Exergy as Criteria for Efficient Energy Systems: Maximising Energy Efficiency from Resource to Energy Service

The Shift from Energy to Exergy in Decarbonisation

Traditional energy planning often relies on the first law of thermodynamics, which dictates that energy is conserved. However, the pursuit of a fully decarbonised system requires a more nuanced conceptual framework. Exergy, rooted in the second law of thermodynamics, describes the technical working capacity of a system. Unlike energy, exergy is not conserved; it is destroyed through internal irreversibilities or lost in waste flows. By focusing on exergy destruction and loss, researchers at Exerginity and partner institutions can identify the true sources of inefficiency across complex Multi-Energy Systems (MES).

The Necessity of Exergy for Multi-Energy Systems

Modern decarbonisation strategies require the integration of various energy carriers, including electricity, heat at multiple temperature levels, and chemical fuels such as hydrogen or sustainable methane. Exergy analysis provides a common comparison basis for these diverse flows. For instance, exergy associated with heat transfer is calculated via the Carnot factor, depending on the temperature of both the system and the environment, while the exergy of electrical or mechanical transfers is equal to the energy transferred. This unified metric allows for an integrated design of the entire conversion chain, identifying the most efficient pathways between resource extraction and final energy service.

Addressing Technical Potentials and Passive Systems

The transition to a climate-neutral society faces significant resource constraints. In the case of Austria, current technical renewable potentials alone cannot cover the primary energy consumption (PEC). This shortfall necessitates a massive expansion of renewable generation alongside a drastic increase in system-wide exergy efficiency. Achieving these goals requires a holistic view that includes the end of the conversion chain: the passive systems. Passive systems, such as thermal insulation in buildings or the weight of vehicles, represent the point where useful energy is consumed to fulfill a service, such as thermal comfort or illumination. Because these systems are at the final stage of the chain and do not convert energy into further usable forms, improvements here—such as increasing insulation—are critical for reducing the total exergy demand that the supply system must meet.

By applying exergy-based optimisation, the overall efficiency of a national energy system can be significantly raised—potentially from 34% to 56%. This framework enables the selection of technology mixes, such as heat pumps and electric drives, that maximise the workability of available resources while minimizing the exergy destroyed by internal irreversibilities.

System Boundaries and Modelling Architecture

The analytical framework for the Austrian case study is constructed upon an integrated, four-block structure that tracks the conversion and flow of exergy across the entire national energy landscape. This architecture ensures a holistic perspective, moving beyond isolated sector analyses to capture the interdependencies between supply and demand. The system is defined by the following four segments:

• Renewable Potentials: This block represents the primary national generation capacity, including photovoltaics, wind power, hydropower, and biomass production.
• Energy Supply System (ESS): The ESS acts as the central processing hub, utilizing national generation and imports to provide final exergy at the required time and form. This block manages conversion units—such as electrolyzers and gasifiers—and storage facilities to balance supply and demand.
• Final Energy Applications (FEA): This segment encompasses the technologies that convert final energy into useful forms, such as electric drives for transport or heat pumps for space heating.
• Current Useful Exergy Demand (CUED): The final block represents the theoretical minimum exergy required to fulfill all energy services (e.g., thermal comfort, illumination, shaft work) across residential, industrial, and transport sectors.

A greenfield approach is employed to model the system, allowing the optimization to identify a future technology portfolio based on thermodynamic ideals without the constraints of legacy infrastructure or contemporary market biases. The modeling scope assumes a system with unlimited internal energy-transportation capacities to focus exclusively on technical efficiency. To account for the inherent volatility of a renewable-heavy system, the model adopts a one-year time horizon with a temporal resolution of one day. This resolution is sufficient to capture seasonal and weekly flexibility requirements, such as the increased demand for space heating in winter and the peaking of photovoltaic generation in summer, while treating short-term (sub-daily) fluctuations as a lump sum loss factor.

The mathematical formulation utilizes a linear programming approach where the objective function is designed to minimize total exergy loss and destruction. This is achieved by minimizing the net exergy imports required over the national borders. Since exergy is not conserved, the model quantifies internal irreversibilities (destruction) and unused waste flows (losses). The objective function is formally expressed as:

min f = ∑ Ex_Imp,j − ∑ Ex_Exp,k

This formulation ensures that the resulting technology mix—such as the ratio between battery electric vehicles and fuel cell vehicles or the utilization of industrial excess heat via district heating—is driven by the imperative to maximize the technical working capacity of the entire energy conversion chain.

Optimal Energy Supply System (ESS) Results

The optimization identifies a sophisticated technology mix designed to maximize exergy efficiency across the national energy landscape. The resulting Energy Supply System (ESS) is anchored by a centralized infrastructure comprising methane-fired combined heat and power (CHP) plants, electrolysis units, and woody biomass gasification facilities. To facilitate efficient heat distribution, the system utilizes a dual-temperature district heating network. This network operates at a low-temperature level (34 °C feed-in) and a medium-temperature level (92 °C feed-in), primarily supplied by the total utilization of available industrial excess heat. Thermal storages with capacities of 25 GWh for the low-temperature grid and 64 GWh for the medium-temperature grid are integrated to decouple heat generation from demand fluctuations.

A critical characteristic of the ESS is its heavy reliance on renewable gases to maintain a controllable electricity supply, particularly during winter months when volatile generation from photovoltaics and hydropower is lower. Renewable gases, including hydrogen and sustainable methane, account for 93% of total exergy imports. While electricity imports represent only 7% of the total exergy import mix, the system requires 43 TWh/y of sustainable methane to drive controllable national electricity generation via CHPs or fuel cells. This configuration ensures that the energy system can meet a final electrical consumption that has increased by 44% compared to 2018 levels, driven largely by the electrification of heat pumps and transport.

The ESS utilizes specific mechanisms to manage residual loads, which are predominantly positive for 73% of the year. However, during periods of negative residual load—where volatile renewable generation exceeds immediate demand—the system captures this surplus exergy. These negative loads are utilized to power electrolysis units for hydrogen production and to charge the thermal storages within the district heating networks. This approach minimizes exergy destruction by ensuring that intermittent renewable surpluses are converted into storable chemical or thermal forms rather than being lost.

The efficiency of this optimized ESS is further evidenced by the reduction of exergy losses and destruction. While the ESS accounts for 38% of the total exergy reduction in the system, its conversion units are largely equipped with excess heat utilization, leading to a lower share of exergy losses (approximately 10%) compared to final energy applications. The integration of centralized heat pumps to lift ambient or low-temperature excess heat to higher service temperatures exemplifies the system's ability to minimize the temperature spread, thereby reducing the exergy destruction associated with thermal energy provision.

Electrification of Final Energy Applications

The transition to a decarbonized energy system necessitates a fundamental shift in how end-use sectors transform final exergy into services. In the exergy-optimized model for Austria, the final electrical demand increases by 44% compared to 2018 levels. This surge is driven by massive electrification across residential, industrial, and transport sectors, where electricity serves as the highest-quality exergy carrier, minimizing internal irreversibilities during conversion into useful energy like shaft work or light.

Thermal services, which represent a significant portion of the Current Useful Exergy Demand (CUED), are transformed through a hierarchical application of heat pumps and excess heat recovery. To maximize efficiency, the system assumes that all heat supply up to 150 °C is entirely covered by heat pumps and recovered industrial excess heat. Specifically, low-temperature space heating is serviced by decentralised heat pumps drawing from ambient air or low-temperature industrial waste heat (averaging 34 °C). For process heat between 80 °C and 150 °C, the system utilizes medium-temperature district heating grids and centralized heat pumps to lift the exergy level of waste heat. This cascading mechanism ensures that the work-potential of electricity is only used to "pump" existing thermal energy rather than generating heat through inefficient resistive means.

The transport sector undergoes a radical exergetic transformation. Road transport shifts to 56% exergy efficiency through the adoption of battery electric vehicles (BEV) and fuel cell electric vehicles (FCEV). This is a substantial improvement over the 27% efficiency recorded in 2018. BEVs are prioritized for land transport due to their superior drive-train efficiency, while FCEVs are deployed for heavy-duty or long-range applications where battery weight and charging times present technical limitations. In these vehicles, passenger comfort heating is achieved by utilizing the drive-train's excess heat, further reducing the exergy destruction associated with maintaining thermal comfort.

Despite the broad trend toward electrification, certain hard-to-abate sectors face persistent technological constraints. Aviation remains dependent on kerosene produced via Fischer-Tropsch synthesis from hydrogen. This conversion path is notably less efficient, with approximately 19.8% of exergy reduction in the supply chain caused by losses during the synthesis process. The reliance on liquid fuels for aviation results in high exergy destruction and losses due to the high exhaust gas temperatures of internal combustion engines, which can reach 950 °C. This highlight a critical limitation: while land-based services can be nearly entirely electrified to boost system-wide exergy efficiency, high-density energy requirements in aviation necessitate the continued use of chemical exergy carriers.

Exergy Destruction and Loss Analysis

The transition to a decarbonized energy system reveals a distinct quantitative breakdown of how work potential is utilized or wasted. Across the entire Austrian case study, total exergy destruction is calculated at 87.3 TWh/y, representing 38% of the primary exergy input. In contrast, exergy losses—defined as unused exergy remaining in waste flows—account for 15.1 TWh/y, or approximately 7% of the input. This distinction is critical for system optimization: while losses can sometimes be captured through better heat recovery, destruction represents an absolute disappearance of available work due to internal process irreversibilities.

The mechanisms driving these figures vary significantly across different sectors and technologies. Within the energy supply system (ESS), the largest destruction of exergy is concentrated in methane-fired combined heat and power (CHP) plants, accounting for 13.4 TWh/y. Significant destruction also occurs during the gasification of woody biomass (9.4 TWh/y). In the realm of final energy applications (FEA), decentralized heat pumps represent the single largest point of exergy destruction at 17.2 TWh/y. This high value is a function of the massive scale of heat pump deployment required to satisfy thermal demands, despite their relative efficiency compared to direct electric heating.

A technical assessment of relative efficiency reveals that internal combustion engines (ICE) are the most wasteful components in terms of relative exergy losses. These engines show a loss rate of 61.6% relative to their total exergy reduction. This is primarily attributed to the high temperature of the exhaust gases, such as those found in aviation reaching up to 950 °C, which carry away substantial work potential that remains unrecovered. By comparison, fuel cell drives and battery systems exhibit lower relative loss shares at 20.1% and 17.2%, respectively.

Industrial assumptions and limitations also play a vital role in these figures. Currently, industrial plants suffer significant exergy losses when high-temperature exhaust is mixed with environmental air for cooling or cleaning purposes instead of being directed toward useful work. If processes were redesigned to utilize this heat at higher temperature levels, such as feeding high-temperature local heating grids, much of this destruction could be avoided. Furthermore, while the ESS manages to keep its loss-to-destruction ratio relatively low (approx. 10%) through integrated excess heat utilization, FEAs struggle with a higher loss ratio (approx. 17%) because recovering excess heat in mobile transport applications is technically difficult or impossible.

Sensitivity and Parameter Variation

The overall exergy efficiency of an integrated energy system is not a static value; it is highly responsive to changes in renewable expansion targets, import constraints, and the operational characteristics of conversion units. Sensitivity analysis indicates that the Annual Average Electricity Supply Efficiency (AAESE) is a primary determinant of system-wide performance. This metric accounts for the ratio of controllable generation to volatile supply, as well as the exergy efficiency of power plants and distribution networks. When the AAESE remains high, deep electrification of final energy applications (FEA) is the optimal path. However, should this efficiency drop significantly, the system begins to favor alternative conversion chains, such as shifting heavy-duty transport from Battery Electric Vehicles (BEV) back to Fuel Cell Electric Vehicles (FCEV) to maintain thermodynamic balance.

Impact of Expansion and Import Limits

Fluctuations in the expansion of volatile renewables, such as wind and solar, directly influence the requirement for controllable generation. A reduction in volatile expansion necessitates a higher reliance on gas-fired combined heat and power (CHP) plants to meet demand, particularly during winter months. Similarly, the capacity for electricity imports serves as a critical boundary condition. In a scenario where electricity import capacity is restricted to 0 GW, the system compensates by increasing national CHP generation by 24.3%. This shift increases the consumption of imported renewable gases to ensure that the positive residual load—the deficit between volatile generation and electricity demand—is covered.

Heat Utilisation and Technology Shifts

The synergy between power generation and thermal demand is a cornerstone of exergetic optimization. The system is designed to utilize all available excess heat from CHPs and industrial processes. If power plants are assumed to operate without excess heat utilization, the AAESE decreases to a level where the electrification of certain thermal demands becomes less efficient. In such instances, heat supply for high-temperature processes (e.g., 150 °C) shifts from heat pumps to the direct incineration of woody biomass. Furthermore, the lack of co-generated heat forces the system to reconfigure its transport and heating sectors to minimize total exergy destruction, as shown in the table below.

Ultimately, these variations highlight that the maximum exergy efficiency of 56% is contingent upon a specific infrastructure of flexible imports and highly efficient co-generation. Limitations in these areas force the model to rely more heavily on the gas-to-power conversion chain, which, while flexible, introduces greater exergy destruction compared to the direct utilization of volatile renewable electricity.

Key findings

• Efficiency Ceiling — Exergy efficiency can be raised from 34% to 56%, reducing primary energy consumption by 38% (140 TWh/y).
• Persistence of Gas — Gaseous chemical energy remains essential, covering 52% of primary exergy and 42% of final exergy demand.
• Self-Sufficiency Limits — Despite massive renewable expansion, 49% of required primary exergy (112 TWh/y) must still be imported.
• Thermal Transformation — Incineration is only exergy-efficient for temperatures above 150 °C; below this, heat pumps and excess heat are optimal.
• Transport Efficiency — Shifting to electric and fuel cell drives increases road transport exergy efficiency from 27% to 56%.

Method and assumptions

The study utilizes a bottom-up linear programming optimisation model implemented in the Open Energy Modelling Framework (oemof). It defines the system boundaries at the Austrian national level, considering all energy carriers and sectors (residential, industry, transport, etc.). The model assumes a greenfield approach to determine the technology mix for a fully decarbonised system using targeted 2030 renewable capacities as inputs. The analysis distinguishes between exergy loss (waste flows) and exergy destruction (irreversibilities). A temporal resolution of one day over a full year is used to account for seasonal volatility, while spatial resolution is aggregated to a single national node with unlimited internal transmission. Efficiency factors and temperatures for over 50 conversion technologies were calculated based on current state-of-the-art technical data.

Where it applies

• National Energy Planning — Assists governments in identifying the most efficient technology mix to meet 2040 climate neutrality goals.
• Infrastructure Strategy — Provides a basis for the design of dual-temperature district heating grids and hydrogen import facilities.
• Industrial Waste Heat Policy — Informs regulations regarding exhaust gas temperatures and the integration of industrial excess heat into public grids.

Terms used

• Exergy — The technical working capacity of a system, representing the maximum useful work possible as it brings a system into equilibrium with its environment.
• Exergy Destruction — The permanent loss of work potential caused by internal irreversibilities like friction or uncontrolled heat transfer.
• Exergy Loss — The unused work potential found in waste flows, such as exhaust gases or coolant, that exit the system boundaries.
• Carnot Factor — A temperature-dependent coefficient used to calculate the exergy associated with heat transfer based on the environment's temperature.
• Current Useful Exergy Demand (CUED) — A technology-independent metric describing the theoretical minimum exergy required to fulfill specific energy services like heating or movement.
• Greenfield Approach — A modelling strategy that designs an optimal system from scratch without considering the constraints or existing assets of current infrastructure.
• Residual Load — The difference between total electrical demand and the supply provided by volatile renewable generation like wind and solar.

Questions and answers

Why is exergy a better metric than energy for system efficiency?

Energy analysis alone treats 1 kWh of heat and 1 kWh of electricity as equal, whereas exergy recognizes that electricity has a higher quality (work potential). This allows researchers to identify 'low-quality' demands, like space heating, that can be met by low-grade waste heat instead of high-grade electricity or gas.

Can Austria become completely energy self-sufficient by 2030?

According to the study, no; even with the expansion of renewables by 27 TWh/y and maximizing exergy efficiency, approximately half of the primary energy (49%) must be imported to balance the system, particularly during winter periods of high demand.

Are hydrogen-based fuels (e-fuels) suitable for passenger cars?

The model suggests that e-fuels are significantly less efficient than battery electric or fuel cell drives for land transport. E-fuels like kerosene should be reserved for sectors with no other technical alternatives, such as aviation, to minimize total exergy destruction.

How does the model handle the variability of solar and wind power?

The model uses a one-day temporal resolution over a year to manage seasonal and weekly fluctuations. It employs controllable CHPs, electrolysis, and thermal/chemical storages to bridge gaps in volatile generation and provide necessary system flexibility.

How to cite

Sejkora, C., Kühberger, L., Radner, F., Trattner, A., & Kienberger, T. (2022). Exergy as criteria for efficient energy systems - Maximising energy efficiency from resource to energy service, an Austrian case study. Energy, 239, 122173. doi:10.1016/j.energy.2021.122173