming. It presents fundamental concepts in a rigorous manner, emphasising underlying physical modelling assumptions and limitations, and provides detailed explanations of how to implement the finite element method to explore these concepts using Python. It includes explanations of the conversion of concepts into algorithms, and algorithms into code, and examples building in complexity, from simple linear-motion electromagnets to rotating machines. Over 100 theoretical and computational end-of-chapter exercises test understanding, with solutions for instructors and downloadable Python code available online. Ideal for graduates and senior undergraduates studying electric machines, electric machine design and control, and power electronic converters and power systems engineering, this textbook is also a solid reference for engineers interested in understanding, analysing and designing electric motors, generators, and transformers.

Recent developments in semiconductor device technology have seen the advent of wide-bandgap (WBG) devices that enable operation at high switching frequencies. The use of these devices in electric drive systems has resulted in increased voltage edge rates that give rise to various undesirable effects including large common-mode currents, electromagnetic interference, transient overvoltages, insulation failure due to the overvoltages, and bearing failures due to microarcs. To predict these high-frequency (HF) effects, accurate and efficient simulation tools are needed. A new heterogeneous multirate simulation approach for WBG-based electric drive systems is presented in this paper. In particular, the approach is applied to a wideband (WB) model of a permanent-magnet ac (PMAC) machine supplied by a WBG-based inverter.

This article performs a novel comparison of the life-cycle costs of the series and parallel architectures for plug-in hybrid electric vehicles. Economic viability is defined as having a payback period less than 2 years and number of battery replacements less than or equal to three over a vehicle life of 12 years along-with drivability and gradability constraints. Economic viability is compared for two plug-in hybrid electric vehicle applications (Medium-duty Truck and Transit Bus) using series and parallel architectures over multiple drivecycles, for three economic scenarios (viz. 2020, 2025 and 2030 where the fuel price, battery price and motor price are varied such that latter scenarios are more favorable for hybridization). One battery overnight recharge is assumed. The results demonstrate that by 2020 the plug-in hybrid electric vehicle transit buses are viable for the duty cycles Manhattan, Orange County, and China (Normal and Aggressive). By 2025, plug-in hybrid electric vehicle Class 6 trucks are viable for all duty cycles considered (Pick-up and delivery, Refuse and New York Composite). The parallel architectures generally require less than 50% of the initial cost of the series architecture, due to smaller motor sizes, driving earlier viability for parallel architectures. The transit bus scenarios generally achieve payback sooner than the medium-duty truck due to higher fuel cost savings, driving earlier viability for transit bus applications.

From the design space explored for series architecture plug-in hybrid electric vehicle transit buses by the authors, one powertrain and control design is selected to provide maximum benefit to investment ratio. Sensitivity analysis is performed for this powertrain configuration. Vehicle parameters (including vehicle mass, coefficient of drag, coefficient of rolling resistance), usage parameters (drivecycle, annual vehicle miles traveled, number of recharges in a day, recharge current, and battery temperature), and economic parameters (fuel price, motor price, and battery price) are varied to understand their effect on the number of required battery replacements, net present value, payback period, and fuel consumption reduction. It is shown that battery temperature has the most significant impact, particularly on the number of battery replacements and net present value and, as such, must be well controlled in practice. It is shown that to maintain the battery at 20°C, for ambient temperatures between −5°C and 45°C, 0.8–1.8% excess fuel is required across all drivecycles for the considered plug-in hybrid electric vehicle transit bus powertrain configuration. In addition, the well-to-wheel emissions of criteria pollutants resulting from the usage of this plug-in hybrid electric vehicle transit bus in Indiana and California are calculated and compared with the conventional transit bus, using the GREET (Greenhouse Gases, Regulated Emissions and Energy Use in Transportation) Model. With a single over night charge, the plug-in hybrid electric vehicle transit bus operating in either Indiana or California produces 50% less CO 2 and other greenhouse gases as compared to a conventional transit bus.

Due to the instabilities that may occur in dc power systems with regulated power-electronic loads such as those used in aircraft, ships, as well as terrestrial vehicles, many analysis techniques and design methodologies have been developed to ensure stable operation for expected operating conditions. However, these techniques do not guarantee large-displacement stability following major disturbances such as faults, regenerative operation, large pulsed loads, and/or the loss of generating capacity. Recently, a design paradigm was set forth that ensures large-displacement stability for any single positive or negative step change in commanded load power PL provided the step change lies within the steady-state rating of the source. In this paper, a formal mathematical definition of large-displacement stability is set forth and the previous results are extended to show that it is possible to design a dc system that is large-displacement stable for any piecewise continuous PL(t) that is bounded by the steady-state rating of the dc source. Moreover, and a new largedisplacement stability margin is set forth and illustrated for two example systems.

To increase switching frequencies while limiting switching losses in voltage-source inverters, power switches have been made significantly faster with achievable switching times now less than 100 ns. However, faster switches generate larger inverter output voltage edge rates ( ${dv/dt} $ ) and result in deleterious effects in variable-speed drive systems including transient overvoltages at motor terminals, electromagnetic interference, and bearing failures due to microarcs. A common approach for limiting peak ${dv/dt} $ involves using a ${dv/dt} $ filter. However, the ${dv/dt} $ filter introduces extra power losses and increases the overall size and weight of the system. Soft-switching circuits, which were originally developed to reduce switching losses, can help reduce ${dv/dt} $ , but using soft-switching to accurately control ${dv/dt} $ has not been fully explored. In this paper, a new soft-switching circuit, entitled the auxiliary resonant soft-edge pole (ARSEP), is set forth. ARSEP improves the available soft-switching circuits so that ${dv/dt} $ can be accurately controlled through the circuit parameter design. An ARSEP inverter prototype was designed, simulated, and constructed to verify its performance and benefits. Compared to a conventional hard-switched inverter with a ${dv/dt} $ filter, the ARSEP inverter prototype results in a significant reduction in overall power loss, inductor volume, and weight.

Wide-bandgap (WBG) switches can achieve switching times on the order of several nanoseconds. However, faster switches generate larger inverter output dv/dt. Various deleterious effects attributed to large inverter dv/dt have been observed in various applications, especially in motor drive systems. The effects include false turn-on of WBG switches due to crosstalk, transient over-voltages at motor terminals, electromagnetic interference, and motor bearing failures due to micro arcs. A common approach for limiting peak inverter dv/dt involves the insertion of a dv/dt filter. However, the dv/dt filter introduces extra power losses and increases the size/weight of the heat sink. Soft-switching circuits can reduce inverter dv/dt and switching losses, but using soft-switching to accurately control dv/dt has not been fully explored. A new soft-switching circuit, entitled the auxiliary resonant soft-edge pole (ARSEP), is set forth. The ARSEP improves the available soft-switching circuits so that the dv/dt can be accurately controlled through circuit parameter design. An ARSEP inverter prototype based on SiC MOSFETs was designed, simulated, built, and tested to verify its performance and benefits. Compared to a conventional hard-switched inverter with a dv/dt filter, the ARSEP inverter results in a significant reduction in overall power loss, inductor volume, and weight.

Electric machine performance (peak torque versus speed) and efficiency characteristics are frequently estimated using magnetic finite element analysis (FEA). In this paper, it is shown that the governing mathematical relationships that are solved in such an analysis allow for the implementation of straightforward scaling laws. Instead of rerunning the FEA code for a variety of electric machine lengths, diameters, excitation frequencies, and number of winding turns, only one FEA simulation or experimental characterization is required. The results from that single FEA or experimental result can then be incorporated into the scaling laws derived here to determine the performance and efficiency of permanent-magnet machines with a variety of lengths, diameters, excitation frequencies, and number of winding turns. The utility is a significant speedup in the computation of a variety of design choices as a result of not having to re-execute the FEA for each design iteration or option. Following a mathematical development, scaling-law-based performance/efficiency estimates and those from FEA are directly compared and shown to he exactly the same.

Physically-based Li-ion electrochemical cell models have been shown capable of predicting cell performance and degradation, but are computationally expensive for optimization-oriented design applications. Faster empirical models have been developed from experimental data, but are not generalizable to operating conditions outside of the range established by the calibration data. In this paper, a reduced-order capacity-loss model for graphite anodes is derived based upon the salient physical loss mechanisms to improve computational efficiency without sacrificing model fidelity. This model captures the two primary degradation mechanisms that occur in the graphite anode of a typical lithium ion cell: a) capacity loss due to Solid Electrolyte Interface (SEI) layer growth, and b) capacity loss due to isolation of active material. The model is calibrated and validated for a commercial 2.3-Ah cell with a Lithium Iron Phosphate (LFP) cathode and graphite anode. One data set is used for calibration, another four experimental data sets are used for validation. The model matches experimental capacity degradation results within a 20% error. Moreover, the reported model is 2400× faster than currently existing more complex physically-based electrochemical models that are only slightly more accurate (in some cases).

In the late 1920s, R. H. Park published a change of variables that provided a means of analyzing the performance of synchronous machines. He transformed the stator variables to substitute variables that eliminated the rotor-position-dependent terms from the self- and mutual inductances. This transformation has become the bedrock of machine analysis and simulation; however, Park's derivation involves a maze of three-phase trigonometric identities with generator action and we are left searching for a more concise analytical development. In this paper, a direct connection is established between Tesla's rotating magnetic field and reference frame theory. In particular, an analytical basis for the change of variables is established from the expression of Tesla's rotating magnetic field combined with an expression that relates stationary and rotating coordinates. This leads directly to reference frame theory and an array of transformations that yield the same advantages as Park's transformation. It shows that all transformations used in the analysis of power systems, electric machines, and drive systems have a common origin. Also, the magnetic poles can be analytically located during transient operation and on a phasor diagram during steady-state operation, thereby providing a vivid visualization of machine and drive operation.

Within electrified vehicle powertrains, lithium-ion battery performance degrades with aging and usage, resulting in a loss in both energy and power capacity. As a result, models used for system design and control algorithm development would ideally capture the impact of those efforts on battery capacity degradation, be computationally efficient, and simple enough to be used for algorithm development. This paper provides an assessment of the state-of-the-art in lithium-ion battery degradation models, including accuracy, computational complexity, and amenability to control algorithm development. Various aging and degradation models have been studied in the literature, including physically-based electrochemical models, semi-empirical models, and empirical models. Some of these models have been validated with experimental data; however, comparisons of pre-existing degradation models across multiple experimental data sets have not been previously published. Three degradation models, a 1-d electrochemical model (AutoLion ST, or ALST), a semi-empirical model (from the National Renewable Energy Laboratory) and an empirical model (published in the literature), are compared against three published experimental data sets for a 2.3-Ah commercial graphite/LiFePO 4 cell. The results show that the physically-based model is best able to capture results across all three representative data sets with an error less than 10 %, but is 24× slower than the empirical model, and 4000× slower than the semi-empirical model, making it unsuitable for powertrain system design and model-based algorithm development. Despite being computationally efficient, the semi-empirical and empirical models, when used under conditions that lie outside the calibration data set, exhibit up to 60% error in capacity loss prediction. Such models require expensive experimental data collection to recalibrate for every new application. Thus, in the author's opinion, there exists a need for a physically-based model that generalizes well across operating conditions, are computationally efficient for model-based design, and simple enough for control algorithm development.

Physically-based Li-ion electrochemical cell models have been shown capable of predicting cell performance and degradation, but are computationally expensive for optimization-oriented design applications. Faster empirical models have been developed from experimental data, but are not generalizable to operating conditions outside of the range established by the calibration data. In this paper, a reduced-order capacity-loss model for graphite anodes is derived based upon the salient physical loss mechanisms to improve computational efficiency without sacrificing model fidelity. This model captures the two primary degradation mechanisms that occur in the graphite anode of a typical lithium ion cell: a) capacity loss due to Solid Electrolyte Interface (SEI) layer growth, and b) capacity loss due to isolation of active material. The model is calibrated and validated for a commercial 2.3-Ah cell with a Lithium Iron Phosphate (LFP) cathode and graphite anode. One data set is used for calibration, another two data sets are used for validation. The model matches experimental capacity degradation results within 10% error. Moreover, the reported model is 2400× faster than currently existing more complex physically-based electrochemical models that are only slightly more accurate (less than 8% error).

Interior-permanent-magnet (IPM) motor drive systems are widely used in industrial applications. As power transistors are made faster, it is important to establish accurate high-frequency (HF) models of IPM motor drive systems so that transient overvoltages, electromagnetic interference (EMI), and motor/converter losses can be predicted more accurately to facilitate system design and verification. In this paper, a HF IPM motor model is proposed. A conventional qd0 IPM motor model is augmented to portray the HF transients. The motor model is parameterized using measured differential-mode (DM) and common-mode (CM) impedance characteristics. In addition, a HF cable model is proposed whose parameters can be established from DM and CM impedance measurements under short- and open-circuit conditions. An αβ0 model is used to implement the cable model in simulation. Both models can readily be implemented using circuit-based simulators, such as LTspice, so that established SPICE transistor models can be used to predict switching transients, EMI and losses.

The light-duty vehicle market has seen some adoption of hybrid electric vehicles that is not reflected in the heavy-duty market. The major challenges associated with the heavy-duty segment are: (i) greater emphasis on economic viability, (ii) reluctance to take on risk associated with new technologies, and (iii) numerous diverse applications that preclude a one-size-fits-all approach to hybrid-electric power train design. To overcome these challenges, a model-based framework is required that enables the exploration and optimal design of powertrain architectures for diverse applications while capturing the impact of hybridization on the economics of ownership under different economic scenarios. This paper demonstrates such a framework that incorporates powertrain simulation and battery degradation models to predict fuel consumption, electrical energy consumption, and battery replacements. These results are combined with economic assumptions to enable the exploration of a large design space (which spans powertrain design & control variables, noise variables, and economic scenarios) from a total cost-of ownership perspective to provide better insights to vehicle integrators, component manufacturers, and buyers of heavy-duty hybrid electric vehicles. The methodology is applied to series plug-in hybrid electric and extended-range electric powertrain architectures for medium duty truck applications. The results show that under the assumptions made, economically favorable solutions for series plug-in hybrid electric medium-duty trucks exist in the 2020 time-frame for the NY Composite Truck drive cycle, while for the HTUF Refuse Truck and HTUF Class 6 P&D Truck drive cycles, feasible solutions are not obtained until 2025 and 2030 time-frames respectively. (C) 2017 Elsevier Ltd. All rights reserved.

A computationally efficient simulation framework is set forth in which the semiconductor devices are represented by the physical phenomena relevant to the accurate prediction of high-frequency circuit-level transients and energy losses. Key elements of this framework include an encapsulated diode model and a method of coupling device models with those of external circuit elements given a user-specified SPICE-like netlist. The framework is applied to a single-phase full-bridge diode rectifier circuit with a discussion on time-step requirements and overall computational performance. Comparisons between simulated and measured waveforms are also provided revealing excellent agreement.

In this paper, a diagram that depicts a mild parallel hybrid electric vehicle is used to simulate the energy usage and efficiency. MATLAB and Simulink were used for the simulation. All aspects of this vehicle are governed by the law of conservation of energy. The system uses a drive schedule of a driver within an urban setting. Many aspects were taken into account such as the vehicle speed, battery state of charge, and tractive power needed to propel the vehicle. This simulation helps us understand how a hybrid electric vehicle operates and may give some insight on how to improve the design of such vehicles. Related work can also be used to further improve the bigger picture. Wireless charging and automated control of large scale charging can improve the transfer of energy from sources to homes and charge stations.

Multiport dc-dc converters offer an efficient approach for combining several energy sources under a centralized supervisory controller. In this brief, a systematic approach to the design and implementation of a centralized controller for N-port dc-dc converters is presented. An optimization algorithm associated with such a controller is also proposed, which offers the flexibility to meet the desired control and energy optimization objectives. More specifically, the controller is a robust linear feedback controller (LFC) based on state-space design and the optimization algorithm is implemented using sequential quadratic programming (SQP). Newton's algorithm is also introduced to obtain approximated solutions to the controlled inputs and to initialize the SQP algorithm. The implementation of the LFC and SQP algorithm is demonstrated, simulated for performance evaluation, and then validated using a hardware prototype for a four-port dc-dc converter. The optimization algorithm yields a 14% reduction in transformer winding losses.

A new method of hierarchically partitioning the numerical calculations associated with the finite-element analysis of rotating electrical machinery is set forth. In this method, the device is partitioned geometrically and hierarchically into its constituent subsystems. Each Newton-Raphson iteration in a magnetically nonlinear device involves the hierarchical solution of relatively compact linear algebraic equations. This is contrasted with conventional approaches involving the formation or updating and solution of a single but large-dimensional sparse equation. In addition to an improvement in the computational efficiency, this approach facilitates efficient management of rotation. The proposed approach is demonstrated to require less than one-fourth the computation time, while producing identical results to those of a conventional formulation when solving for cogging torque and back electromotive force (back-EMF) of a permanent-magnet synchronous machine. The numerical results are also shown to be in agreement with the measured data.

Recently introduced Si/SiC devices allow switching frequencies of several MHz with switching losses comparable to those in slower Si IGBTs. The losses of different Si/SiC devices working in a full-bridge active-clamped isolated dc-dc converter with different switching frequencies are calculated and compared in order to explore the improvements in losses. Furthermore, various transformers are designed for the converter with different switching frequencies while limiting the temperature rise. The benefits of high-frequency devices can be readily illustrated by comparing the total transistor power losses and transformer sizes of the Si/SiC-based converters.