Electrically assisted engine boosting systems lend themselves to better throttle response, wider effective operating ranges, and can provide the ability to extract excess energy during deceleration and high-load events (and store it in a vehicle's onboard batteries). This can lead to better overall vehicle performance, emissions, and efficiency while allowing for further engine downsizing and increased power density. In this research effort, a hybrid-electric turbocharger, variable-frequency drive (VFD), and novel sensorless control algorithm were developed. An 11 kW permanent-magnet (PM) machine was coupled to a commercial turbocharger via an in-line, bolt-on housing attached to the compressor inlet. A high-efficiency, high-temperature VFD, consisting of custom control and power electronics, was also developed. The VFD uses SiC MOSFETS to achieve high-switching frequency and can be cooled using an existing engine coolant loop operating at up to 105 °C at an efficiency greater than 98%. A digital sliding mode-observer sensorless speed control algorithm was created to command and regulate speed and achieved ramp rates of over 68,000 rpm/s. A two-machine benchtop motor/generator test stand was constructed for initial testing and tuning of the VFD and sensorless control algorithm. A gas blow-down test stand was constructed to test the mechanical operation of the hybrid-electric turbocharger and speed control using the VFD. In addition, a liquid-pump cart was assembled for high-temperature testing of the VFD. Initial on-engine testing is planned for later this year. This paper intends to present a design overview of the in-line, hybrid-electric device, VFD, and performance characterization of the electronics and sensorless control algorithm.

## Introduction

Hybridized and fully electrified boosting technologies have become increasingly popular in recent years. Engine-boosting provides advantages in terms of fuel efficiency and emissions improvements, as well as the potential for engine downsizing with increased power density. However, even with implementation of variable-geometry designs, turbocharging devices still have deficiencies in their transient response and effective operating range. These devices also lack ability to recover excess engine exhaust energy, especially during deceleration events. Hybridizing these devices allows for decreased response time to transient events by adding torque via an electric motor, leading to better vehicle throttle response. Boost can also be completely decoupled from engine operating condition using a variable-frequency drive (VFD) to control turbocharger shaft speed. In addition, use of a permanent-magnet (PM) style electric motor allows the device to operate as a generator during deceleration events, adding surplus power that can be used for electrification of accessories or stored for hybrid powertrains.

Electrically assisted turbochargers and electric-turbocharger compounding have been studied computationally by a number of authors [15], but examples of reducing the concept to practice are still scarce in the scientific and engineering literature, especially in regards to the electronics and control of these hybrid devices. Ryder et al. [6] reported on implementation of an electrically assisted turbocharger (T/C) for a heavy-duty truck application but is limited to performance and testing of the boosting device itself. Other works on these devices have discussed electric machine designs [7,8] vehicle system level control and coordination [911], VFD topology comparisons [1214], and sensorless motor control algorithms [15]. However, many of these works focus solely on individual aspects on not the system as a whole. Also, these works do not discuss the achievable dynamic ramp-rates (kRPM/s), which determine T/C spool up time, volumetric and gravimetric power densities, and overall efficiencies of the power electronics for application in electric vehicles. Furthermore, previous works have characterized performance at room temperature (25 °C) and have not shown integration with typical vehicle cooling systems, whose cooling fluid can range in temperature from 65 °C to 105 °C, nor exposure to elevated ambient air temperatures.

This paper describes not only the design of an in-line style electrically assisted turbocharger, but also the power and control electronics developed for the device along with a sensorless motor control strategy. The system includes an 11 kW PM electric motor, coupled in-line to a commercially available turbocharger via a custom housing and an 18 kW continuous (29 kW peak) VFD. The drive is capable of sensorless control of the motor at speeds up 153 kRPM and is cooled from an existing 105 °C 50/50 aqueous-glycol cooling loop. Thus far, the system has achieved dynamic motor control performance of >68 kRPM/s.

## Materials and Methods

### Hybrid-Electric Turbocharger

#### System Architecture.

Figure 1 shows a general overview of the hybrid-electric turbocharger (HE-T/C) system architecture, including an internal combustion diesel engine, engine control unit (ECU), and turbocharger (composed of the compressor and turbine), which is coupled to a PM-integrated motor/alternator (IMA), VFD, and an energy storage system (ESS). During vehicle acceleration, the VFD transfers power from the ESS into the IMA, applying additional torque to the turbocharger shaft. The additional torque decreases turbine spool time and provides boost to the engine with less lag. During braking and deceleration events when excess exhaust energy is available, the VFD extracts power from the IMA and stores it in the ESS.

Fig. 1
Fig. 1
Close modal

#### Turbocharger.

A commercially available, variable-geometry style turbocharger (Borg Warner S200V-2667N, Borg Warner Inc. Auburn Hills, MI) was used for this program, which has a maximum operating speed of 153,000 RPM. The relative size of this turbocharger is representative of those used in medium-to-heavy duty diesel engines found in vehicles such as buses, delivery trucks, and refuse vehicles. Vehicles like these, that make frequent starts and stops, will benefit from the increased throttle response and ability to generate and store excess power during deceleration/stopping that can be provided by the HE-T/C system.

#### Integrated Motor/Alternator.

A permanent-magnet synchronous motor (PMSM, E+A Elektromaschinen und Antriebe AG, Möhlin, Switzerland) was selected for the IMA. PMSMs have high power density, desirable sinusoidal back-electromotive force (EMF), and potential for lower torque ripple, as compared to other motor technologies. A two-pole machine was chosen due to the extremely high operation speeds (153 kRPM) and resulting pole-pair output fundamental frequency (2550 Hz).

For the electric motor/alternator to be successfully integrated into the turbocharger, the following relation (Eq. (1)) must be satisfied [17]. This relation ensures that the added inertia from the electric motor is more than compensated for by the torque provided by the electric motor
$ηmTCτT−τC+τEMGTC+EM>ηmTCτT−τCGTC$
(1)

where ηmTC is the mechanical efficiency of the shaft, τT, τC, and τEM are the torque of the turbine, compressor, and electric motor, respectively, and GTC+EM and GTC are the mass moment of inertias of the shaft with and without the electric motor. For our device, the rotational moment of inertia of the new rotating assembly is 61% higher than the stock turbocharger shaft. This additional moment of inertia is more than offset by the additional 0.698 N·m (6.18 in lb) of shaft torque provided by the electric motor.

A photo of the final stator and PM rotor sleeve is shown in Fig. 2 and the measured IMA parameters are given in Table 1. The rotor sleeve has a nonferrous metal sleeve with two neodymium-iron-boron (NdFeB) magnetic poles and a carbon fiber wrap for strength because of the centrifugal force of the magnets at high-speed. The stator is a conventionally stacked and wound core.

Fig. 2
Fig. 2
Close modal
Table 1

HE-T/C PMSM IMA design/measured operating parameters

 Max. operating speed 153 kRPM Number of poles 2 Max. output power 11 kW Max. torque 0.698 N·m Bemf constant 0.72 V/kRPM Stator resistance 0.009 Ω Stator inductance 37 μH
 Max. operating speed 153 kRPM Number of poles 2 Max. output power 11 kW Max. torque 0.698 N·m Bemf constant 0.72 V/kRPM Stator resistance 0.009 Ω Stator inductance 37 μH

#### Housing/Coupling.

A housing was developed for the IMA to attach in-line with the turbocharger. A cutaway rendering of the IM housing is shown in Fig. 3. Only minor modification of the stock turbocharger was needed to mount and align the IMA housing and device; a pilot outer diameter and four radial mounting holes were machined into the inlet flange of the turbocharger compressor. The IMA housing inlet section (orange) retains the same inlet flange geometry as the stock turbocharger housing, so the device can be dropped directly into the intake system.

Fig. 3
Fig. 3
Close modal

The housing encases and protects the stator and rotating assembly in a central, aerodynamically shaped center section. An outer shell that mounts to the compressor housing, which has radial support ribs connecting it to the center section, provides an annular flow region for compressor intake air. As pictured, air flows into the inlet portion of the housing, around the center section and converges into the compressor inlet. The aerodynamic shape helps reduce turbulence entering the compressor, and the air flowing around the center sections helps to forced-air cooling of the IMA. The lightweight 6061 aluminum housing consists of three main sections: the inlet (left), main body (center), and outlet section (right). The main body houses the IMA, which includes the stator and the entire rotating assembly (described later). A bearing cap and nose cone also attach to the main body. The outlet section converges the flow into the compressor. The outlet has a precision machined pilot diameter to center the entire IMA housing on the compressor and is used to mount the device.

Two high-speed angular contact bearings were used on either end of the shaft, one fixed and one floating which uses a spring to produce the desired axial preload. The preload is needed to push on the angular contact bearings so there is no undesirable axial clearance inside of the bearing. A custom, high-speed, precision-balanced, bellows shaft coupling was used to mate the IMA shaft to the turbocharger shaft. A modified compressor wheel nut was machined which included a hub for attaching the coupling. The rotor assembly also features a shaft grounding ring that shunts common-mode ground current through the ring and into the housing instead of flowing through the bearings, which would reduce bearing life and could eventually lead to failure. This common-mode ground current is caused by the high switching speed of the silicon carbide (SiC, Wolfspeed - Fayetteville, Fayetteville, AR) MOSFETs used in the VFD.

A completed prototype of the HE-T/C can be seen in Fig. 4. The overall housing adds less than 18.4 cm (7.25 in) to the length of the turbocharger and has a diameter of 13.34 cm (5.25 in) with a total weight of 4.54 kg (10 lbs).

Fig. 4
Fig. 4
Close modal

### Variable Frequency Drive.

The VFD developed for this application is capable of 18 kW continuous power and 29 kW peak power. It has volumetric and gravimetric densities of 3.5 kW/L and 3.8 kW/kg, respectively. It can be cooled from an existing 50/50 aqueous-glycol engine cooling loop operating at up to 105 °C (221 °F) at efficiencies greater than 98%, minimizing the impact on the vehicle cooling system. SiC power modules are used for high-temperature operation and for their high switching frequency (40–50 kHz). The current iteration of the VFD interfaces with 200–300 V (low-voltage) vehicle ESSs and can be easily modified to interface with higher-voltage (600–800 V) vehicle power systems for driving high-power traction motors. The fully assembled VFD is shown in Fig. 5. The VFD is contained within a fully environmentally sealed enclosure that has an integrated, externally sealed, liquid coldplate. This allows the VFD to be installed in a variety of vehicle locations and eliminates any contamination concerns from the outside environment or possibility of coolant leakage that could cause catastrophic electronics failure.

Fig. 5
Fig. 5
Close modal

#### Sensorless Control Algorithm.

The VFD speed and current controllers are built around a synchronous reference frame proportional-integral control system. The full control loop diagram is shown in Fig. 6 and includes the speed loop, current loop, and sliding mode observer (SMO). A more detailed description of the SMO is provided in Fig. 7.

Fig. 6
Fig. 6
Close modal
Fig. 7
Fig. 7
Close modal
The digital SMO equation for iαβ estimation is given by Eq. (2), and the minimum stability criteria for selection of the SMO gain K, is given by Eq. (3), where iαβ represents the measured alpha-beta frame motor currents, Ts is the sampling interval, Rs is the stator resistance, Ls is the stator inductance, eαβ is the back EMF, vαβ is the VFD output voltage, and n is the sampling instant [18]
$iαβn+1=1−TsRsLsiαβn−TsLseαβ+TsLsvαβ$
(2)
$K>eαβ$
(3)

A saturation function is used to reduce chattering effects associated with SMO, and a phase-locked loop is used to improve the tracking and filtering properties. A dead-time compensation method was implemented which reconstructs the current measurement to more accurately predict the magnitude and phase of the current waveforms fundamental frequency component. To accomplish this, an adaptive notch filter was used, which accounted for the variable frequency operation of the VFD. The details of these methods and implementations are given by Beechner and Carpenter [16]. The total harmonic distortion in the current waveform was reduced to 3.08% from 5.32% with a noticeable lack of fifth and seventh harmonic currents using these methods.

### Experimental Setup

#### Variable-Frequency Drive Pump Loop Cart.

A test cart was built to measure VFD efficiency and control performance data. It consisted of the SiC VFD, a temperature-controlled 50/50 aqueous-glycol variable-speed, pumped cooling loop, a dynamic brake for overvoltage protection during testing, and ultra-capacitors to mimic the ESS found on electric vehicles. RTD temperature sensors were included on the inlet and outlet of the VFD coldplate along with a differential pressure transducer to measure pressure drop.

#### Gas Blow-down Test Stand.

A gas blow-down test stand, where pressurized air is used to spool-up the turbine, was constructed for preliminary shakedown testing of the HE-T/C. The design of the test stand drew guidance from the SAE Turbocharger Gas Stand Test Code (SAE J1826) [19]. The schematic for the turbine blow-down test stand is shown in Fig. 8. The test stand includes two 1.5 kL (400 gallon) air reservoirs with a maximum pressure rating of 1.138 MPa (165 psi) that are charged using shop air and a cradle of compressed gas cylinders. Air exits the tank through an on/off ball valve and flows through a butterfly metering valve and into a flow straightener before entering the turbine. The outlet of the compressor is sufficiently long for flow to fully develop for flow measurements and has a butterfly valve on the exit for backpressure control. The test stand is fully instrumented to measure inlet and outlet temperatures and pressures on the compressor and turbine sides as well as a volumetric flow meter to calculate mass flow rate through the turbine. These sensors are monitored by a common data acquisition system and processed in LabVIEW along with the data from the VFD pump loop cart and turbine speed from the turbocharger's stock variable reluctance sensor. The test setup also included an oil pump loop to supply the turbocharger stock viscous bearings with oil.

Fig. 8
Fig. 8
Close modal

## Computational Modeling

### Engine/Vehicle Simulations.

Preliminary engine and vehicle simulations were performed to demonstrate technical feasibility in improving effective engine operating range and reducing fuel consumption. A validated Ricardo WAVE model for a six-cylinder, turbocharged, 10-L diesel truck engine was used as the starting point for the engine simulations. The model included a proportional-integral-derivative (PID) control loop that extracted shaft power from the turbocharger shaft to keep the intake manifold pressure from exceeding the limit value (set at 2.5 bar). Figure 9 shows the shaft power that can be extracted from the turbocharger shaft over the speed/load map with heavy heavy-duty diesel truck (HHDDT) transient drive cycle test points overlaid on the figure. The extracted shaft power reached as high as 19,400 W for this particular engine/turbocharger combination and choice of maximum acceptable boost pressure (2.5 bar). The maximum shaft power generated for boost pressure control was 4400 W at the regions of the map accessed during the HHDDT transient drive cycle. Additional shaft power can be extracted from the turbocharger shaft during deceleration events (shown as green crosses), where the HE-T/C would provide additional engine braking while generating useful power up to the rated 11 kW. The average electrical power that can be produced over the drive cycle is 1800 W (85% efficiency for the conversion of turbocharger shaft power to conditioned DC electrical power was assumed).

Fig. 9
Fig. 9
Close modal

For comparison, additional calculations were performed to see how efficiency was affected by the additional back pressure caused by extracting work from the turbocharger shaft instead of wastegating. For these simulations, the largest efficiency penalties were seen at the highest speed, highest load conditions. At the maximum speed (2200 rpm) and maximum fueling rate (ϕ = 0.85) the brake thermal efficiency was 0.3% lower for the HE-T/C case (37.7%) than the wastegated case (38.0%).

This information was fed forward into vehicle simulations for a Class 8 truck over the HHDDT transient drive cycle using the autonomie software package. The baseline fuel economy for the truck was 2.087 km/L (4.917 mpg). Assuming the electrical power was added back to the driveline, the fuel economy would be improved by 4.4% to 2.181 km/L (5.13 mpg). Approximately 4.3% of that reduction was attributed to power generation during deceleration events, while the remaining 0.1% was due to power generation for intake pressure control in this scenario.

Additional simulations were performed where the IMA was run in both generator- and motor-mode. The revised PID loop sought to maintain the intake pressure at a target value of 2.5 bar by extracting power from the turbocharger shaft or adding power back to the shaft (up to the IMA rated power of 11 kW). Only high load conditions were considered (ϕ > 0.5) because additional boost pressure is not required at low fuel/air equivalence ratios. Figure 10 shows the intake pressure over the speed/load range. As shown, allowing the HE-T/C to function in motor mode allows for additional low speed torque. The maximum torque curve for the baseline engine with a conventional (wastegated) turbocharger is also shown. The operating range for the turbocharged engine equipped with the HE-T/C was 17% larger than the baseline engine. The “torque curve shaping” enabled by the HE-T/C would allow for engine downsizing, which can provide secondary fuel economy benefits.

Fig. 10
Fig. 10
Close modal

### Shaft Rotordynamics.

The shaft design required a dynamic analysis to characterize the rotating assembly deflections, stresses, and lateral and torsional natural frequencies of the coupled assembly. A lumped-mass finite element approach was used. Figure 11 shows the model of the complete HE-T/C rotating system, including the turbocharger shaft on the left coupled to the IMA shaft on the right. The representations of model elements are as follows: the springs represent bearing stiffness, the vertical arrows are mass imbalances, horizontal arrows are axial loads, and different color elements represent different materials. Figure 12 shows an example of the output from the rotordynamic analysis for the fourth mode. The solid purple line indicates the normalized deflection of the centerline of the rotor at the critical speed and is referred to as the mode shape. This mode is relevant, because it occurs near the optimal operating range of the compressor on the performance map. The relevance of this modeling is to ensure the HE-T/C is not continuously running at or near a mode. Doing so can lead to decreased bearing life from the large deflections and stresses or even catastrophic failure. Table 2 summarizes the modes for the entire operating range of the HE-T/C device. Active control of the HE-T/C speed would avoid operation at these speeds, or any other operating points that could be detrimental to the device (such as operating the compressor into the surge region).

Fig. 11
Fig. 11
Close modal
Fig. 12
Fig. 12
Close modal
Table 2

Summary of rotordynamic analysis predicted modes

ModeSpeed
114,016 RPM (233.60 Hz)
229,735 RPM (495.58 Hz)
361,948 RPM (1032.47 Hz)
488,467 RPM (1474.45 Hz)
5160,683 RPM (2678.04 Hz)
6186,651 RPM (3110.86 Hz)
ModeSpeed
114,016 RPM (233.60 Hz)
229,735 RPM (495.58 Hz)
361,948 RPM (1032.47 Hz)
488,467 RPM (1474.45 Hz)
5160,683 RPM (2678.04 Hz)
6186,651 RPM (3110.86 Hz)

### Integrated Motor/Alternator Housing

#### Structural Analysis.

Finite element analysis (FEA) was used to ensure the stress in the housing, mostly due to the interference fit of the stator, would be sufficiently low as to not cause any structural damage to the housing. Figure 13 shows the result of the of the FEA analysis with equivalent Von Mises stress contours on the left and factor of safety (FoS) on the right. Areas of higher stress concentration can be seen where the supports that run from the outer shell meet the center section; however, these stresses are still relatively low and per the FoS shown on the right, it is approximately 3 or more in all locations.

Fig. 13
Fig. 13
Close modal

#### Thermal Modeling.

Computational fluid dynamics (CFD) flow and conjugate heat transfer simulations were performed on housing. The design was iterated to minimize pressure drop through the housing, ensure the stator could be sufficiently cooled by the forced convection, and predict intake air temperature increases through housing. Simulations were run at various inlet conditions to determine worst-case stator cooling (minimum intake mass flow rate) and worst-case pressure drop (maximum intake mass flow rate), and at the optimal operating region of the turbocharger (near the center of compressor map). Example results from the CFD analyses for temperature (case 1), velocity (case 3), and pressure drop (case 2) are shown in Fig. 14. Worst case scenarios for losses in the stator, intake air temperature, and exterior convection were used for all analyses. A summary of the boundary conditions is given in Table 3. For case 1, the housing (at the stator interface) reached a maximum temperature of 373K (211 °F). For case 2, given an inlet velocity of 43 m/s, a pressure drop of 900 Pa (0.13 psi) was observed. The pressure drop data were validated by benchtop flow testing.

Fig. 14
Fig. 14
Close modal
Table 3

Summary of CFD boundary conditions

DescriptionCase 1 worst coolingCase 2 worst ΔPCase 3 optimal efficiency
InletMass flow Rate0.05 kg/s0.28 kg/s0.16 kg/s
Inlet velocity8 m/s43 m/s24 m/s
temperature322 K (120 °F)
Stator LossesPower427 W
Heat flux152 kW/m2
ExteriorConvection5 W/m2 K
temperature366 K (200 °F)
DescriptionCase 1 worst coolingCase 2 worst ΔPCase 3 optimal efficiency
InletMass flow Rate0.05 kg/s0.28 kg/s0.16 kg/s
Inlet velocity8 m/s43 m/s24 m/s
temperature322 K (120 °F)
Stator LossesPower427 W
Heat flux152 kW/m2
ExteriorConvection5 W/m2 K
temperature366 K (200 °F)

## Results and Discussion

### Dynamic Control Performance.

The VFD was used to drive the motor-generator load to determine the performance of the sensorless control algorithm. The results of this testing are shown in Fig. 15, which compares the actual measured rotor angle to that of the estimated rotor angle. The maximum estimation error was found to be one sample delay, corresponding to 6.3% difference at full speed of 153 kRPM, and 2.1% difference at the measured speed of 50 kRPM.

Fig. 15
Fig. 15
Close modal

The measurements for Figs. 15 and 16 were made on a motor + generator test stand, using two PM machines on a single shaft, one operated as a motor, and the other as a generator. The currents represent those going into the motor machine, and the Bemf voltage is measured at the output of the generator terminals. The generator was very lightly loaded, so the measured voltage is, for all practical purposes, the Bemf voltage.

Fig. 16
Fig. 16
Close modal

In initial low-speed test runs, the IMA was ramped from 10 kRPM to 50 kRPM with 1 per-unit torque. This acceleration speed transient is shown in Fig. 16. The generator back EMF shows that final speed was reached with no overshoot and a maximum ramp rate of 68 kRPM/s was achieved.

Next, the VFD's overall efficiency and thermal performance was experimentally measured at 25, 50, 70, and 105 °C coolant inlet temperatures. The results are shown in Fig. 17 and show relatively little variation with regard to coolant temperature. In all cases, the maximum efficiency is >98%.

Fig. 17
Fig. 17
Close modal

### Blow-down Experiments.

Blow-down experiments were performed to ensure sound mechanical operation of the HE-T/C device before on-engine testing. Initial experiments consisted of ramp rate and control strategy testing to investigate transient operation. The results of one transient test are shown in Fig. 18. The VFD was used to speed up the HE-T/C assembly while blowing down the turbine, mimicking airflow conditions similar to that of the diesel engine at idle. The VFD was then used to speed up the turbine assembly to a nominal test speed (40 kRPM). Power is presented as a percent of maximum power at this operating condition, normalized to 2.9 kW. The VFD then regulated turbine speed while the airflow through the turbine assembly was varied with the butterfly valve, simulating the engine changing speed and allowing the VFD to draw power from the system. Notated on the figure are points when the VFD is first enabled, when it is used as a motor to speed up the turbine, and when it is used as a generator to draw power from the system. Once the steady-state speed was reached, the VFD controller seamlessly changed from sourcing power to drawing power from the turbine assembly. For initial testing, the VFD was set to ∼0.6 PU (per unit) torque.

Fig. 18
Fig. 18
Close modal

## Conclusions

A hybrid-electric turbocharger was designed including the associated power and control electronics, and sensorless speed control algorithm. We are currently making preparations for future experiments on a medium duty diesel engine, which will allow operation at higher load points with the availability of hot gas to drive to the turbine, unlike the blow-down experiment. The diesel engine test bed is part of a generator that allows loading of the engine using a switchable load bank.

The major results of this engineering application and research effort were:

1. (1)

An in-line, bolt-on, IMA was retrofit to a commercial-off-the-shelf turbocharger with minimal modification via a custom IMA housing.

2. (2)

A SiC-based VFD was developed, which can be cooled from existing 50/50 aqueous-glycol engine coolant loops operating up to 105 °C. The efficiency of the VFD over the operating temperature range of 25–105 °C coolant is greater than 98% at full load.

3. (3)

The VFD power and control electronics were packaged into an environmentally sealed enclosure with a resulting volumetric and gravimetric power density of 3.5 kW/L and 3.8 kW/kg, respectively, operating at 105 °C and 200–300V. The volumetric and gravimetric power densities increased to of 5.2 kW/L and 5.6 kW/kg, respectively, operating at 25 °C. The power density can be further increased to 16.9 kW/L and 18.3 kW/kg when modified for high voltage (600–800 V) applications.

4. (4)

The sensorless control algorithm achieved dynamic ramp rates of over 68 kRPM/s when one-per-unit torque was applied.

## Funding Data

• Phase I and Phase II SBIR grants awarded by U.S. Department of Energy (DE-SC0009235).

## Nomenclature

• EMF =

electromotive force, V

•
• G =

mass moment of inertia, lbm·in2

•
• HE-T/C =

hybrid-electric turbocharger

•
• IMA =

integrated motor/alternator

•
• MOSFET =

metal oxide field effect transistors

•
• P =

pressure, bar

•
• PMSM =

permanent-magnet synchronous motor

•
• SiC =

silicon carbide

•
• τ =

torque, in·lb

•
• THD =

total harmonic distortion, %

•
• VFD =

variable-frequency drive

•
• VGT =

variable-geometry turbocharger

•
• η =

efficiency, %

•
• ϕ =

equivalence ratio

### Subscripts

Subscripts

• C =

compressor

•
• EM =

electric motor

•
• T =

turbine

•
• TC =

turbocharger

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