Assessment of the Energy Efficiency of a Hybrid Turboprop Power Plant of a Regional Aircraft Considering the Mission Profile

Abstract

With the tightening of international environmental requirements for civil aviation and the implementation of initiatives aimed at reducing specific greenhouse gas emissions, the transition to hybrid power plants for regional aircraft is becoming increasingly relevant. This paper proposes an approach to the integrated energy assessment of a parallel hybrid turboprop power plant at the conceptual design stage while taking the aircraft mission profile into account. The considered power plant includes a gas turbine engine, a reversible electric machine located on the same shaft as the reduction gearbox and propeller, an electrical energy storage system, and power electronics. The mission profile is represented as a sequence of segments—takeoff, climb, cruise, descent, and approach/landing. For each segment, energy balances are formulated and allowable operating ranges for the gas turbine and electric subsystems are defined. The key parameter is the hybridization factor, which determines the share of power transmitted to the propeller from the electric machine in different mission segments. The primary integrated performance metric is the energy consumption per ton-kilometer of transported payload. The analysis shows that for ranges up to 500 km, the hybrid configuration reduces specific energy consumption per ton-kilometer by up to 9%.

1. Introduction

International initiatives aimed at reducing greenhouse gas emissions from air transport, notably ICAO and European strategic aviation roadmaps, envisage a substantial decrease in specific carbon dioxide and other pollutant emissions by 2050 [1,2], posing serious challenges for aircraft engine and power plant developers. Traditional approaches to improving the thermodynamic efficiency of gas turbine engines are gradually exhausting their potential, particularly in the regional aviation segment, where mass, dimensional, and cost constraints largely determine the attainable level of power plant performance [3].

Under these circumstances, hybrid power plants (HPPs) combining a gas turbine circuit and an electrical subsystem are regarded as a promising avenue for enhancing energy efficiency while reducing local emissions and noise. A significant contribution to the theoretical foundations of hybrid-electric aircraft was made by Pornet and Isikveren [4], who introduced the hybridization factor as a metric for quantitatively assessing the influence of the electrical subsystem on the aircraft and power plant sizing. Brelje and Martins [3] provided a comprehensive review of electric, hybrid, and turboelectric configurations, demonstrating that the regional segment offers the greatest potential for reducing specific fuel consumption at moderate energy storage specific-energy requirements. Voskuijl, van Bogaert, and Rao [5] examined hybridization options for a regional turboprop aircraft and methods for evaluating fuel consumption benefits across different architectures. The practical effectiveness of hybridization is substantially governed by the specific energy and power of the energy storage system, as well as the losses and mass of electrical components, since these define the trade-off between mass increase and potential energy cost reduction [6,7,8]. Of particular interest are studies devoted to the analysis of hybrid architectures and the optimization of HPP working-process parameters considering the mission profile [9,10,11,12,13,14].

Significant results on regional aircraft hybridization have been obtained within large-scale international projects. The IMOTHEP project [15] demonstrated a fuel consumption reduction of approximately 10% for a regional aircraft with a parallel hybrid power plant at a hybridization factor of about 15% per flight. The FutPrInt50 project [16] developed a roadmap for a 50-seat hybrid aircraft entering service in 2035–2040, while the HE-ART project [17] targets up to a 30% reduction in greenhouse gas emissions through turboprop engine hybridization and power plant improvement. For the retrofitting of the regional ATR42-600 aircraft, researchers [18] showed that a significant reduction in CO₂ emissions is achievable at a battery specific energy of approximately 1500 Wh/kg, whereas NASA studies on a parallel hybrid architecture based on the C-130H aircraft [19,20] demonstrate a fuel consumption reduction potential of 27–44% upon reaching projected 2030–2050 technology levels.

A number of studies address series, parallel, and distributed configurations, as well as the integration of electric machines and energy storage systems into the power plant and airframe [3,5,10,21,22]. Important contributions to the modeling and assessment of parallel hybrid turboprop configurations have been made within the journal Aerospace. Cameretti et al. [23] developed a detailed model of a parallel hybrid electric propulsion system for a regional aircraft by analyzing mission segments and battery sizing. Palaia et al. [24] proposed a mission-profile-based methodology for evaluating hybrid-electric regional aircraft performance, with a focus on power split strategies directly related to the hybridization factor concept used in the present study. Habermann et al. [25] investigated a regional turboprop with an electrically assisted turboshaft, demonstrating a 9.6% fuel burn reduction for a 200 nm mission, underscoring the potential of hybridization for short-range operations.

Nevertheless, a substantial portion of the literature focuses either on the individual engine and its thermodynamic cycle or on the overall aircraft architecture, without always ensuring a consistent link between the power plant working-process model, the integral mission-profile performance metrics, and the power split between the gas turbine engine (GTE) and the electric machine (EM) [2,22].

The objective of the present study is to develop an approach that enables, at the conceptual design stage, a quantitative assessment of the influence of key parameters of a parallel hybrid turboprop power plant on the integral metric of energy cost per ton-kilometer of transported payload while taking the regional aircraft mission profile into account [2,8,10,22].

Current research addresses the sizing of parallel hybrid-electric power plants for regional aircraft in detail [11]. Approaches to energy management of hybrid power plants are also being actively developed [12,13]. Furthermore, the analysis of architectural trade-offs (mass/efficiency/constraints) remains a key step in the configuration selection for regional hybrid aircraft [14].

2. Methods and Methodology

2.1. Structure of the Considered Power Plant

A parallel hybrid power plant for a regional turboprop aircraft is considered. It comprises a gas turbine engine with a reduction gearbox and propeller, a bidirectional electric machine (motor–generator) mechanically coupled to the gearbox shaft, an electrical energy storage system (battery pack), and power electronics (DC/AC converter and energy distribution control system) [3,5,6,7,8,10].

During takeoff and climb, the electric machine operates in motor mode, supplying additional power to the propeller shaft [3,5]. In the cruise segment, when the gas turbine engine has a power reserve, the electric machine is switched to generator mode, converting part of the mechanical power into electrical energy to recharge the batteries [2,12,22].

The mathematical model was developed in the ASTRA-GTE conceptual design environment [10] and is presented in the form of an XDSM diagram (Figure 1). ASTRA-GTE is a specialized cross-platform CAE system for conceptual modeling, developed at Samara National Research University (Academician S.P. Korolev Samara University) for the automated design, thermodynamic analysis and simulation of gas turbine engines. The system enables the creation of virtual prototypes of aircraft engines at the conceptual design stage. Its main capabilities include calculation and analysis of gas turbine engines, including modeling of combustors, compressors, turbines, and hybrid power plants; selection of standard engine layouts or construction of a custom multi-level model from individual modules; automatic residual formulation (if an output parameter is assigned a numerical value or linked to another parameter, a residual is created automatically); support for parallel computing (an unlimited number of instances, limited only by the computer configuration); and application at the stage of conceptual thermodynamic and gas-dynamic design, as well as analyzing component matching and preparing for the production of advanced engines.

The mathematical model combines three subsystems: the gas turbine engine (green blocks), the propeller with a reduction gearbox (purple blocks), and the electrical system (yellow blocks). The XDSM diagram in Figure 1 shows how these components are interconnected. This representation helps organize the model architecture, analyze energy and data flows, and improve the accuracy of performance predictions for the hybrid power plant.

In the considered configuration, the nominal power of the GTE ranges from 500 to 1500 kW, which corresponds to the class of regional turboprop aircraft (e.g., L-410 and ATR42). The electric machine is sized to deliver up to 30% of the shaft power—this defines the maximum hybridization factor considered in this study. The battery capacity is limited by the condition that its mass does not exceed 5% of the aircraft maximum takeoff mass; for the baseline aircraft this corresponds to a stored energy of up to 200 MJ. All calculations are performed while respecting the minimum battery state-of-charge constraint (not lower than 20% of the rated capacity).

Operating modes for each mission segment: For each flight segment (warm-up and taxi, takeoff roll, liftoff, climb, cruise, and descent, landing), the following operating modes of the GTE and the EM are defined:

•

Warm-up, taxi, takeoff roll, and liftoff: GTE at takeoff power and EM in motor mode (additional power to the propeller).

•

Climb: GTE at climb power and EM in motor mode.

•

Cruise: GTE at cruise power (n = 96% or 100% depending on the control law); EM switches to generator mode to recharge the battery if the current state of charge permits.

•

Descent: GTE at flight idle and EM off or charging from excess GTE power.

•

Landing and taxi-in: GTE at low power and EM off.

This segmentation allows correct modeling of the energy balance at each segment and accounts for changes in aircraft mass due to fuel burn and battery charge variation.

2.2. Performance Metrics and Input Parameters

To evaluate the effectiveness of the hybrid power plant within the aircraft system, a model that integrates the mission profile calculation, mass characteristics, and energy balance is employed (Figure 2).

The block diagram consists of four main blocks. The "Relationship" block determines the rated power of the gas turbine engine and the electric machine, calculates engine characteristics, and estimates the total power plant mass. The "FC" block performs mission simulations across phases and determines the required battery capacity. The "MASS" block calculates the mass of all components based on the obtained data. The "FC-parameters" block outputs the mission cycle parameters (fuel consumption, battery charge variation, and flight time), which are used to compute the energy cost per ton-kilometer of payload.

The input parameters for calculating the HPP efficiency metrics in the aircraft system are listed in

Table 1. Input parameters for calculating HPP efficiency metrics.

Parameter	Unit	Description
$H_u$	kJ/kg	Heat of combustion of fuel
$E_{bat. start}$	MJ	Initial battery energy
$E_{bat. end}$	MJ	Final battery energy
$m_{fuel}$	t	Fuel mass consumed during the flight
$m_{payload}$	t	Payload mass
$L$	km	Aircraft range
$N_{em.nom }$	kW	Rated power of the electric machine
$N_{pp.nom}$	kW	Rated total power of the power plant

.

The output energy performance metrics are determined by the following expressions:

Electrical energy consumed during the flight:

$$E_{el}=E_{bat. start}-E_{bat. end}, \mathrm{MJ}$$

(1)

Fuel energy consumed during the flight:

$$E_{fuel}=m_{fuel}{H}_u, \mathrm{MJ}$$

(2)

Total energy consumed during the flight:

$$E_{total}=E_{fuel}+E_{el}, \mathrm{MJ}$$

(3)

Energy cost per ton-kilometer of transported payload:

$$E_{t·km}=E_{total}/(m_{payload}L), \mathrm{MJ}/\left(\mathrm{t}·\mathrm{km}\right) (\mathrm{megajoules} \mathrm{per} \mathrm{ton-kilometer} \mathrm{of} \mathrm{payload})$$

(4)

The hybridization factor (by power) is defined as

$$k_{hyb}=N_{em.nom }/N_{pp.nom}\times 100,\%$$

(5)

2.3. Mission Profile Modeling

The mission profile is modeled stage by stage: the state parameters at the output of each stage serve as input data for the subsequent stage. The flight scheme of a passenger aircraft includes engine warm-up and taxiing on the runway (model “1–warm-up/taxi”), a takeoff roll (model “2–takeoff-roll”), liftoff (model “3–takeoff-liftoff”), climb (model “4–climb”), the cruise segment (model “5–cruise”), descent (model “6–descent”), and landing (Figure 3).

The input data include the aircraft mass characteristics (takeoff mass, airframe mass, power plant mass, payload mass, initial fuel mass and initial battery energy), aerodynamic parameters of the airframe, and flight conditions (altitude, Mach number, and range). At each phase, the current values of fuel mass, aircraft mass, speed, altitude and distance are calculated, as well as the battery state of charge (taking into account whether the electric machine operates in motor or generator mode). The output data are the total fuel consumption, the change in battery charge, the flight time, and the final mass characteristics, which allow the energy cost per ton-kilometer of payload to be computed.

2.4. Electrical Subsystem Parameters and Constraints

For the parametric analysis, specific parameters of the electrical components corresponding to the projected 2030 technology level were used, as given in

Table 2. Main design data for the electrical subsystem.

Parameter	Description	Unit	Projected Value (2030)
$N_{em.sp}$	Specific power of the electric machine	kW/kg	12
$N_{pp.sp}$	Specific power of the power electronics	kW/kg	30
$E_{bat. sp}$	Battery specific energy	MJ/kg	1.8
${\eta }_{es}^{+}$	Electrical system efficiency in motor mode	—	0.975
${\eta }_{es}^{-}$	Electrical system efficiency in generator mode	—	0.975
$\delta E_{bat.res}$	Battery capacity reserve coefficient	—	0.2

.

The electrical subsystem model was verified by comparing the predicted round-trip efficiency (motor + generator) with data from the IMOTHEP project [15] and Cameretti et al. [23]. For a 200 kW electric machine operating at 90% of its rated power, the combined efficiency (battery-to-propeller efficiency in motor mode and propeller-to-battery efficiency in generator mode) was found to be 0.94, which is within 1% of the values reported in the literature for similar technology levels. The 20% minimum state-of-charge constraint is consistent with typical aviation battery rules and operational limits discussed in [18,26]. The scaling of component mass with power is based on the specific power values given in Table 2, which are typical of the projected 2030 technology level.

Two control laws for the cruise regime were selected for the investigation:

• – Control law 1: gas generator speed n = 96%.
• – Control law 2: gas generator speed n = 100%.

Control law 2 (n = 100%) is adopted in this study as an upper bound to assess the theoretical potential of hybridization. In real operation, continuous operation at maximum power is limited by the turbine creep life, exhaust gas temperature constraints, and maintenance schedules.

The battery energy level during the cruise segment was chosen as a constraint. The battery state of charge must not fall below 20% of the rated capacity.

The battery’s specific energy of approximately 1.8 MJ/kg (500 Wh/kg) adopted in the calculations corresponds to an optimistic estimate of solid-state battery technology at the cell level by the 2030 horizon. According to NASA studies [19,20], economically viable hybridization of a regional aircraft requires achieving a specific energy of 750–1000 Wh/kg, and results from the European IMOTHEP project [15] indicate the need for at least 600 Wh/kg for parity performance compared to the baseline 2035-horizon aircraft. Analysis of the ATR42-600 retrofitting [18] process shows that a noticeable reduction in CO₂ emissions becomes possible at a specific energy of approximately 1500 Wh/kg, while industry forecasts for solid-state batteries [26] give an estimate of 400–500 Wh/kg by 2030. In this context, the chosen value of 500 Wh/kg can be regarded as a lower bound of the range at which hybridization provides a positive effect for a regional turboprop aircraft.

3. Results

3.1. Model Verification

To verify the adequacy of the developed model in the ASTRA-GTE environment, a comparative analysis of the calculated results against the official data of the LET L-410 UVP-E aircraft was performed (

Table 3. Comparison of calculated results with official data (LET L-410 UVP-E, M601D engine).

Parameter	Description	Official Data	Calculated Value	Deviation
$C_e$	Equivalent specific fuel consumption	395 g/(kW·h)	394 g/(kW·h)	0.25%
$T_5^{*}$	Total temperature before power turbine	983.2 K	983.3 K	0.01%
$G_{air}$	Air mass flow rate	3.60 kg/s	3.58 kg/s	0.56%
$m_{eng}$	Engine mass	200 kg	198.6 kg	0.50%
$R_{jet}$	GTE jet thrust	1.0 kN	0.99 kN	1.00%
$R_{total}$	Total thrust (GTE + propeller)	9.807 kN	9.811 kN	0.05%
$m_{fuel}$	Fuel mass consumed during the flight	800 kg	795 kg	0.63%

). Verification was performed for the static takeoff regime (maximum power) of the LET L-410 UVP-E aircraft with two M601D engines. The conditions were as follows: altitude: 0 m, ambient temperature: +15 °C, and pressure: 101.325 kPa. Official data were taken from the LET Aircraft Industries Flight Manual (document No. L-410-F-01, 2015 revision). All parameters in Table 3 correspond to this regime.

The discrepancies for all key parameters, including specific fuel consumption, engine mass, and fuel consumed during the flight, were less than 1%, which confirms the adequacy of the developed model.

3.2. Investigation of Energy Cost per Ton-Kilometer Versus the Hybridization Factor

An analysis of the dependence of the energy cost per ton-kilometer of transported payload ($E_{t\cdot km}$) on the hybridization factor helps identify optimal operating conditions for hybrid systems in order to minimize energy consumption.

Figure 4 and Figure 5 present the dependencies of the energy cost per ton-kilometer of transported payload on the hybridization factor for two cruise-regime control laws. The flight range in the study was varied from 150 to 1000 km.

The step-wise fluctuations of the specific energy cost $E_{tkm}$ with varying hybridization-factor values (Figure 4 and Figure 5) are related to the discrete nature of electric machine control during the cruise segment. Each step of the cruise flight of fixed length is characterized by a constant operating mode of the electric machine (motor or generator). At the beginning of a step, the battery has its maximum charge (peak on the graph), while at the end of the step, if the electric machine operated in motor mode, the charge drops to the minimum permissible level (trough). Switching the mode at the next step causes a jump in power and, consequently, a change in energy consumption. When constructing the $E_{tkm}$ dependence on the hybridization factor with a discrete step of 1%, these step-wise switches appear as oscillations.

For ranges beyond 500 km, the benefit disappears because the mass of the batteries and electrical system outweighs the fuel savings. The maximum hybridization factor is limited by the 20% minimum state-of-charge constraint to 16.7% at n = 96% and 28% at n = 100%.

A comparison of the HPP control laws for the 2030 technology level (Figure 4 and Figure 5) shows that they differ primarily in the attainable maximum hybridization factor: under control law 1, the maximum permissible hybridization factor is 16.7%, whereas under control law 2, it can be increased to 28%, thereby extending the range of the investigated values. At the same time, a positive effect of the hybrid configuration is observed only for flight ranges up to 500 km.

The maximum reduction in specific energy cost amounts to approximately 9% compared with the baseline configuration without an electrical subsystem.

4. Discussion

The dependencies of specific energy cost per ton-kilometer on the hybridization factor obtained in this work show that the considered parallel hybrid power plant provides a positive effect (up to 9% in $E_{t\cdot km}$) predominantly on routes up to 500 km in length; as the flight range increases, the growing mass of batteries and electrical components diminishes the benefit. This pattern is consistent with the results of the IMOTHEP project [15], which reported a positive hybridization effect for a regional aircraft of a similar class at ranges of about 700 km (9.6%), as well as with ATR42-600 retrofitting studies [18], which demonstrated a decline in the advantages of the hybrid configuration for route lengths exceeding 1000 km. A similar fuel consumption reduction of 9.6% for a 200 nm mission was reported by Habermann et al. [25] for a regional turboprop with an electrically assisted turboshaft, further confirming that hybrid benefits are most pronounced on short- to medium-range routes.

NASA studies on a parallel hybrid power plant based on the C-130H aircraft [19,20] demonstrate a comparable trend: the peak fuel savings are achieved on short- and medium-range missions at moderate hybridization factors and sufficiently high battery specific-energy values. Against this background, the 500 Wh/kg level adopted in the present study can be considered a lower bound of the range at which hybridization of a regional turboprop aircraft still yields a measurable benefit in energy cost.

It should be noted, however, that the presented model does not account for the mass and energy consumption of auxiliary cooling systems for electrical components, provides a simplified description of the electrical subsystem, and does not include constraints related to certification requirements for continued takeoff following a single-engine failure [11]. As shown in the literature, accounting for engine-failure scenarios may lead to an increase in required power plant output and a fuel consumption rise of 10–13%, which could reduce the hybridization benefit. Refinement of these aspects, as well as expanding the range of the investigated control laws and electrical subsystem parameters, represents a direction for further development of the proposed methodology.

Notwithstanding the above simplification regarding thermal management, a first-order estimate can be made based on literature data. For a parallel hybrid turboprop with an electric machine power of up to 30% of the shaft power, the thermal management system (TMS) typically adds 10–15% to the mass of the electrical subsystem and consumes 3–5% of the electric machine’s rated power as parasitic losses. Applying these corrections to the baseline case (500 km range and a hybridization factor of approximately 20%) reduces the calculated energy benefit from approximately 9% to approximately 7–8%. Hence, while the TMS penalty is not negligible, it does not alter the key qualitative conclusion: hybridization yields a measurable reduction in specific energy consumption for missions up to 500 km, and the net benefit remains positive at the 2030 technology level assumed in this study.

5. Conclusions

As a result of this work, a methodology for the energy assessment of a parallel hybrid turboprop power plant at the conceptual design stage was developed and verified. The main results and conclusions are as follows:

• A comprehensive approach that integrates the GTE working-process model in the ASTRA-GTE environment, an electrical subsystem model with projected 2030 parameters, mass characteristic estimation, and an aircraft mission profile model has been proposed. The specific energy cost per ton-kilometer of transported payload was adopted as the key integral performance metric.
• The developed model was verified using the LET L-410 UVP-E aircraft as a test case. The discrepancy between calculated data and official specifications did not exceed 1%, confirming the model’s adequacy and the correctness of the adopted assumptions.
• parametric analysis of the influence of the hybridization factor on $E_{t\cdot km}$ was performed for two cruise-regime control laws (n = 96% and n = 100%). It has been established that application of the hybrid power plant of the considered architecture enables a reduction in specific energy cost for flight ranges up to 500 km; at greater ranges, the positive effect diminishes due to the growing mass of electrical components.
• It has been demonstrated that the choice of control law significantly affects the hybridization potential: the mode with n = 100% in the cruise segment allows the maximum permissible hybridization factor to be increased from 16.7% to 28%, thereby expanding the design space for rational configurations.
• The proposed methodology and the obtained dependencies can be used at early design stages for a substantiated selection of parameters for both the gas turbine and electrical components of the power plant and for shaping the configuration of prospective regional aircraft with hybrid power plants.

It should be emphasized that the presented results were obtained under a number of assumptions regarding the electrical subsystem parameters and do not account for the mass and energy consumption of the cooling and conditioning systems for electrical components, nor for the possibility of engine failure, which limits the applicability of the quantitative estimates. Refinement of these factors and expansion of the investigated range of battery specific-energy values and HPP control laws constitute the subject of further research.