# Impact of Optimization Variables on Fuel Consumption in Large Four-Stroke Diesel Marine Engines with Electrically Divided Turbochargers

Anibal Aguillon Salazar, Georges Salameh, Pascal Chesse, Nicolas Bulot, Yoann Thevenoux

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Anibal Aguillon Salazar, Georges Salameh, Pascal Chesse, Nicolas Bulot, Yoann Thevenoux. Impact of Optimization Variables on Fuel Consumption in Large Four-Stroke Diesel Marine Engines with Electrically Divided Turbochargers. Machines, 2024, 12 (12), pp.926. 10.3390/machines12120926. hal-05074076

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Article

# Impact of Optimization Variables on Fuel Consumption in Large Four-Stroke Diesel Marine Engines with Electrically Divided Turbochargers

Anibal Aguillon Salazar<sup>1,2,*</sup> <sup>1D</sup>, Georges Salameh<sup>1D</sup>, Pascal Chesse<sup>1D</sup>, Nicolas Bulot<sup>2</sup> and Yoann Thevenoux<sup>2</sup>

**Abstract:** The objective of this study is to understand how each variable impacts the optimal configuration of a marine diesel engine equipped with an electric hybrid air-charging system that allows energy assistance and recovery. The aim is to minimize CO₂ emissions by reducing fuel consumption. The hybrid system offers flexibility in adjusting parameters from both the engine and air-charging system. It is compared with the baseline engine, which uses a free-floating turbocharger. The results show a significant improvement at low engine loads, where the baseline engine struggles to provide sufficient air. While turbine speed has little influence, compressor power reduces fuel consumption at low loads. However, at mid loads, resizing the turbomachine is necessary for further improvements. At high loads, full optimization of all variables is required to reduce fuel consumption. The electric hybrid system is particularly effective in tugboat-like conditions, where low loads dominate, but less impactful for ro-pax ferries. Despite the potential of the hybrid system, a fully optimized turbocharger could provide greater benefits due to reduced losses. Future studies could explore combining the adaptability of the hybrid system with a highly efficient turbocharger to reduce emissions across all load conditions.

**Keywords:** electric hybrid turbocharger; electric compressor; power recovery turbine; fuel consumption; marine diesel propulsion engine; CO₂ reduction

## 1. Introduction

Global greenhouse gas (GHG) emissions are continuously increasing. To achieve the objective of zero GHG by 2050, the maritime industry needs to start to reduce emissions as soon as possible. Given the long lifespan of vessels (15–40 years), it is necessary to retrofit the existing fleet before the end of their life to reduce GHG emissions. Reducing fuel consumption, and, therefore, increasing engine efficiency, directly reduces the amount of CO₂ emissions. Marine diesel engines are typically turbocharged in order to increase the power output they can deliver. The coupling of turbomachines and the reciprocating engine requires a carefully conducted dimensioning process, referred to as turbo-matching. The thermal efficiency of the system depends on this dimensioning process [1]. The simplest and most common marine propulsion matching is free-floating without waste-gate valves, matched for a nominal engine operating point (100% of load and 100% of speed) [2]. Under these conditions, the system operates at its highest efficiency only at the matching point. Any other operating point is considered a trade-off in efficiency [3].

As marine propulsion plants become more electrified, electric hybridization has gained interest in the transport industry. Electric hybridization introduces a new approach to turbo-matching, creating new opportunities to reduce fuel consumption and, with it, CO₂ emissions. Electric hybridization in the air-charging system can complement the exhaust

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**Citation:** Salazar, A.A.; Salameh, G.; Chesse, P.; Bulot, N.; Thevenoux, Y. Impact of Optimization Variables on Fuel Consumption in Large Four-Stroke Diesel Marine Engines with Electrically Divided Turbochargers. *Machines* **2024**, *12*, 926. https://doi.org/10.3390/machines12120926

Academic Editor: Simeon Iliev

Received: 21 November 2024

Revised: 10 December 2024

Accepted: 13 December 2024

Published: 17 December 2024

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**Copyright:** © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">1 LHEEA, CNRS, École Centrale Nantes, Nantes Université, UMR 6598, F-44000 Nantes, France; georges.salameh@ec-nantes.fr (G.S.); pascal.chesse@ec-nantes.fr (P.C.)</footnote>

<footnote n="2">2 MAN Energy-Solutions France SAS, F-44600 Saint-Nazaire, France; nicolas.bulot@man-es.com (N.B.); yoann.thevenoux@man-es.com (Y.T.)</footnote>

<footnote>* Correspondence: anibal.aguillon-salazar@ec-nantes.fr</footnote>
gas energy with energy. Providing an additional energy source increases the energy available for the compressor. Excess energy also can now be converted into electric energy for immediate use or storage, replacing the energy sink of a waste-gate. Two functions can be identified for the electric hybridization: source and sink [4].

A compressor driven by an electric motor, generally installed together with a tur-
bocharger, works as an electric source for the air-charging system. This approach is mainly
used to reduce the response time due to turbo-lag [5,6]. In steady-state applications, the
electric compressor can increase engine torque at low engine speeds at the expense of
fuel consumption [7–9]. Reducing response time and increasing engine torque are com-
peting objectives for CO₂ emissions reduction [9]. Some authors claim that reducing the
response time can reduce fuel consumption along a driving cycle [10]. However, if there
is the opportunity, it is faster and more efficient to use the electric energy directly in the
engine shaft [11,12]. To reduce fuel consumption with an electric compressor, the operating
range of the compressor must be optimized for the specific application. In spark-ignition
engines, for example, fuel consumption can be reduced at the nominal operating point
with a properly dimensioned compressor, as, initially, a rich mixture was being used to
prevent knock [13]. Marine diesel engines require a different approach, as they run mostly
on lean mixtures. A study by Mitsubishi Heavy Industries® [14] reports an improvement
of 2.8% at low loads in the net fuel consumption of a four-stroke diesel engine by adding
an electric motor to the turbocharger’s shaft. This reduction is estimated considering the
fuel consumption of the electric power source; however, the study does not give further in-
formation about the behavior at other operating points in four-stroke applications. Further
improvements could be achieved in two-stroke applications, as this device can replace the
low efficiency auxiliary blowers, but two-stroke engines are out of the scope of this study.
It is possible to use the torque increase at low speeds to downsize engines for a specific
application during the conception and design phase. Fuel consumption by downsizing is
reduced by up to 12% compared with a not-downsized system [15]. In marine propulsion
applications, the torque of the engine is related to the rotational speed (propeller law). To
profit from the increase in torque at low speeds, some large redesign of the power plant
would be necessary by adding a high-torque electric machine in parallel to the propeller
or driving more than one propeller with one engine [16]. Diesel engines can reduce fuel
consumption by means of electric assistance only when the complete engine adaptation
is optimized for reducing fuel consumption; adjusting the air-to-fuel ratio to obtain faster
combustion can increase close-cycle efficiency, reducing fuel consumption by 8.8% [17].
Additionally, it is possible to re-tune the valve timing, creating a Miller effect to increase
efficiency. This can be done by reducing the intake valve opening time, without scarifying
the air mass-flow rate, due to the increased boost pressure [18].

An electric generator linked to the turbine in the exhaust line works as a sink to
divert the excess energy from the exhaust gases. The harvesting of energy with an electric
recovery turbine has negative impacts on the engine's efficiency caused by increased
backpressure and pumping losses [19], as well as increased exhaust temperature [20,21].
Besides the negative effects in the engine side, the efficiency of the system as a whole can be
increased [22]. Some marine engines currently use power recovery turbines in parallel with
the turbocharger to improve efficiency at high engine loads; this technology is preferred
over steam turbines as they are simpler and have lower capital costs [23]. In a free-floating
turbocharged marine engine, an excess of energy at a steady state does not occur; this
can be solved by adapting the size of the turbomachinery. A re-tuning of the engine can
extend the benefits of an electric recovery turbine. The valve timing of the exhaust valve
is more relevant for the recovery than the intake valve [24], which is more important for
the assistance. Advancing the opening of the exhaust valve reduces engine efficiency but
increases the energy available for the turbine. Increasing valve overlap can reduce pumping
losses at high loads but reduces efficiency at low loads [25]. The start of injection (SOI)
determines how much energy is recovered inside the cylinder and how much is available
for the turbines; at high engine loads, delaying SOI can increase turbine power at the expense of engine power [26].

An electric machine in the turbocharger's shaft allows both functions: source and sink. The best of both functions can be achieved with one device: increasing torque at low engine speed [27] and power recovery at high engine speeds [4]. However, the electric machine in the turbocharger's shaft presents technical difficulties to operate under steady-state conditions in small applications, due to overheating [28] and vibrations near the natural modes [27,29]. For this reason, most applications do not sustain continuous electric operation, which means that the turbocharger's shaft should carry an added inertia and added viscous losses [6], reducing its efficiency when the electric machine is not operating [30].

When both functions are available, different studies propose different configurations of exhaust valve timing; some recommend an early opening [31] accompanied by a larger turbine; meanwhile, others recommend a late opening [32] due to the losses in electric production with a smaller turbine. The size of the turbomachinery determines if the electric machine should function as a source or as a sink. A complete redesign of the turbomachine should be carried out to take into consideration both usages for every specific application [33]. A larger turbine could improve system efficiency at low engine loads [31] but requires assistance at high engine loads [34]. Meanwhile, a smaller turbine could achieve a surplus of energy at high loads, requiring assistance at low loads [4].

Waste-gate turbochargers have more potential to improve system efficiency by recovering the wasted energy at high engine speeds. Marine bi-fuel engines should have turbochargers adapted for diesel and natural-gas operation. When running on natural gas, there is a large portion of compressed air which is released to avoid knock. The reduction in CO₂ emissions by recovering this energy, without re-tuning the engine or the turbocharger, is estimated at between 3% [35] and up to 6% [36,37]. In the same manner, free-floating turbocharged marine engines with a redesigned turbocharger for both sink and source steady operation could, theoretically, reduce CO₂ emissions by up to 3% [4].

This study aims to obtain a deep understanding of the effect of each variable in the optimal fuel consumption when both functions, source and sink, are available. As large marine engine prototyping is expensive, this study should identify not only the potential of hybridization in the air-charging system, but it also should help to understand the strengths and weaknesses of the system to provide a guide to decide the best configuration before building a prototype. Even if it has been demonstrated that the electric hybrid turbocharger outperforms the electrically separated turbocharger in terms of efficiency [5], the present study focuses on the separated device approach, as it enables the analysis of the turbine and compressor individually, allowing a full understanding of their contribution to the system. A similar arrangement has been already studied in vehicle applications, demonstrating the high potential of this architecture to reduce fuel consumption by controlling independently the turbine and compressor [5]; however, low information about the losses estimation is given, and the effect of each parameter is not clearly stated. Another study based on vehicle diesel engines studied the same architecture with a rule-based control for turbine and compressor, with several assumptions to simplify the complex system, and shows that improvements are dependent of the driving-cycle: the system can reduce fuel consumption on urban cycles but increases fuel consumption on highway cycles [38]. In an study of an electrically separated turbocharger which does not include an adaptation of turbomachine size, it has been concluded that it is not possible to obtain any improvement in fuel consumption due to the conversion losses [22].

In this study, a marine free-floating matched turbocharged diesel engine is equipped with a hybrid air-charging variation. The modification involves decoupling the turbocharger shaft and connecting the compressor and turbine to independent electric machines (EMs). Additionally, an extra EM is installed on the engine crankshaft, serving as a shaft motor-generator. This machine has the function of maintaining an electric energy balance between the compressor and turbine, ensuring their demand and production are
aligned. The model of the engine is based on an existing prototype engine, in which all electric hybrid modifications are applied in a purely theoretical approach.

The objective of this study is centered on retrofitting existing engines, minimizing fuel consumption by keeping the same engine power delivery (the same propeller law). The retrofit proposed in this study consists of adding an electric hybridization in the air-charging system together with a re-tuning of the engine variables that allow adjustment in the current engine: (fixed) exhaust and intake valve timing, and the start of injection. All other engine modifications, such as the redesign of engine components, are not considered in the retrofit solution of this study. The identification of the influence of each variable on the optimal of the hybrid configuration is conducted by performing several optimizations, adding one variable at the time.

Comparing the results of the progressive optimizations, the effect of including certain parameters in the optimization or not is identified. Finally, the architecture is evaluated on three different operating profiles in a quasi-stationary approach to identify which real application could benefit the most from a hybrid electric air-charging system.

## 2. Methodology

In this section the models used in this study and the optimization methodology used are described.

### 2.1. *Baseline Engine Model*

The engine chosen for this study is a prototype version of the engine type PA6B, developed by MAN Energy Solutions® (France SAS, F-44600, Saint Nazaire, France), Franceit is a four cylinder in V developed for testing new technologies, a variant of the PA6B family of engines, which typically ranges from 12 to 20 cylinders. The main characteristics of the engine are listed in Table 1. The engine studied is equipped with fixed cam timing and individual electronic fuel pumps. In marine applications, the PA6B engines typically employ two turbochargers, as shown in the engine diagram in Figure 1. These engines are not equipped with EGR.

<table><caption>**Table 1.** Main characteristics of prototype 4 V PA6B MAN-Pielstick™ engine [39].</caption><thead><tr><td>Variable</td><td>Value</td></tr></thead><tbody><tr><td>No. of cylinders</td><td>4 in V</td></tr><tr><td>Bore</td><td>280 mm</td></tr><tr><td>Stroke</td><td>330 mm</td></tr><tr><td>Nominal speed</td><td>1050 RPM</td></tr><tr><td>Nominal power</td><td>405 kW/cyl</td></tr><tr><td>Air-charging system</td><td>2-parallel free-floating turbochargers</td></tr><tr><td>Start of injection</td><td>13° before TDCF</td></tr><tr><td>Intake valve opening (IVO)</td><td>57° before TDC</td></tr><tr><td>Intake valve closing (IVC)</td><td>81° after BDC</td></tr><tr><td>Exhaust valve opening (EVO)</td><td>85° before BDC</td></tr><tr><td>Exhaust valve closing (EVC)</td><td>79° after TDC</td></tr></tbody></table>

The 4 V engine is installed in a test bench in which the flywheel of the engine is coupled to an AVL-Zöllner® (G-64625, Bensheim, Germany) hydraulic dynamometer. This arrangement allows precise control of the engine speed. Data acquisition from thermocouples and pressure sensors are obtained by the Allen-Bradley™ data-acquisition unit and transferred to the internal data processing system of the test bench from MAN-Energy Solutions® (France SAS, F-44600, Saint Nazaire), France. Cooling water and oil are fed by external pumps, not included in the diagram of Figure 2. All instrumentalization and data acquisition are according to the ISO-8178 standard [40].
<figure><img src="image_5.png" /><figcaption>Figure 1. Diagram of the prototype 4 V PA6B MAN-Pielstick engine.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 2. Propeller law (kN³) for a PA6B engine.</figcaption></figure>

The present study is centered in marine propulsion applications; therefore, the engine is tested using the E3 cycle described in ISO-8178-4 [40]. In these tests, the brake power of the engine ($P_{brake}$) is always related to the engine speed ($N$) with a cubic relationship, known as the light-propeller law, described in Equation (1):

$$P_{brake} [kW] = k * N^3 \qquad (1)$$

The function multiplier $k$ (1.39942 × 10⁻⁶) is selected to represent the light conditions from the propeller (calm water assumption), obtaining the relationship seen in Figure 2. When the engine is coupled to a certain propeller, in steady-state conditions, the brake engine power (torque) is the direct consequence of the propeller design and the rotational speed. Tests along propeller law varying demanded engine load (percentage of nominal power) are inferring an engine speed associated to the load, related by Equation (1) (kN³).
Engine power in the engine map of Figure 2 is currently limited by the engine limits defined by MAN-Energy Solutions® France SAS, F-44600, Saint Nazaire, France based on their experience of mechanical limits such as maximum in-cylinder pressure, oil-film thickness, turbocharger surge, material mechanical limits, in-cylinder heat exchange, etc.

In large marine engines, increasing power output directly impacts major components such as the pistons, connecting rods, cylinder heads, and crankshaft, necessitating their modification. Additionally, all auxiliaries (particularly heat exchangers), the propeller shaft line, and the propeller itself are designed for a specific initial power rating. At the time of a vessel's construction, classification societies certify it based on this power rating. As a result, modifying the engine's power output would require a comprehensive reclassification study for the vessel.

This study focuses on retrofit solutions that can be implemented on existing engines without the need for extensive redesign or reclassification of the vessel.

The engine is modeled on the commercial software from Gamma Technologies®, Westmont, IL, USA called GT-Suite™, as it is widely used for engine applications. The engine sub-models used are DI-Pulse for combustion, the Woschni model for heat-transfer at the cylinder wall, linear variation with piston speed for friction, and the Zeldovitch model for emissions. The combustion model has been calibrated using experimental data from a 12 V PA6B engine, as shown in a previous publication [39]. The rest of the sub-models used are calibrated for the 4 V PA6B engine following the classic approach of marine engine modeling using GT-Suite [41], which also includes atmospheric conditions.

Figure 3 compares the temperature measurements with the model at three different locations; Figure 4 compares the pressure measurements and model after the compressor and before the turbine of the turbochargers, and, lastly, Figure 5 compares the turbocharger speed between measurements and model. In all comparisons, the engine is running along the propeller law of Figure 2. The atmospheric conditions during tests are recorded and imposed in the model for the validation section (39 °C ± 5 °C; 1013 mbar ± 1 mbar) For the rest of this study, the atmospheric conditions are imposed as the standard reference conditions, as stated in the norm ISO 15550-5 (25 °C; 1000 mbar) [42]. The parallel turbochargers are operating here sequentially, with the second turbocharger being activated at loads above 50%. The sequential parallel turbocharger is not a common practice for marine civil applications; for this reason, this study considers simple parallel turbocharging without a deactivating/activating ability. The model has good predictability of the turbocharger operating conditions of pressure, temperature, and speed.

Brake-specific fuel consumption (BSFC) represents the amount of fuel consumed to generate a specific amount of power over time and is commonly used to compare efficiency and fuel consumption of ICEs. The error of the prediction of the BSFC of the model is observed to be almost constant along the propeller law, with an average value of 9.89%, as seen in Figure 6 (standard deviation of 0.985) between model and measurements. To avoid the influence of this error in this study, the results of the modified engine will be shown relative to the baseline engine.

Engines compliant with Tier III standards of the International Maritime Office (IMO) are equipped with a selective catalytic reduction (SCR) filter. The baseline engine and the optimized engine require the presence of this element. Due to the difficulty of knowing the exact characteristics of the SCR, it was decided to not integrate it in the simulation. Eventually, its impact on the engine back-pressure will be considered the same in both cases (considered the same size as the SCR).

The PA6B engines use individual conventional plunger jerk-type fuel pumps, with a constant fixed start of injection (SOI). The 4 V prototype engine is equipped with new fuel pump technology for these large engines. The electronic fuel injection, almost standard in small-vehicle applications, has been recently adopted for the 4 V engine. The fuel pump uses the mechanics of the conventional plunger jerk-type fuel pump with a new electronic command for the fuel valve opening, which allows the SOI to be adjusted during engine operation. This was not possible with the conventional plunger jerk-type fuel pump. A
proportional-integral-derivative (PID) controller acts on the duration of the injection, to regulate the injected mass of fuel. A feed-back loop from the brake power allows the PID to achieve the specific demanded target load.

<figure><img src="image_7.png" /><figcaption>**Figure 3.** Temperature comparison between measurements and model results along the propeller law (kN³).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 4.** Pressure comparison between measurements and model results along the propeller law (kN³).</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Figure 5.** Turbocharger speed comparison between measurements and model results along the propeller law (kN³). Sequential operation deactivates turbocharger-A below 50%.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 6.** Relative error of brake-specific fuel consumption between model and measurements of the 4 V engine along the propeller law (kN³).</figcaption></figure>

The baseline configuration using simple parallel turbochargers is found by optimizing the intake and exhaust valve profiles and the SOI for each operating point with the single objective of reducing fuel consumption, while considering physical constraints such as maximum cylinder pressure, turbine inlet temperature, and surge-free operation.

The free-floating turbocharger is characterized experimentally by the manufacturer in form of maps regulated by the Society of American Engineers (SAE), known as SAE curves [43]. These curves are obtained by ensuring the compressor is not operating outside of the limits of choke and surge. For any operation inside these limits, specific interpolation methods are used [44]. However, it is known that the turbine can operate outside the limits of the compressor [45]. For this reason, a turbine model is adapted, based on the SAE curves, to extrapolate the turbine operation. The turbine model used is the model developed by Gamma Technologies (software GT-Power v2023), as it is proven that it can outperform other 0D physic-based models [46]. Both parallel turbochargers are identical; the size of the compressors and turbines is selected from the discretely available commercial turbochargers. These turbochargers are capable of providing up to 6 bars of compression ratio in a single stage. A theoretically perfectly matched turbocharger is searched by adding
mass-flow and pressure-rate multiplicators in both the turbine and compressor maps. These
multipliers are referred to as turbomachine-size multipliers.

## 2.2. Elements of the Hybrid Electric Air-Charging Architecture

The turbocharged calibrated engine model is modified with a hybrid electric air-
charging system to inspect the effects of different variables in a theoretical approach. The
modified air-charging architecture consists of an electrically split turbocharging system,
as seen in Figure 7. The two turbochargers are separated using electric machines (EMs),
with each turbine connected to an electric generator, and each compressor connected to an
electric motor. Additionally, an EM acting as a shaft-motor-generator (PTX) is added to the
engine crankshaft output. This PTX can function as a motor, also known as power-take-in
(PTI), and as a generator, or power-take-off (PTO). The electric connections indicate the
consumption or production of electric power: the motors driving the compressors consume
electric power; meanwhile, the turbines produce electric power. The PTX can consume and
produce electric power.

<figure><img src="image_11.png" /><figcaption>**Figure 7.** Diagram of the hybrid air-charging system studied.</figcaption></figure>

In the following sections, the elements that constitute the electric hybrid air-charging
system of this study are presented.

2.2.1. Power Electronics

In Figure 7, the power electronics model represents the controller and converter of electric power between EMs, in an energetic approach. As this study does not include a battery at this stage, the power electronics model is configured to maintain an electric power balance. This means that all the electric power produced is being consumed. If, after the electromechanical and gearboxes losses, the electric power of the turbines ($P_{e,turbines}$) is fulfilling exactly the electric power required by the compressors ($P_{e,compressors}$), the PTX machine should not be necessary. In case of any unbalance between the turbines and compressors, in terms of electric power, the unbalanced electric power is transferred as electric power to the PTX ($P_{e,PTX}$). Without considering conversions losses, this statement can be expressed in terms of the power of the EMs using Equation (2):
$$P_{e,compressors} + P_{e,turbines} + P_{e,PTX} = 0 \qquad (2)$$

This equation implies that, if there is a surplus power from the turbines, the PTX will operate as a motor, reducing the engine power to maintain the same system brake power, and vice versa.

The energetic approach of the model determines the power consumed and produced and the losses in the system. The model is not interested in the details of the electronics. Including the conversion losses ($\eta_{PE}$) in Equation (2) depends on whether the PTX is working as a generator or as a motor. Equation (3) states the same electric balance as Equation (2) but includes the conversion losses.

$$\eta_{PE} = \begin{cases} \frac{|P_{e, compressors}|}{|P_{e, turbines}| + |P_{e, PTX}|}; & \text{with PTX as generator} \\ \frac{|P_{e, compressors}| + |P_{e, PTX}|}{|P_{e, turbines}|}; & \text{with PTX as motor} \end{cases} \qquad (3)$$

A similar study in the literature considered the conversion efficiency of a similar arrangement to be constant and equal to 95% [22], which is a common assumption for electric converters in marine propulsion plants [47]. This study assumes the conversion efficiency to be constant and equal to 95%. Equation (3) allows the determination of the electric demand from the PTX based on the production and consumption of the turbine and compressor. The diagram of Figure 8 summarizes how this strategy is integrated in the system; only end conditions without errors are taken as valid solutions. A proper initialization and other convergence criteria avoid falling into the error end before the steady state has been achieved.

<figure><img src="image_12.png" /><figcaption>Figure 8. Schemes of the functioning of the electric hybrid architecture.</figcaption></figure>
### 2.2.2. Electric Machines

The electromechanical efficiency of an EM varies according to the speed and torque on the shaft. This efficiency is typically represented on contour maps with rotational speed and torque on the x and y axes, respectively. For this study, we selected the surface permanent magnets (SPM) type of machine, as it is the most commonly used type of EM for forced air-charging applications [48].

It is a common practice to model the electromechanical efficiency of EMs as a constant efficiency value; however, this study treats the EMs as maps to obtain a detailed approach to the losses in the system. To model the electromechanic efficiency of the Ems, there are two possible approaches: physics-based models and regression models. The regression model proposed by Mahmoudi et al. [49] requires much less information than any physical model to create a map of electromechanic efficiency. For the theoretical electric machines in this study, the nominal losses are dimensioned to limit the maximum efficiency to 96%, as for most permanent magnet EMs [50].

The EM mounted on the main engine shaft (PTX) is represented in the model with a value of requested electrical power and a map of electromechanical efficiency. The output of the model is the mechanical output power on the shaft. Nominal torque and base speed are selected from an existing EM used for marine applications. This EM is, in the model, only capable of working as a motor (positive torque) and as a generator (negative torque). The compressor is driven by a motor; both elements are connected via a gearbox. The modeling principles of the motor are the same as used in the PTX; electromechanical efficiency determines mechanical power given an electric demanded power.

The turbine cannot be modeled using the same principles as previous machines. Imposing a demanded electric power in the generator creates a constant resistive torque, while the turbine can provide different torques according to the gas conditions. If the turbine produces more torque than the EM is resisting, the speed of the system increases, creating over-speeding. If the turbine produces less torque, the system speed reduces progressively until the complete stop of the shaft. For this reason, the turbine arrangement is controlled by the rotating speed; a sensor reads the power produced by the turbine at the imposed speed and imposes the same resistive power in the generator. This control strategy for power recovery turbines has already been employed in other studies [51].

Both gas lines, A and B, are controlled equally. This arrangement creates two new degrees of freedom in the system, the compressor electric power and the turbine speed. The PTX power is a consequence of the operation of both (see Equation (3)).

The dimensioning of the compressor motor and turbine generator, and their gearboxes, is carried using the maximum allowable speed of the turbocharger, 56,500 RPM, and the maximum allowable power, estimated around 300 kW. With these characteristics, the combination of EM and gearbox selected is shown in Tables 2 and 3. The PTX is considered connected via a direct-drive connection to the crankshaft, due to the relatively low engine speed (1050 RPM maximum), and the power is considered arbitrarily as 15% of engine nominal power. The mechanical efficiency of the gearbox is imposed as 99.3%, as the nominal efficiency of the RENK® Helicoidal Gearbox GD™ [52]; these gearboxes are used in similar applications.

<table><caption>**Table 2.** Main characteristics of the EMs used in this study. (Source: AEM [53]).</caption><thead><tr><th>Position</th><th>EM Model</th><th>Variable</th><th>Value</th></tr></thead><tbody><tr><td rowspan="2">PTX</td><td rowspan="2">SE 315 S4</td><td>Rated speed</td><td>1500 RPM</td></tr><tr><td>Rated power</td><td>250 kW</td></tr><tr><td rowspan="2">Compressor</td><td rowspan="2">AH 315 M2</td><td>Rated speed</td><td>2965 RPM</td></tr><tr><td>Rated power</td><td>315 kW</td></tr><tr><td rowspan="2">Turbine</td><td rowspan="2">SE 315 LL4</td><td>Rated speed</td><td>1500 RPM</td></tr><tr><td>Rated power</td><td>360 kW</td></tr></tbody></table>
<table><caption>**Table 3.** Main characteristics of gearboxes used in this study.</caption><thead><tr><td>Position</td><td>Gearbox Type</td><td>Gear-Ratio</td></tr></thead><tbody><tr><td>Compressor</td><td>High-speed planetary</td><td>1:23.14</td></tr><tr><td>Turbine</td><td>High-speed helical</td><td>1:35</td></tr></tbody></table>

### 2.2.3. Electric Hybrid Air-Charging Model

The model of the electric hybrid air-charging architecture is implemented using the elements previously described. Figure 9 shows the energy losses in a turbocharger diagram. Generally, in turbocharger SAE maps, turbocharger mechanical efficiency is not measured separately, as it is already included in the turbine SAE map as turbine efficiency [54]. In this study, the efficiency of the shaft is included in the turbine SAE map.

<figure><img src="image_13.png" /><figcaption>**Figure 9.** Efficiency chain on a simple turbocharger.</figcaption></figure>

Figure 10 illustrates the efficiency chain on the electrically separated turbocharger. According to this efficiency chain, if the electromechanical, gearbox efficiency, and conversion efficiency are equal to one, the remaining efficiency chain becomes equivalent to the turbocharger efficiency shown in Figure 9. The losses in the air-charging system would be only due to the turbine and compressor efficiencies.

<figure><img src="image_14.png" /><figcaption>**Figure 10.** Efficiency chain on the electrically divided turbocharger.</figcaption></figure>

To verify that the electric hybrid model is equivalent to the baseline, an initial test was conducted with all the electromechanical, gearboxes, and conversion efficiencies set to one. By matching the compressor power and turbine speed of the baseline turbocharger configuration, the electrical turbocharger successfully reproduces the results of the fuel consumption of the baseline, as shown in Figure 11. When the efficiency is set back to values below 100% from the models described before, the system increases fuel consumption, as new losses are now introduced into the system.
<figure><img src="image_15.png" /><figcaption>**Figure 11.** BSFC evolution along propeller law (kN³). Comparison between baseline turbocharged engine and electrically divided (Turbosplit) configuration, with and without the added losses.</figcaption></figure>

## 2.3. Optimization Methodology

The objective of this study is to provide a retrofit solution which increases the efficiency of marine propulsion diesel engines. In this context, the propeller of the vessel is assumed to be kept the same as the baseline, which means the brake power of the Turbosplit architecture follows the same propeller law, with the same brake power demand.

The hybridization of the air-charging system and the addition of the EM in the engine's shaft introduces a variety of degrees of freedom to the system. The dimensioning of these, together with the re-tuning of the internal combustion engine (ICE), is carried out through an optimization process. The optimization problems are composed of the factors listed in Tables 4 and 5, while the constraints are listed in Table 6. The turbine maximum speed and compressor maximum power are the maximum allowable range from the baseline turbocharger, which have been electrically divided to obtain the turbine and compressor. The SOI maximum advancement angle is the maximum that has been tested on the electronic fuel pump in the 4 V engine. The size of the turbomachines is limited to 25% times larger and smaller than baseline, as further scaling factors would require a correction in the speed curves. The valve timing is modified by adding shifters for the crank-angle value corresponding to the opening and closing. These shifters act on the angle value of the original cam profile. It is important to note that the shifter for the opening affects the whole cam profile, also affecting the moment of closing. This means that the effective closing angle is the addition of opening shifter and closing shifter. All shifters are arbitrarily limited to 30 degrees in advance and retard. For simplicity, the results will show the closing angle as the effective angle shift by adding both shifters. This may result in the closing angle being effectively shifted beyond the 30-degree limit.

<table><caption>**Table 4.** Configuration of baseline-optimized values relative to baseline values.</caption><thead><tr><th>Type</th><th>Name</th><th>Unit</th><th>Factors</th><th>Along Cases</th></tr></thead><tbody><tr><td rowspan="2">State variables</td><td>Start of injection</td><td>[deg]</td><td>SOI</td><td>Independent (x4)</td></tr><tr><td>Turbomachine size</td><td>[-]</td><td>m<sub>tau; turb</sub><br>m<sub>mass; turb</sub><br>m<sub>tau; comp</sub><br>m<sub>mass; comp</sub></td><td>Case sweep (x1)</td></tr><tr><td rowspan="4">System properties</td><td rowspan="4">Valve timing</td><td rowspan="4">[deg]</td><td>IVO</td><td rowspan="4">Case sweep (x1)</td></tr><tr><td>IVC</td></tr><tr><td>EVO</td></tr><tr><td>EVC</td></tr></tbody></table>
<table><caption>**Table 5.** Optimization factors categorized by state variable or system properties.</caption><thead><tr><th>Type</th><th>Name</th><th>Unit</th><th>Factors</th><th>Along Cases</th></tr></thead><tbody><tr><td rowspan="3">State variables</td><td>Turbine speed</td><td>[rpm]</td><td>N<sub>turb</sub></td><td>Independent (x4)</td></tr><tr><td>Compressor power</td><td>[kW]</td><td>P<sub>comp</sub></td><td>Independent (x4)</td></tr><tr><td>Start of injection</td><td>[deg]</td><td>SOI</td><td>Independent (x4)</td></tr><tr><td rowspan="6">System properties</td><td rowspan="3">Turbomachine size</td><td rowspan="3">[-]</td><td>m<sub>tau; turb</sub></td><td rowspan="3">Case sweep (x1)</td></tr><tr><td>m<sub>mass; turb</sub></td></tr><tr><td>m<sub>tau; comp</sub></td></tr><tr><td rowspan="3">Valve timing</td><td rowspan="3">[deg]</td><td>m<sub>mass; comp</sub></td><td rowspan="3">Case sweep (x1)</td></tr><tr><td>IVO</td></tr><tr><td>IVC</td></tr><tr><td rowspan="2"></td><td rowspan="2"></td><td>EVO</td><td rowspan="2">Case sweep (x1)</td></tr><tr><td>EVC</td></tr></tbody></table>

<table><caption>**Table 6.** Limits and constraints for the optimization problem.</caption><thead><tr><th>Name</th><th>Unit</th><th>Minimum</th><th>Maximum</th></tr></thead><tbody><tr><td>Turbine speed</td><td>[rpm]</td><td>5000</td><td>56,500</td></tr><tr><td>Compressor power</td><td>[kW]</td><td>5</td><td>300</td></tr><tr><td>SOI</td><td>[deg]<sup>1</sup></td><td>-12</td><td>0</td></tr><tr><td>Turbomachine size</td><td>[-]<sup>2</sup></td><td>0.75</td><td>1.25</td></tr><tr><td>Valve timing</td><td>[deg]<sup>2</sup></td><td>-30</td><td>30</td></tr><tr><td>Max. in-cylinder pressure</td><td>[bar]</td><td>Ignore</td><td>Same maximum than baseline</td></tr><tr><td>Max. Turbine inlet temperature</td><td>[K]</td><td>Ignore</td><td>Same maximum than baseline</td></tr><tr><td>Surge margin</td><td>[%]</td><td>15</td><td>Ignore</td></tr></tbody></table>

Additionally, three physical constraints are included: the maximum inlet turbine temperature limited to protect the turbine blades; the maximum in-cylinder pressure as a limitation from the engine itself; and the compressor surge margin to ensure a surge-free operation. As retrofits have no intents to redesign the engine power pack system (piston, conrod, cylinder head, crankshaft, etc.), all physical limits are considered same as the baseline limits.

The optimization has a single objective, and the objective is to reduce the average system brake-specific fuel consumption (BSFC<sub>sys,AVG</sub>) along an operating cycle. In the hybrid arrangement, the system BSFC (BSFC<sub>sys</sub>) differs from the BSFC of the isolated engine (BSFC<sub>ICE</sub>) due to the addition of the PTX machine. The brake power of the system (P<sub>brake, sys</sub>) in the new arrangement is defined as the addition of the engine brake power (P<sub>brake,ICE</sub>) and the mechanical power from the PTX machine (P<sub>mech, PTX</sub>); this last one being positive when acting as a motor and negative when acting as a generator. System BSFC is calculated using Equation (4):

$$BSFC_{sys} = \frac{BSFC_{ICE} * P_{brake, ICE}}{P_{brake, sys}} = \frac{BSFC_{ICE} * P_{brake, ICE}}{P_{brake,ICE} + P_{mech, PTX}} \quad (4)$$

The average system BSFC is calculated using a weighted summation of system BSFC at four different operating points of the propeller law, defined in the procedure found in the ISO 8178-E3 cycle, as seen in Equation (5).

$$BSFC_{sys,AVG} = \frac{\sum_i (BSFC_{sys, i} * P_{brake,sys,i} * w_i)}{\sum_i (P_{brake,sys,i} * w_i)} \quad (5)$$

This procedure is recommended by the International Maritime Office for average brake-specific variables. The weights ($w_i$) used are shown in Table 7.

<footnote n="1">¹ Value relative to angle currently used in conventional plunger-type crank injection. ² Values relative to baseline configuration.</footnote>
<table><caption>**Table 7.** Weights for the ISO 8178-E3 cycle along the propeller law.</caption><tr><td>Load (i) [%]</td><td>100</td><td>75</td><td>50</td><td>25</td></tr><tr><td>Weight (w<sub>i</sub>)</td><td>0.2</td><td>0.5</td><td>0.15</td><td>0.15</td></tr></table>

For comparison purposes, the theoretically perfectly matched turbocharged engine, referred to as baseline-optimized, is included in this study. This configuration is obtained by optimizing the turbocharger size of components (turbine and compressor multipliers), SOI, and the moment of opening and closing of intake and exhaust valves, with the single objective of reducing fuel consumption. Table 4 shows the factors used in the optimization. Table 5 shows the factors used in the optimizations made in the electric hybrid air-charging architecture. Table 6 shows the optimization constraints and limits.

The design space is the space formed by all the possible input variables, or dimensions. For a low dimensional design space (below 3), it is possible to use brute-force research, which means evaluating all possible combinations. This method is not the most effective, but it provides a visual representation of the solution surface which allows for interpretability of the results. When the dimensions grow above of what can be graphically handled, the optimization is carried out with stochastic algorithms [55], specifically in this case, the genetic algorithm (GA). The use of stochastic algorithms, however, makes the interpretation of the influence of each factor difficult.

To analyze the effect of each variable independently, five different optimizations are applied. All these are the minimization of the average system BSFC along the ISO 8178-E3 cycle with the same constraints. The difference between them resides in the optimization factors used. In Figure 12, the process to obtain the five optimal configurations is shown; each stage represents the addition of one factor into the optimization.

The first parameter analyzed is the turbine speed (Turbosplit-A). The average system BSFC is minimized using brute-force searching inside the limits shown in Table 6, with a resolution of 500 rpm. The rest of the parameters are kept equal to the baseline values. This single factor is translated into four factors for the optimization, as four cases in the ISO 8178-E3 cycle are evaluated. The optimal points are then interpolated every 5% of brake load, to complete the propeller-law curve between them. This configuration is stored for comparison purposes.

The second stage minimizes the average system BSFC by optimizing the compressor power together with the turbine speed (Turbosplit-B), in a 2D exploration process using brute-force searching inside the limits of Table 6, with a resolution of 2 kilowatts. As for the previous combination, the four optimal operating points from the E3 cycle create eight factors, a combination of turbine speed and compressor power for each operating point. These points are interpolated, and the optimal propeller-law operation is stored for comparison.

Similarly, the SOI is added (Turbosplit-C), leading to a 3D brute-force exploration for every point of the E3 cycle, to determine the optimal combination of turbine speed, compressor power, and SOI. The same resolution is applied for the turbine speed and compressor power, and SOI is evaluated at every one crank-angle degree between the limits of Table 6, as smaller resolutions of SOI are already difficult to obtain in large marine engines. The interpolated optimal propeller-law operation is then stored.

The addition of turbomachines sizes (Turbosplit-D) into the optimization adds four new factors (two multipliers for compressors and turbines), which expand the design space to a total of eighteen factors, including four turbine speeds, four compressor powers, and four SOI. Due to the large number of factors, GA is used to solve the optimization. As for the brute-force searching, the GA is set to minimize the average system BSFC along the ISO 8178-E3 cycle within the constraints of Table 6. The optimal propeller law is then interpolated and stored.
<figure><img src="image_16.png" /><figcaption>Figure 12. Flow-chart of the optimization process.</figcaption></figure>
Finally, the effect of adding the valve timing into the optimization is studied (Turbosplit-E). Four new factors are added, which represent the angle shifters for the moment of intake valve opening (IVO), intake valve closing (IVC), exhaust valve opening (EVO), and exhaust valve closing (EVC). A total of twenty-two factors are optimized to minimize the average system BSFC along the ISO 8178-E3 cycle. The configuration of the GA used for this configuration (Turbosplit-E) and the previous (Turbosplit-D) are shown in Table 8. Due to the increased number of factors, the optimization Turbosplit-E increases the population size. The baseline-optimized result was found using the GA as well, as seen in Table 8.

<table><caption>**Table 8.** Genetic algorithm parameters.</caption><thead><tr><th></th><th>Baseline-Optimized</th><th>Turbosplit-D</th><th>Turbosplit-E</th></tr></thead><tbody><tr><td>Population size</td><td>40</td><td>80</td><td>100</td></tr><tr><td>No. of generations</td><td>60</td><td>75</td><td>80</td></tr><tr><td>Cross-over rate</td><td>50%</td><td>50%</td><td>50%</td></tr><tr><td>Mutation rate</td><td>50%</td><td>50%</td><td>50%</td></tr></tbody></table>

There are two approaches for configuring the GA: one considers the algorithm primarily driven by the crossover term, while the other emphasizes the importance of the mutation rate [55]. A reduced crossover rate of 50% is employed alongside a mutation rate of 50%. This configuration, coupled with a large population size, ensures an extensive exploration of the design space, even in advanced stages of the optimization, thus avoiding premature convergence. However, compared to the approach primarily driven by crossover, this configuration may require an increased number of generations to achieve convergence.

## 3. Results

In this section, the effect of state variables (Section 3.1) and system properties (Section 3.2) on different engine variables such as power on the turbomachines and the power of the PTX are analyzed. The effect on the final system BSFC is specifically analyzed in Section 3.3. An analysis of added losses is included in Section 3.4. Finally, the results are applied to real operating profiles in Section 3.5.

### 3.1. Influence of State Variables

The graph in Figure 13 is obtained by imposing the same efficiency chain as the turbocharger (without electromechanical, gearbox, and converter losses), allowing for a direct comparison with the baseline turbocharger configuration, as the efficiency chains are equivalent. The variation of turbine speed does not significantly affect the system BSFC. Without considering added losses, the optimal turbine speed obtains a marginal benefit below a 1% reduction in BSFC. This benefit is lost when the efficiency chain is converted back to the hybrid electric architecture.

Figure 14 shows the turbomachines' power along the engine propeller law. The baseline curves correspond to the turbocharger power, while the Turbosplit results are separated between turbine and compressor power. The baseline-optimized configuration significantly increases the turbocharger power by adapting the turbine and compressor sizes. Due to the high compressor power, at high engine loads, the system must reduce the injection advance, as shown in Figure 15, due to the constraints on maximum in-cylinder pressure.

In the Turbosplit architecture, freely adapting the compressor power allows for an increase in the compressor power at low engine loads, similar to the baseline-optimized configuration. However, at high engine loads, it becomes possible to maintain a high injection advance by reducing the compressor power. This combination of an early SOI and a reduction in the compressor power enables the turbine to produce a surplus of power at high engine loads, which is then recovered by the PTX machine. Figure 16 illustrates that the PTX machine remains working as a generator only until SOI is added to the optimization.
<figure><img src="image_17.png" /><figcaption>**Figure 13.** Variation of turbine speed on Turbosplit architecture with efficiency chain equivalent to turbocharger. Comparison with turbocharger stock operating points.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 14.** Power on a single turbomachine along the propeller law (kN³).</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 15.** SOI along propeller law (kN³). Angles are shown relative to the SOI used on the actual conventional plunger-type jerk fuel pump configuration.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Figure 16.** PTX power evolution along the propeller law (kN³) for different optimizations. Negative power indicates generator mode (PTO), and positive power indicates motor mode (PTI).</figcaption></figure>

## 3.2. Influence of System Properties

The first system property to be included is the size of the turbomachines. This property is parameterized with four multiplier factors: pressure ratio and mass-flow rate multipliers on compressors and turbines maps. Due to the high number of variables, the optimization is conducted using the genetic algorithm with the settings shown in Table 8. The optimal combination of the size multiplier factors for the turbine and compressor is presented in Table 9, and the resulting maps are displayed in Figure 17.

<table><caption>**Table 9.** Optimal turbomachine sizes.</caption><thead><tr><th rowspan="2">Multipliers</th><th colspan="3">Compressor</th></tr><tr><th>Baseline-Optimized</th><th>Turbosplit-D</th><th>Turbosplit-E</th></tr></thead><tbody><tr><td>m<sub>tau</sub></td><td>1.002</td><td>1.041</td><td>0.842</td></tr><tr><td>m<sub>mass</sub></td><td>0.796</td><td>0.858</td><td>0.779</td></tr></tbody><thead><tr><th rowspan="2">Multipliers</th><th colspan="3">Turbine</th></tr><tr><th>Baseline-optimized</th><th>Turbosplit-D</th><th>Turbosplit-E</th></tr></thead><tbody><tr><td>m<sub>tau</sub></td><td>1.187</td><td>1.202</td><td>1.229</td></tr><tr><td>m<sub>mass</sub></td><td>0.754</td><td>0.751</td><td>0.779</td></tr></tbody></table>

<figure><img src="image_21.png" /><figcaption>**Figure 17.** Comparison of turbomachine sizes: (a) compressor SAE map size comparison; (b) turbine SAE map size comparison.</figcaption></figure>
Regarding the compressor maps of Figure 17a, the baseline-optimized compressor has been modified with a smaller mass-flow capacity, and the pressure ratio remains almost invariant. This modification shifts the surge limit, enabling higher pressure ratios for the same mass-flow rates. In the Turbosplit-E configuration, the pressure ratio is scaled down due to the reduced maximum compressor power in the hybrid architecture. The Turbosplit-E optimal map shows a high-efficiency area at lower pressure ratios. Comparing curves Turbosplit-C and Turbosplit-D, below 50% of brake load, the new compressor size obtained similar boost pressures (see Figure 18a) with less demanded compressor power (See Figure 19a).

<figure><img src="image_22.png" /><figcaption>**Figure 18.** Optimal pressure in the turbomachines along the propeller law (kN³): (a) compressor outlet pressure; (b) turbine inlet pressure.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 19.** Power on turbomachines along the propeller law (kN³): (a) compressor power; (b) turbine power.</figcaption></figure>

Regarding the turbine maps of Figure 17b, both optimal maps are similar since the turbine mass-flow rate multiplier reaches the limit of 25% smaller scale (0.75). Smaller mass-flow rate capacity pushes the turbine to produce more power. Turbine-generated power has significantly increased due to the turbine's new scale, as seen in Figure 19b.

At nominal brake load, the modified size of the turbomachine enables a surplus of energy to be obtained, which it is not possible to achieve by only modifying turbine speed, compressor power, and SOI when starting from a free-floating turbocharger. The PTX, working as a PTI, can satisfy 4.04% (65 kW) of the brake power demand with the surplus of energy recovered from the turbines when the size of the turbomachine is included (Turbosplit-D) and 4.67% of brake power demand (75.7 kW) when all factors are included (Turbosplit-E).
The effect of modifying the moment of opening and closing of the intake and exhaust valves was studied last (Turbosplit-E). The new optimized intake and exhaust valve lift profiles are shown in Figure 20. In the optimized baseline version, the increase in the boost pressure (Figure 18a) with respect to baseline allows for a more effective Miller effect by reducing the total opening of the intake valves without decreasing the airflow. In the baseline-optimized version, the valve overlap increases from 136 degrees to 150 degrees, and the EVO occurs 10 degrees later than in the stock version. In the optimized Turbosplit (E), the valve overlap increases further, to 158 degrees, while the EVO delays to 16 degrees. In addition, the total duration of the exhaust valve opening is reduced by 8 degrees, and the duration of the intake valve opening is increased by 10 degrees compared to the baseline-optimized version.

<figure><img src="image_24.png" /><figcaption>**Figure 20.** Intake and exhaust valve profiles. Comparison of baseline stock with baseline-optimized and Turbosplit-optimized (E).</figcaption></figure>

The new camshafts in both optimized configurations improve the indicated engine efficiency by extending the closed-cylinder expansion, despite the increment in engine pumping losses observed in Figure 21.

<figure><img src="image_25.png" /><figcaption>**Figure 21.** LogP vs. LogV cycle Diagram. Comparison between turbocharger stock configuration and Turbosplit-E configuration. Nominal operating point (100% load–100% speed).</figcaption></figure>
### 3.3. Effect of Each Factor in System BSFC

Figure 22 shows the relative difference in system BSFC with different configurations compared with the baseline configuration. Each curve represents the optimal BSFC when progressively including the optimization factors. As a reminder, all the curves are evaluated along the propeller law, relating demanded brake load with engine speed by Equation (1).

<figure><img src="image_26.png" /><figcaption>**Figure 22.** Difference in system BSFC relative to baseline values along the propeller law (kN³), in percentage.</figcaption></figure>

The turbine speed (Turbosplit-A), and consequently turbine efficiency, have a low impact on brake efficiency. Combining its effect with compressor power (Turbosplit-B), improves fuel consumption at low loads. Comparing curve Turbosplit-B with the baseline curve shows that fuel consumption is reduced by 6% at 25% of brake load; however, for loads above 52%, the losses overcome the benefits, and no benefits on fuel consumption are observed. The combined effect of previous parameters together with SOI (Turbosplit-C) allows fuel consumption to be reduced at high engine loads above 88% of brake load. Below these loads, the SOI is already at its optimal value, and improvements can be achieved compared with the previous curve (Turbosplit-B).

The addition of the size of the turbomachine to the optimization (Turbosplit-D) obtains the deepest impact on BSFC of all the variables studied. Compared with the previous case, Turbosplit-D obtains 7 [g/kWh] less than Turbosplit-C almost consistently along the propeller law and lower fuel consumption than the baseline curve for loads below 78% of the brake load. The effect of the valve timing is observed mainly at high loads, reducing BSFC with respect to the previous curve (Turbosplit-D) at loads above 63%. The added losses are higher at high brake loads, and the optimization of all the parameters cannot overcome the losses, increasing fuel consumption relative to baseline at loads above 83%. At loads below 63%, the fuel consumption is kept as Turbosplit-D, being 8.8% lower than the baseline at 25% of load.

### 3.4. Added Losses in the System

A deeper insight into the electromechanical efficiency maps of the EMs shows that the motor associated with the compressor, in Figure 23, reaches the limits of maximum torque at nominal brake load. The optimization shifts the torque curve towards the high efficiency region. Regarding the generator associated with the turbine in Figure 24, the speed control allows a different shape of the torque-speed curve, keeping a constant increasing power, as seen in Figure 19b. The PTX machine is the only one capable of motor/generator operation in the system, as seen in Figure 25. In the optimized configuration, the demanded torque from the PTX reduces when brake load increases, the torque curve of the PTX approaching to the x-axis. At near zero torque, the electromechanical efficiency of the PTX drops to near zero values.
<figure><img src="image_27.png" /><figcaption>Figure 23. Electromechanical efficiency map of the motor which drives the compressor-A.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Figure 24. Electromechanical efficiency map of the generator linked to the turbine-A.</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>**Figure 25.** Electromechanical efficiency of the PTX machine.</figcaption></figure>

### 3.5. Weighted Average BSFC in Real-Life Cycles

Table 10 shows the relative difference between both optimized architecture, baseline-optimized, and Turbosplit-E, according to the weighted averaged BSFC on the ISO 8178-E3 cycle; the results are expressed relative to baseline values. The Turbosplit-E configuration obtains higher fuel consumptions due to the efficiency losses, and it cannot overcome a perfectly matched turbocharger with an optimized engine for this specific cycle operation. This section examines how these two configurations perform along three different real-life cycle operations.

<table><caption>**Table 10.** Weighted average system BSFC for the optimized architectures; values relative to baseline configuration.</caption><thead><tr><td>Case</td><td>Δ BSFC Averaged E3 Cycle</td></tr></thead><tbody><tr><td>Baseline-optimized</td><td>-3.58%</td></tr><tr><td>Turbosplit-E</td><td>-1.36%</td></tr></tbody></table>

The three different operating profiles of vessels to analyze are obtained from the MAN Energy Solutions® (France SAS, F-44600, Saint Nazaire database). These data are represented in form of a histogram in Figure 26, where each bar represents the percentage of running hours under a certain interval of engine load for each operating cycle.

The total fuel consumption associated with each type of ship is calculated by applying the BSFC to each interval of the histogram and then scaling it to its respective nominal vessel power from Table 11. The differences in the operating profiles of the three types of vessels are significant: tugboats operate mainly at low engine loads, fishing vessels operate most of the time at mid-engine loads, and the Ro-pax ferries are driven mostly at high engine loads.
<figure><img src="image_30.png" /><figcaption>**Figure 26.** Three different operating profiles, shown in the form of a histogram of percentage of running time and engine load.</figcaption></figure>

<table><caption>**Table 11.** Characteristics of vessel operating profiles compared in this study.</caption><thead><tr><td>Vessel Type</td><td>Nominal Power</td><td>Running Time (% of the Year)</td></tr></thead><tbody><tr><td>Tugboat</td><td>2040 [kW] x2</td><td>22.6%</td></tr><tr><td>Fishing vessel</td><td>2970 [kW]</td><td>60.9%</td></tr><tr><td>Ro-pax ferry</td><td>10,350 [kW]</td><td>54.3%</td></tr></tbody></table>

When both configurations are evaluated in the ISO 8178-E3 cycle, the Turbosplit-E configuration obtains -1.36% less fuel consumption than baseline. When evaluated in a tugboat profile, the improvement increases up to -5.3% less fuel consumption, as the benefits of Turbosplit-E are focused on low brake loads, where the tugboats are mainly driven. In a fishing vessel, the Turbosplit-E configuration obtains an improvement of -2.7% less fuel consumption than baseline, which is still higher than the estimation with the fictional ISO 8178-E3 cycle. Due to the fact that ro-pax ferries are mainly driven at high brake loads, the Turbosplit-E cannot overcome the baseline consumption.

Compared with the baseline-optimized configuration, the benefits obtained with Turbosplit-E are no match for a perfectly matched turbocharger. However, in terms of total tons of fuel consumed per year in a tugboat, the difference between the baseline-optimized (-42 tons) and Turbosplit-E (-34 tons) is 8 tons per year, as seen in Table 12. This demonstrates that improving the air-changing system by electric hybridization has more potential in reducing fuel consumption in vessels being driven like tugboats, more than ro-pax ferries, and the adoption of different arrangements of turbochargers and electric machines could overpass a baseline-optimized configuration.

<table><caption>**Table 12.** Fuel consumption of both optimized architectures, relative to baseline values.</caption><thead><tr><td>Vessel Type</td><td>Baseline Fuel Consumption (tons/year)</td><td>Δ Consumption Baseline-Optimized (tons/year [%])</td><td>Δ Consumption Turbosplit-E (tons/year [%])</td></tr></thead><tbody><tr><td>Tugboat</td><td>636</td><td>-42 [-6.6%]</td><td>-34 [-5.3%]</td></tr><tr><td>Fishing vessel</td><td>1773</td><td>-90 [-5.1%]</td><td>-47 [-2.7%]</td></tr><tr><td>Ro-pax ferry</td><td>16,029</td><td>-127 [-0.8%]</td><td>+2 [+0.01%]</td></tr></tbody></table>
## 4. Discussion

Figure 27 shows the evolution of system BSFC for a constant demanded brake load (75% of brake load, propeller law), while varying compressor power, turbine speed, and SOI. The results are presented in terms of air-to-fuel ratio (in-cylinder trapped). An increase in air-to-fuel (A/F) ratio accelerates the combustion, as seen in Figure 28, improving engine gross efficiency [56].

<figure><img src="image_31.png" /><figcaption>**Figure 27.** System BSFC variation according to A/F ratio (trapped) when modifying turbine speed and compressor power, for three different configurations of SOI. (75% of brake load).</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>**Figure 28.** Variation of turbine speed and compressor power for the same three configurations of SOI on combustion duration. (75% of brake load).</figcaption></figure>
However, due to the electric energy balance, increasing the A/F ratio requires additional compressor power, increasing the power demand from the PTX. To maintain the same load demand, the internal combustion engine (ICE) must produce more power to meet the PTX power requirement. This results in extending the injection duration for a constant SOI, leading to longer combustion durations. The balance of these competing factors requires finding an optimal operational point that minimizes the combustion duration and, thus, system BSFC. The importance of addressing the source of electric power resides in obtaining a proper model of both competing factors. If electricity is free, the system increases air-to-fuel just until some physical limitation is reached [17].

Turbine speed, and therefore turbine efficiency, have a low impact on fuel consumption, as found for a configuration of a turbocharger with a recovery turbine [51], which indicates that a mechanical linkage could be more interesting in the turbine side than the compressor side [57]. Previous studies demonstrated that the electric compressor could be used to increase the air-to-fuel ratio, obtaining a faster combustion, increasing closed-cycle efficiency, and reducing CO₂ emissions [17], as confirmed in Figures 27 and 28. In the free-floating turbocharger at low engine loads, the compressor does not provide sufficient pressure for an efficient combustion; improving air-to-fuel ratio conditions with an increased compressor power has a high impact on reducing fuel consumption. This confirms the findings of this study of the electric assist in a large marine four stroke engine, where they share only the results at low engine loads [14].

However, at high engine loads, the SOI has a larger impact on fuel consumption than compressor power. With the ability of controlling the compressor power, it could increase the advance of injection in detriment to the compressor power to keep the same maximum in-cylinder pressure, if the SOI was originally limited by the cylinder pressure.

The effect of the system properties is difficult to interpret due to the choice of using genetic algorithm upfront brute-force searching. A smaller turbine size considerably increases turbine power, as seen in Figure 19; this aligns with previous studies [4], which found that a smaller turbine increases engine efficiency at every operating point. The new compressor size allows the power demand to be reduced, which increases the surplus of energy, as observed in the literature [4]. The size of the turbomachinery has the largest impact of all parameters studied, explaining why, when it is not considered, it is not possible to obtain appreciable improvements in fuel consumption [22]. The effect of valve timing, observed at high engine loads in Figure 22, is mainly due to the increase in valve overlapping. It has been already demonstrated that increasing valve overlapping leads to an increased amount of residual gas at low engine loads, increasing the combustion duration and having a negative impact on fuel consumption; however, at high engine loads, it can reduce pumping losses and reduce fuel consumption [25]. The Miller effect achieved with a reduced intake opening time is accompanied by an increased boost pressure at loads below 70%, as seen in Figure 18, to keep the same air-to-fuel ratio. A similar configuration has been obtained with an electric compressor and a turbocharger [18], where, additionally, the geometric compression-ratio (CR) of the engine has been increased, to keep a constant effective CR. Exhaust valve opening is delayed, preferring in-cylinder engine gas expansion upfront to turbine expansion. This exhaust valve configuration is the opposite of the configuration found in an earlier study of an electric hybrid turbocharger [31] but aligns with more recent results [32].

Tugboat operating profiles are similar to the urban driving cycles of vehicles, as they are mainly at low engine loads. It has been previously demonstrated that urban driving cycles have more potential to reduce fuel consumption with an hybrid air-charging system than highway cycles [38]. This study confirms that tugboat operating profiles have a larger potential for improvement than other types of vessels. This finding is corroborated by some studies based on the optimization of vessels with electric hybrid propulsion [57,58].

While this study demonstrates that purely adapting the engine operation without batteries can reduce fuel consumption compared to the stock version, optimizing the existing turbocharged engine may offer greater fuel savings with reduced complexity.
Future studies should explore how to combine the benefits of a turbocharger with an electric hybrid air-charging system by minimizing the effect of added losses. Different arrangements of turbochargers and electric machines could improve the benefits obtained with a purely electrically divided turbocharger. The ability to control the A/F ratio might be attractive for new applications requiring specific control of the combustion, such as new alternative decarbonized fuels. The effect of adding an energy storage system should be analyzed once the best configuration of the hybrid air-charging system is identified in a balanced steady state. The storage system then should be added, and the balance could be shifted all along the dynamic operation to improve the benefits, by charging and discharging the batteries.

## 5. Conclusions

The presented study presents the effects of several engine variables and characteristics when optimized to reduce fuel consumption in retrofit marine applications using a source/sink hybridization in the air-charging system. At low loads, the system can drastically reduce the fuel consumption due to the poor breathing of the baseline free-floating turbocharger. At higher loads, the baseline turbocharger approaches its optimum at the nominal operating point, leaving small room for relative improvements. This theoretical arrangement is not recommended for real applications as it is, as the comparison with an optimized turbocharger demonstrates, but, for education purposes, it helped to understand the effect of each parameter separately. Future studies should first analyze the best of the possible arrangements of an electric hybrid air-charging system including a turbocharger, then study the inclusion of an energy storage system.

**Author Contributions:** Conceptualization, A.A.S., G.S. and P.C.; methodology, A.A.S. and G.S.; software, A.A.S.; investigation, A.A.S.; resources, Y.T.; writing—original draft preparation, A.A.S.; writing—review and editing, G.S. and Y.T.; supervision, N.B.; project administration, P.C. and N.B.; funding acquisition, P.C. and N.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Association Nationale de la Recherche et de la Technologie (CIFRE 2020/1035) and MAN Energy Solutions® France SAS.

**Data Availability Statement:** The original contributions presented in this study are included in this article; further inquiries can be directed to the corresponding author.

**Acknowledgments:** The authors wish to thank Olivier Giroux and Vivien Leroy for their technical support during this study.

**Conflicts of Interest:** The authors declare no conflicts of interest.

## Abbreviations

<table><tr><td>A/F ratio</td><td>Air-to-fuel ratio</td></tr><tr><td>BSFC</td><td>Brake-specific fuel consumption [g/kWh]</td></tr><tr><td>CR</td><td>Compression ratio</td></tr><tr><td>EM</td><td>Electric machine</td></tr><tr><td>EVC</td><td>Exhaust valve closing shifter value</td></tr><tr><td>EVO</td><td>Exhaust valve opening shifter value</td></tr><tr><td>GA</td><td>Genetic algorithm</td></tr><tr><td>GHG</td><td>Greenhouse gas</td></tr><tr><td>ICE</td><td>Internal combustion engine</td></tr><tr><td>IMO</td><td>International maritime office</td></tr><tr><td>IVO</td><td>Intake valve opening shifter value</td></tr><tr><td>IVC</td><td>Intake valve closing shifter value</td></tr><tr><td>m<sub>mass</sub></td><td>Scale multiplier factor of mass-flow rate</td></tr><tr><td>m<sub>tau</sub></td><td>Scale multiplier factor of pressure ratio</td></tr></table>
<table><tr><td>N<sub>turb</sub></td><td>Turbine speed [rpm]</td></tr><tr><td>P<sub>brake</sub></td><td>Brake power [kW]</td></tr><tr><td>P<sub>comp</sub></td><td>Compressor power [kW]</td></tr><tr><td>P<sub>mech</sub></td><td>Mechanical power [kW]</td></tr><tr><td>P<sub>e</sub></td><td>Electric power [kW]</td></tr><tr><td>PID</td><td>Proportional integrative derivative controller</td></tr><tr><td>PTO</td><td>Power take-off</td></tr><tr><td>PTI</td><td>Power take-in</td></tr><tr><td>PTX</td><td>Power take-off and power take-in</td></tr><tr><td>SAE</td><td>Society of automotive engineers</td></tr><tr><td>SCR</td><td>Selective catalytic reduction</td></tr><tr><td>SOI</td><td>Start of injection</td></tr><tr><td>SPM</td><td>Surface permanent magnets</td></tr><tr><td>sys</td><td>System</td></tr><tr><td>w</td><td>Weights for weighted averaged</td></tr><tr><td>η<sub>PE</sub></td><td>Conversion efficiency of the power electronics</td></tr></table>

## References

1. Haddad, S.D.; Watson, N. *Watson Principles and Performance in Diesel Engineering*; U.S. Department of Energy, Office of Scientific and Technical Information: Oak Ridge, TN, USA, 1984.

2. Hiereth, H.; Prenninger, P. *Charging the Internal Combustion Engine*; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2007.

3. Watson, N.; Janota, M.S. *Turbocharging the Internal Combustion Engine*; Macmillan International Higher Education: London, UK, 1982.

4. Yang, M.; Hu, C.; Bai, Y.; Deng, K.; Gu, Y.; Qian, Y.; Liu, B. Matching method of electric turbo compound for two-stroke low-speed marine diesel engine. *Appl. Therm. Eng.* **2019**, *158*, 113752. [CrossRef]

5. Tavčar, G.; Bizjan, F.; Katrašnik, T. Methods for improving transient response of diesel engines-influences of different electrically assisted turbocharging topologies. *Proc. Inst. Mech. Eng. Part D J. Automob. Eng.* **2011**, *225*, 1167–1185. [CrossRef]

6. Breitbach, H.; Jausel, H.; Garrard, T.; Metz, D. Electrically Assisted Supercharging Status Quo and Outlook. *MTZ Worldw.* **2018**, *79*, 28–35. [CrossRef]

7. Shibata, N.; An, B.; Jinnai, Y.; Ebisu, M.; Yamashita, Y. Electric Supercharging Technology for Automobiles. *Mitsubishi Heavy Ind. Tech. Rev.* **2019**, *56*, 1.

8. Mattarelli, E.; Rinaldini, C.A.; Agostinelli, E. *Comparison of Supercharging Concepts for SI Engine Downsizing*; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2016.

9. Menegazzi, P.; Wu, Y. Thomas Design of an electric supercharger for downsized engines. *MTZ Worldw.* **2013**, *74*, 36–41. [CrossRef]

10. Aymanns, R.; Uhlmann, T.; Nebbia, C.; Plum, T. Electric supercharging new opportunities with higher system voltage. *MTZ Worldw.* **2014**, *75*, 4–11. [CrossRef]

11. Katrašnik, T.; Trenc, F.; Medica, V.; Markič, S. An analysis of turbocharged diesel engine dynamic response improvement by electric assisting systems. *J. Eng. Gas Turbines Power* **2005**, *127*, 918–926. [CrossRef]

12. Katrasnik, T.; Rodman, S.; Trenc, F.; Hribernik, A.; Medica, V. Improvement of the dynamic characteristic of an automotive engine by a turbocharger assisted by an electric motor. *J. Eng. Gas Turbines Power* **2003**, *125*, 590–595. [CrossRef]

13. Xia, F.; Griefnow, P.; Tidau, F.; Jakoby, M.; Klein, S.; Andert, J. Electric torque assist and supercharging of a downsized gasoline engine in a 48V mild hybrid powertrain. *Proc. Inst. Mech. Eng. Part D J. Automob. Eng.* **2021**, *235*, 1245–1255. [CrossRef]

14. Shiraishi, K.; Ono, Y.; Yamashita, Y.; Sakamoto, M. Energy savings through electric-assist turbocharger for marine diesel engines. *Mitsubishi Heavy Ind. Tech. Rev.* **2015**, *52*, 36–41.

15. Pallotti, P.; Torella, E.; New, J.; Criddle, M.; Brown, J. *Application of an Electric Boosting System to a Small, Four-Cylinder SI Engine*; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2003.

16. Rusman, J. Charge Air Configurations for Propulsion Diesel Engines Aboard Fast Naval Combatants: A Simulation Study on Efficiency and Performance. Master’s Thesis, Delft University of Technology, Delft, The Netherlands, 2018.

17. Baek, S.; Lee, H.; Lee, K. Fuel efficiency and exhaust characteristics of turbocharged diesel engine equipped with an electric supercharger. *Energy* **2021**, *214*, 119049. [CrossRef]

18. Chen, B.; Zhang, L.; Han, J.; Zhang, Q. A combination of electric supercharger and Miller Cycle in a gasoline engine to improve thermal efficiency without performance degradation. *Case Stud. Therm. Eng.* **2019**, *14*, 100429. [CrossRef]

19. Kishishita, K.; Miyajima, K.; Hirai, K. A study of an electrical turbo-compound system. *JSAE Rev.* **1995**, *16*, 66–68. [CrossRef]

20. Hountalas, D.; Katsanos, C.; Lamaris, V. *Recovering Energy from the Diesel Engine Exhaust Using Mechanical and Electrical Turbocompounding*; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2007.

21. Ma, Z.; Gu, Y.; Zhu, S.; Yang, M.; Deng, K. Analysis on capability of power recovery of marine diesel engine at high backpressure conditions. *Appl. Therm. Eng.* **2022**, *204*, 117933. [CrossRef]
22. Aghaali, H.; Angstrom, H.-E. Demonstration of Air-Fuel Ratio Role in One-Stage Turbocompound Diesel Engines; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2013.

23. Lion, S.; Vlaskos, I.; Taccani, R. A review of emissions reduction technologies for low and medium speed marine Diesel engines and their potential for waste heat recovery. *Energy Convers. Manag.* **2020**, *207*, 112553. [CrossRef]

24. Thompson, I.G.M.; Spence, S.; McCartan, C.; Talbot-Weiss, J.; Thornhill, D. One dimensional modeling of a turbogenerating spark ignition engine operating on biogas. *SAE Int. J. Engines* **2011**, *4*, 1354–1364. [CrossRef]

25. Jang, J.; Yeom, K.; Bae, C. Effects of Exhaust Throttling on Engine Performance and Residual Gas in an SI Engine; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2004.

26. Ismail, Y.; Durrieu, D.; Menegazzi, P.; Chesse, P.; Chalet, D. Potential of Exhaust Heat Recovery by Turbocompounding; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2012.

27. Carpenter, A.L.; Beechner, T.L.; Tews, B.E.; Yelvington, P.E. Hybrid-Electric Turbocharger and High-Speed SiC Variable-Frequency Drive Using Sensorless Control Algorithm. *J. Eng. Gas Turbines Power* **2018**, *140*, 122801. [CrossRef]

28. Balis, C.; Middlemass, C.; Shahed, S. Design & Development of E-Turbo for SUV and Light Truck Applications; Garrett Engine Boosting Systems (US): Torrance, CA, USA, 2003.

29. Yoshida, T.; Sakamoto, M.; Sasaki, R.; Ono, Y.; Nishimura, H.; Tsuji, T. Vibration Suppression Method and Vibration Suppression Apparatus for Turbocharger Capable of Being Driven by Motor. U.S. Patent 10,316,692, 11 June 2019.

30. Shiraishi, K.; Ono, Y.; Sugishita, K. Development of large marine hybrid turbocharger for generating electric power with exhaust gas from the main engine. *Mitsubishi Heavy Ind. Tech. Rev.* **2010**, *47*, 53–58.

31. Panting, J.; Pullen, K.; Martinez-Botas, R. Turbocharger motor-generator for improvement of transient performance in an internal combustion engine. *Proc. Inst. Mech. Eng. Part D J. Automob. Eng.* **2001**, *215*, 369–383. [CrossRef]

32. Westhoeve, J. Hybrid Electric Turbocharging: Improving the Loading Capability and Efficiency of a Dual Fuel Engine. Master's Thesis, Delft University of Technology, Delft, The Netherlands, 2018.

33. Dimitriou, P.; Burke, R.; Zhang, Q.; Copeland, C.; Stoffels, H. Electric turbocharging for energy regeneration and increased efficiency at real driving conditions. *Appl. Sci.* **2017**, *7*, 350. [CrossRef]

34. Pasini, G.; Lutzemberger, G.; Frigo, S.; Marelli, S.; Ceraolo, M.; Gentili, R.; Capobianco, M. Evaluation of an electric turbo compound system for SI engines: A numerical approach. *Appl. Energy* **2016**, *162*, 527–540. [CrossRef]

35. Figari, M.; Theotokatos, G.; Coraddu, A.; Stoumpos, S.; Mondella, T. Parametric investigation and optimal selection of the hybrid turbocharger system for a large marine four-stroke dual-fuel engine. *Appl. Therm. Eng.* **2022**, *208*, 117991. [CrossRef]

36. Montal Almirall, D. Electric Power Generation from the Hybrid Turbocharger of a Marine Propulsion Diesel Engine. Bachelor's Thesis, Universitat Politècnica de Catalunya, Barcelona, Spain, 2019.

37. Altosole, M.; Balsamo, F.; Campora, U.; Mocerino, L. Marine Dual-Fuel Engines Power Smart Management by Hybrid Turbocharging Systems. *J. Mar. Sci. Eng.* **2021**, *9*, 663. [CrossRef]

38. Divekar, P.S.; Ayalew, B.; Prucka, R. Coordinated Electric Supercharging and Turbo-Generation for a Diesel Engine; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2010.

39. Xavier, T.; Cyril, R.; Simon, P.; Pascal, C.; Georges, S. A New Simulation-Based Methodology to Improve Medium-Speed Diesel Engines BSFC/NOₓ Tradeoff With an Optimized Air Charging System. *J. Eng. Gas Turbines Power* **2023**, *145*, 011009. [CrossRef]

40. ISO 8178-4:2020; Reciprocating Internal Combustion Engines—Exhaust Emission Measurement—Part 4: Steady-State and Transient Test Cycles for Different Engine Applications. ISO: Geneva, Switzerland, 2020.

41. Stoumpos, S.; Theotokatos, G.; Boulougouris, E.; Vassalos, D.; Lazakis, I.; Livanos, G. Marine dual fuel engine modelling and parametric investigation of engine settings effect on performance-emissions trade-offs. *Ocean. Eng.* **2018**, *157*, 376–386. [CrossRef]

42. J1826_199503; Turbocharger Gas Stand Test Code. SAE International: Warrendale, PA, USA, 1995. [CrossRef]

43. Salameh, G.; Chesse, P.; Chalet, D. Mass flow extrapolation model for automotive turbine and confrontation to experiments. *Energy* **2019**, *167*, 325–336. [CrossRef]

44. Salameh, G.; Chesse, P.; Chalet, D.; Talon, V. *Experimental Study of Automotive Turbocharger Turbine Performance Maps Extrapolation*; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2016.

45. Zhu, S.; Deng, K.; Liu, S. Modeling and extrapolating mass flow characteristics of a radial turbocharger turbine. *Energy* **2015**, *87*, 628–637. [CrossRef]

46. Bassam, A. Use of Voyage Simulation to Investigate Hybrid Fuel Cell Systems for Marine Propulsion. Ph.D. Thesis, University of Southampton, Southampton, UK, 2017.

47. Lee, W.; Schubert, E.; Li, Y.; Li, S.; Bobba, D.; Sarlioglu, B. Electrification of turbocharger and supercharger for downsized internal combustion engines and hybrid electric vehicles-benefits and challenges. In Proceedings of the 2016 IEEE Transportation Electrification Conference and Expo (ITEC), Dearborn, MI, USA, 27–29 June 2016; pp. 1–6. [CrossRef]

48. Mahmoudi, A.; Soong, W.L.; Pellegrino, G.; Armando, E. Loss function modeling of efficiency maps of electrical machines. *IEEE Trans. Ind. Appl.* **2017**, *53*, 4221–4231. [CrossRef]

49. Roshandel, E.; Mahmoudi, A.; Kahourzade, S.; Yazdani, A.; Shafiullah, G. Losses in efficiency maps of electric vehicles: An overview. *Energies* **2021**, *14*, 7805. [CrossRef]

50. Katsanos, C.; Hountalas, D. Zannis Simulation of a heavy-duty diesel engine with electrical turbocompounding system using operating charts for turbocharger components and power turbine. *Energy Convers. Manag.* **2013**, *76*, 712–724. [CrossRef]
51. RENK Group AG(r). Turbo-Gear, Helicoidal Gearbox, GD. Available online: https://www.renk.com/en/products/turbo-high-speed/helical-gearboxes/gd (accessed on 12 December 2024).

52. AEM-Anhaltische Elektromotorenwerk Dessau GmbH. Available online: https://www.aemdessau.de/ (accessed on 12 December 2024).

53. Sakellaridis, N.F.; Raptotasios, S.I.; Antonopoulos, A.K.; Mavropoulos, G.C.; Hountalas, D.T. Development and validation of a new turbocharger simulation methodology for marine two stroke diesel engine modelling and diagnostic applications. *Energy* **2015**, *91*, 952–966. [CrossRef]

54. Cavazzuti, M. *Optimization Methods: From Theory to Design Scientific and Technological Aspects in Mechanics*; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012.

55. Yao, Z.-M.; Qian, Z.-Q.; Li, R.; Hu, E. Energy efficiency analysis of marine high-powered medium-speed diesel engine base on energy balance and exergy. *Energy* **2019**, *176*, 991–1006. [CrossRef]

56. Angstrom, H.A.H.-E. Performance sensitivity to exhaust valves and turbine parameters on a turbocompound engine with divided exhaust period. *SAE Int. J. Engines* **2014**, *7*, 1722–1733.

57. Wang, X.; Shipurkar, U.; Haseltalab, A.; Polinder, H.; Claeys, F.; Negenborn, R.R. Sizing and control of a hybrid ship propulsion system using multi-objective double-layer optimization. *IEEE Access* **2021**, *9*, 72587–72601. [CrossRef]

58. Chen, L. Integrated Design and Control Optimization of Hybrid Electric Marine Propulsion Systems Based on Battery Performance Degradation Model. Ph.D. Thesis, University of Victoria, Victoria, BC, Canada, 2019.

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