Techno-Economic Feasibility Assessment of Energy Technologies Through the Integration of Thermodynamics and Life-Cycle Cost Analysis

2.1 System boundaries and basic definitions

The precise definition of system boundaries is a prerequisite for constructing the synchronous mapping model, requiring clear identification of both the physical boundary of the research object and the full life-cycle time boundary [15]. The physical boundary is centered on the core conversion and transmission components of the energy system and includes all units involved in energy conversion, exergy flow transfer, and cost circulation [16]. The time boundary covers the entire life-cycle stages from planning, design, construction, operation, and maintenance to decommissioning [17]. To achieve dynamic matching between cost and exergy flows, discrete full life-cycle costs need to be converted into continuous cost flow rates. The core conversion formula is the annualization formula of life-cycle cost: $\dot{Z}_k=Z_k \cdot C R F$, where $Z_k$ is the total life-cycle cost of component $k, \dot{Z}_k$ is the annualized cost flow rate of component $k$, and $C R F$ is the capital recovery factor, expressed as:

$C R F=\frac{i(1+i)^n}{(1+i)^n-1}$          (1)

where, $i$ is the reference discount rate and $n$ is the service life of the component. Based on the boundary definitions, a three-in-one representation system of “physical system–exergy flow network–cost network” is established by drawing system flow diagrams and exergy Grassmann diagrams. The system flow diagram presents the interactions of material and energy among components, while the exergy Grassmann diagram accurately indicates exergy flow inputs and outputs at each node, the locations of exergy destruction, and the inlets and outlets of cost flows. Combined with the annualized cost flow rate formula, precise correspondence among physical structure, energy quality evolution, and economic cost circulation is achieved. Figure 1 takes an extended supercritical CO₂ Brayton cycle model as an example to construct a vertically layered three-level network structure, clearly showing the one-to-one correspondence and coupling mechanisms among the physical system, the exergy flow network, and the cost network.

Figure 1. Schematic diagram of the three-in-one representation of an energy system: “physical system – exergy flow network – cost network”

2.2 Physical basis: Classical exergy analysis model

Classical exergy analysis is the physical basis of thermodynamic–economic synchronous mapping. Its core lies in quantifying the available quality of energy and the quality degradation caused by irreversible processes. The key parameters and governing equations are given as follows [18]. State exergy is a quantitative indicator of energy availability and is divided into physical exergy and chemical exergy. Physical exergy reflects the available energy resulting from the deviation of system temperature and pressure from the environmental state $\left(T_0, p_0\right)$, and is calculated as: $E_{\text {ex,ph }}= \left(H-H_0\right)-T_0\left(S-S_0\right)$, where $H$ and $S$ are the enthalpy and entropy of the system, respectively, and $H_0$ and $S_0$ are the enthalpy and entropy at the environmental state. Chemical exergy reflects the available energy resulting from the deviation of system composition from the environmental composition. For a single ideal gas component, the simplified calculation formula is:

$E_{e x, c h}=R T_0 \ln \frac{y_0}{y}$          (2)

where, $R$ is the gas constant, and $y$ and $y_0$ are the mole fractions of the component in the system and in the environment, respectively. Exergy destruction is the direct representation of irreversible processes and is obtained through the exergy balance equation. The general exergy balance equation for the system and each component is:

$\sum E_{e x, i n}+\sum W_{i n}=\sum E_{e x, o u t}+\sum E_{e x, d e s t}$          (3)

where, $E_{e x, i n}$ and $E_{e x, o u t}$ are the input and output exergy flows, respectively, $W_{i n}$ is the useful work input from the surroundings, and $E_{e x, d e s t}$ is the exergy destruction caused by irreversible processes. Exergy efficiency reflects the utilization efficiency of exergy and is defined as the ratio of effective output exergy to total input exergy:

$\eta_{e x}=\frac{\sum F_{e x, o u t, e f f}}{\sum F_{e x, i n, t o t a l}}$          (4)

By solving the exergy balance equations of each component, the exergy flow transfer paths and the distribution pattern of exergy destruction throughout the entire system can be quantified. Combined with the quantified results of state exergy and exergy efficiency, this provides a clear physical carrier and evolution path for the subsequent dynamic tracking of economic costs.

2.3 Core innovation: Exergy cost formation rate model and full life-cycle cost tracking

2.3.1 Core definitions and tracking axioms

The core of the exergy cost formation rate model is to establish a dynamic binding relationship between cost flows and exergy flows. For this purpose, the exergy cost flow rate is first defined as the core quantitative indicator. The exergy cost flow rate, $\dot{C}_{e x}$, represents the economic cost flow accompanying exergy transfer per unit time. Its physical and economic implication lies in transforming discrete full life-cycle costs into dynamic variables that evolve synchronously with continuous exergy flows, thereby achieving time-scale matching between the cost transfer process and the exergy flow evolution process. The introduction of this indicator overcomes the limitations of traditional static cost allocation and provides a quantitative carrier for tracking the dynamic circulation of costs among system components. Its unit is €/s to ensure dimensional consistency with the exergy flow rate. Figure 2 presents the core logic of dynamic exergy cost tracking through a composite structure with upper and lower layers and intermediate processes, and accurately maps the supporting nodes and operating mechanisms of the three major cost tracking axioms.

Based on the physical nature of exergy and the economic attributes of full life-cycle costs, three cost tracking axioms are proposed as the logical foundation for dynamic cost tracking. Axiom 1 is the transferability axiom, which clarifies that economic costs strictly accompany exergy flow transfer, and the transfer path of exergy flow is the tracking path of cost. This axiom establishes the physical dependency of cost transfer and avoids the introduction of subjective allocation rules in traditional cost allocation. Axiom 2 is the exergy destruction bearing axiom, which stipulates that the economic cost corresponding to exergy destruction generated by irreversible processes is fully borne by the product exergy output of the system.

Figure 2. Schematic diagram of dynamic exergy cost tracking logic and mapping of the three axioms

The core rationale is that exergy destruction represents irreversible degradation of energy quality and essentially corresponds to a loss of resource value, which should be carried by the final product. Axiom 3 is the cost source injection axiom, which indicates that the full life-cycle cost of each component, as a new cost source, is uniformly injected into its output exergy flow and participates in subsequent transfer. This setting realizes the organic integration of full life-cycle costs, including capital cost and operating cost, with exergy flows, and resolves the rigid integration of capital cost and thermodynamic parameters in traditional exergoeconomics. The three axioms support each other and jointly construct a dynamic tracking logic system of “exergy flow as carrier, cost follows exergy, losses borne by products, and cost source injection,” providing a solid theoretical foundation for subsequent mathematical modeling.

2.3.2 Mathematical modeling and solution algorithm

Based on the above definitions and axioms, a general component-level exergy cost balance equation is established to realize the quantitative coupling between cost flows and exergy flows. For an arbitrary component $k$, the exergy cost balance equation is:

$\sum \dot{C}_{e x, o u t}=\sum \dot{C}_{e x, i n} /+\dot{Z}_k$          (5)

where, $\sum \dot{C}_{e x, i n}$ and $\sum \dot{C}_{e x, o u t}$ are the total exergy cost flow rates corresponding to the input and output exergy flows of the component, respectively; $\dot{Z}_k$ is the annualized full life-cycle cost flow rate of component $k$, which is the key parameter linking full life-cycle cost and dynamic cost tracking. The calculation of $\dot{Z}_k$ covers the full scope of capital expenditure (CAPEX) and operating expenditure (OPEX). CAPEX includes one-time costs such as initial investment and installation and commissioning, while OPEX covers periodic costs such as operation and maintenance, fuel consumption, and decommissioning and disposal. The total full life-cycle cost (TotalLCC)${Z_k}$ is converted into an annualized cost flow rate through the capital recovery factor CRF, namely $\dot{Z}_k=Z_k \cdot C R F$, where the expression of $C R F$ is:

$C R F=\frac{i(1+i)^n}{(1+i)^{n-1}}$          (6)

where, $i$ is the reference discount rate and $n$ is the service life of the component. In terms of quantitative boundaries, CAPEX is aggregated at the time of component commissioning, while OPEX is accounted for based on the actual annual occurrence, ensuring complete coverage and accurate conversion of full life-cycle costs.

The solution of the exergy cost flow rate takes the results of classical exergy analysis as inputs and adopts an iterative algorithm to achieve global solution of cost flows for the entire system. The core procedure consists of three steps. First, the unit exergy cost of fuel $c_f$ is determined as the initial reference for cost flow calculation. $c_f$ is determined based on the ratio of the fuel market price to the fuel exergy value:

$c_f=\frac{P_t}{E_{e x, f}}$          (7)

where, $P_f$ is the market price per unit mass of fuel, and $E_{e x, f}$ is the exergy value per unit mass of fuel, ensuring that fuel cost is directly linked to fuel energy quality. Second, constrained by the exergy balance results of each component, the exergy cost balance equations are solved iteratively. Starting from the fuel input component, the input exergy cost flow rate of each component is calculated sequentially, and the output exergy cost flow rate is obtained by combining $\dot{Z}_k$, thereby yielding the unit exergy cost of component output $c_{e x}$. For components with multiple inputs and outputs, the cost allocation ratio of each output exergy is determined based on the exergy flow distribution proportion. Iteration continues until the unit exergy costs of all components in the system converge, and the final unit exergy cost of the system product $c_p$ is obtained.

To achieve consistency between thermodynamic–economic indicators and commonly used economic evaluation indicators in the energy industry, a direct conversion relationship between $c_p$ and the levelized cost of energy (LCOE) is established. Considering the annual operating time of the system $\tau$ and the annual product energy output $Q_{ {annual }}$, the conversion formula between the product unit exergy cost $c_p$ and LCOE is:

$L C O E=c_p \cdot \frac{E_{{exp }, { annual }}}{Q_{ {annual }}}$          (8)

where, $E_{e x, p, a n n u a l}$ is the total annual product exergy output of the system. This conversion relationship transforms exergy-based thermodynamic–economic indicators into LCOE, which is widely recognized in the energy industry, ensuring comparability of evaluation results and enhancing the engineering applicability of the model. Through the above mathematical modeling and solution process, full-chain dynamic tracking from fuel cost and full life-cycle cost to product cost is realized, as well as quantitative mapping from thermodynamic parameters to economic indicators. Figure 3 presents the complete calculation procedure of MEDCC using the model perturbation method.

Figure 3. Flowchart of the iterative solution algorithm for exergy cost flow rate

2.4 Diagnostic and optimization tool: MEDCC

MEDCC is the core diagnostic indicator linking thermodynamic improvement and economic optimization. Its definition originates from the marginal coupling relationship between exergy destruction and the TotalLCC of the system. The mathematical expression is:

$MEDCC _k=\frac{\partial( { TotalLCC })}{\partial\left({ Ex }_{ {dest }, k}\right)}$          (9)

where, $Ex_{dest,k}$ is the exergy destruction of component $k$. The partial derivative constraint ensures that the independent impact of exergy destruction variation of a single component on the total cost is accurately captured. The core value of this definition lies in overcoming the limitation of traditional exergy destruction analysis that “only evaluates magnitude but not cost,” and realizing the economic value quantification of thermodynamic losses.

The physical–economic significance of MEDCC can be interpreted from two dimensions. From the physical dimension, it quantifies the dynamic response relationship between variations in component exergy destruction and changes in the total system cost, reflecting the economic transmission effect of thermodynamic irreversible processes. From the economic dimension, its value directly represents the “marginal change in TotalLCC induced by reducing a unit of exergy destruction.” When MEDCC is positive, it indicates that reducing exergy destruction will lead to a decrease in total cost and has economic improvement value, and the larger the absolute value, the more significant the economic benefit per unit exergy destruction improvement. When MEDCC is negative or approaches zero, it indicates that reducing exergy destruction may lead to cost increases or no economic benefit, and the optimization priority is low. This characteristic makes MEDCC a key basis for identifying economic improvement hotspots, effectively distinguishing between “thermodynamic hotspots” and “economic improvement hotspots,” and providing a quantitative scale for precise optimization decisions.

The calculation of MEDCC adopts the model perturbation method. The core idea is to induce changes in exergy destruction by applying small perturbations to key thermodynamic parameters of components, while synchronously tracking the response of the TotalLCC of the system, and finally obtaining the coefficient value through numerical solution of the partial derivative. This method avoids the mathematical complexity of direct differentiation and is more suitable for the nonlinear characteristics of engineering systems, with a clear engineering feasibility in its calculation procedure.

The selection of perturbation parameters follows the principle of “relevance priority,” giving priority to core thermodynamic parameters directly related to component exergy destruction, such as heat exchanger effectiveness, turbine expansion efficiency, and reactor reaction temperature, ensuring that parameter perturbations can directly and significantly induce changes in exergy destruction. The determination of perturbation magnitude needs to balance computational accuracy and numerical stability. Typically, 1%–5% of the baseline parameter value is selected as a small perturbation magnitude: excessively large magnitudes may cause system characteristics to deviate from the linear region and introduce nonlinear errors, while excessively small magnitudes may be masked by numerical noise, reducing result reliability. Error control is achieved through bidirectional perturbation and iterative verification. Forward and backward perturbations are applied to the same parameter, and the deviation between the two MEDCC results is calculated. If the deviation exceeds a threshold, the perturbation magnitude is adjusted and recalculated. At the same time, convergence of results under different perturbation sequences is ensured through multiple iterative optimizations.

The specific calculation steps are as follows. First, the baseline thermodynamic parameters, baseline exergy destruction, and baseline TotalLCC of each component are determined. Second, a small perturbation is applied to the key parameter of the target component, and the component exergy destruction $\mathrm{Ex}_{dest, k}$ and the TotalLCC of the system are recalculated. Finally, the partial derivative is approximated based on the differences before and after perturbation:

$M E D C C_k \approx \frac{\Delta { Total LCC }}{\Delta E x_{dest, k}}$          (10)

This method realizes efficient calculation of MEDCC through numerical approximation and provides accurate quantitative support for the formulation of subsequent optimization sequences.

2.5 Framework extension: Environmental exergy destruction and carbon cost internalization

To achieve three-dimensional synergistic evaluation of efficiency, cost, and environment, it is necessary to incorporate the environmental dimension into the synchronous mapping framework. The core lies in the quantification of environmental exergy destruction and the internalization of carbon cost, so that environmental impacts are transformed into quantitative indicators that can be directly coupled with thermodynamic and economic costs. In traditional evaluations, the separation of environmental impacts from thermodynamic and economic analyses may cause optimization decisions to ignore environmental costs. The extension of this framework realizes the fundamental integration of the three while maintaining the consistency of the theoretical system.

The core of environmental exergy destruction quantification is to convert the environmental impact of pollutant emissions into “virtual environmental exergy destruction” and to establish a quantitative relationship with pollutant emissions. Taking an environmental reference state (such as the standard atmospheric environment or a reference ecosystem state) as a benchmark, pollutant emissions disrupt the equilibrium state of the environmental system, leading to a loss of available energy in the ecosystem. This loss constitutes environmental exergy destruction. For typical pollutants such as CO₂ and SO₂, based on the definition of environmental exergy, the quantitative expression can be written as: $E x_{e n v, m}=m \cdot e_{e n v, m}$, where $m$ is the pollutant emission amount and $e_{e n v, m}$ is the environmental exergy destruction coefficient per unit mass of pollutant. This coefficient is determined through thermodynamic analysis of environmental systems and reflects the degree to which pollutants damage environmental available energy. Through this transformation, environmental impacts are incorporated into the exergy flow evolution system and become an important component of exergy destruction.

Carbon cost internalization is the key step in coupling the environmental dimension with the economic dimension. The core is to convert the cost of carbon emission reduction into a part of the full life-cycle cost and include it in the annualized cost flow rate $\dot{Z}_k$ of components. In combination with future carbon tax policies, the annual carbon cost is first calculated based on the CO₂ emissions of components and the unit carbon tax price. Subsequently, it is converted into an annualized carbon cost flow rate $\dot{Z}_{ {carbon, k}}$ through the capital recovery factor. Finally, $\dot{Z}_{ {carbon, k}}$ is added to the original capital and operating cost flow rates to form a comprehensive annualized cost flow rate including environmental cost: $\dot{Z}_k^{\prime}=\dot{Z}_k+\dot{Z}_{car b o n, k}$. This treatment allows carbon cost to accompany exergy flow transfer and evolution, realizing dynamic full life-cycle tracking of environmental costs. The extended framework can synchronously output evaluation results in three dimensions—thermodynamic performance, economic cost, and environmental cost—providing complete theoretical support for three-dimensional synergistic optimization of energy systems.

The thermodynamic–economic synchronous mapping model proposed in this study, by constructing a dynamic coupling mechanism between exergy flow and cost flow, effectively overcomes the inherent limitations of traditional energy system evaluation methods. A systematic comparison with decoupled thermodynamic–economic evaluation, standard thermoeconomics, and traditional LCCA indicates that the proposed method exhibits significant advantages in multiple dimensions: From the evaluation perspective, it achieves a transition from static local evaluation to dynamic full lifecycle evaluation, converting discrete cost accounting into a continuous tracking process synchronized with exergy flow evolution. From the thermodynamic–economic coupling perspective, through the construction of the exergy cost formation rate equation and MEDCC, a continuously differentiable quantitative relationship between the two is established. The coupling depth far exceeds the rigid superposition in standard thermoeconomics and the black-box decoupling in traditional LCCA. From the design guidance perspective, case results show that the optimization scheme based on the proposed method can reduce system LCOE by 5.3%, whereas traditional methods, unable to accurately identify economic improvement hotspots, achieve only 2.1% improvement. From the computational complexity perspective, the model is based on classical exergy analysis and iterative solution; although slightly higher than traditional single evaluation methods, parameterized modeling ensures engineering operability, and the overall cost-performance ratio is significantly better than other integrated methods. The core value of this advantage lies in completely resolving the key issue of “decoupling thermodynamics and economics,” upgrading the evaluation result from a simple performance characterization to precise guidance for design optimization.

This study provides a disruptive guiding idea for energy system design, centered on the concept of “design as managing the cost consequences of exergy loss.” Traditional design often falls into the single-objective trap of “pursuing high exergy efficiency,” whereas case analysis shows that the thermodynamic optimum and economic optimum often diverge, and blindly pursuing high exergy efficiency may cause cost surges. MEDCC, as a quantitative metric connecting thermodynamic improvement with economic benefit, clarifies the design strategy of “prioritize components with the largest absolute MEDCC value,” enabling optimization resources to be precisely matched to high cost-performance improvement elements, substantially enhancing design efficiency. This guiding idea is not only applicable to supercritical CO₂ power generation systems but also broadly generalizable—for complex energy systems such as multi-energy complementary systems and new energy coupled storage systems, where the coupling relationship between exergy flow and cost flow is more complex, the synchronous mapping model can accurately track the dynamic evolution of multiple flow streams and provide scientific support for system integration optimization, potentially becoming a core tool for future energy system design.

Objectively, the theoretical framework proposed in this study still has certain limitations. The model is currently constructed based on a steady-state operation assumption and does not consider the instantaneous coupling between exergy flow and cost flow under dynamic operating conditions. In actual energy systems, load fluctuations and intermittent renewable output often occur, which may reduce the evaluation accuracy of the model under dynamic scenarios. The construction of cost functions relies on existing engineering experience data; for emerging energy technologies, the lack of mature cost data accumulation may limit the accuracy of cost functions, thereby affecting model applicability. In addition, the model does not incorporate the effects of technology learning curves and policy uncertainty. With technology iteration and policy adjustments, the full lifecycle cost of energy systems may change significantly, which the current model cannot reflect.

To address the above limitations, future research can advance in three directions. First, extend the model to dynamic operating conditions by establishing a coupling mapping mechanism between instantaneous exergy flow and dynamic cost flow based on transient exergy analysis, and introduce load forecasting and dynamic control strategies to enhance model adaptability to real fluctuation scenarios. Second, construct data-driven high-precision exergy–cost correlation functions, combining machine learning algorithms to mine implicit patterns in massive engineering data, reducing reliance on empirical data and improving model evaluation accuracy for new energy technologies. Third, incorporate technology learning curves and policy uncertainty factors, quantifying cost and policy risk through methods such as Monte Carlo simulation, and establish a multi-objective optimization framework with both economic performance and robustness. These improvements will further refine the synchronous mapping theoretical system, enabling it to play a greater role in the design of complex energy systems under the energy transition context.