Exergy-Based Assessment of Energy Conversion Efficiency and Structural Optimization in Hydraulic Engineering Systems

2.1 Construction of refined component-level exergy model and optimization of exergy flow network

To overcome the limitation of single-dimensional exergy analysis in traditional hydraulic engineering and to adapt to the operational characteristics of hydraulic engineering in Southwest China, this study constructs a three-dimensional refined component-level exergy model including mechanical exergy, thermal exergy, and chemical exergy. The core innovation is reflected in the refined improvement of the calculation of each component exergy and regional adaptability optimization, and all calculations strictly follow the first and second laws of thermodynamics. For mechanical exergy, the traditional uncorrected calculation mode is abandoned, and the head loss characteristics caused by mountainous terrain in Guizhou are incorporated. The core calculation formula is:

$E_{ {mech }}=\rho g V\left(z+\frac{v^2}{2 g}+\frac{p}{\rho g}\right) \eta_h$                (1)

where, ρ is the water density, g is gravitational acceleration, V is the water volume, z is the water level difference, v is the water flow velocity, p is the water pressure, and η_h is the head loss correction coefficient. This coefficient differs from traditional empirical values and is calibrated based on measured data of along-the-way losses and local losses in pipeline water conveyance in mountainous areas of Guizhou, accurately reflecting the hydraulic characteristics of hydraulic engineering in mountainous regions. For thermal exergy, focusing on the significant water temperature stratification in reservoirs in Guizhou, the thermal exergy calculation formula of water is derived as:

$E_{t h}=m c_p\left(T-T_0-T_0 \ln \frac{T}{T_0}\right)$                 (2)

where, m is the water mass, c_p is the specific heat capacity at constant pressure, T is the actual water temperature, and T₀ is the environmental reference temperature. At the same time, considering the high-temperature and high-humidity climate in Southwest China, a dynamic environmental temperature and humidity influence factor is introduced to correct the thermal exergy loss model of electromechanical equipment heat dissipation. For chemical exergy, based on the thermodynamic chemical potential theory, the chemical exergy calculation formula of dissolved gases in water is derived as:

$E_{ {chem }}=R T \sum n_i \ln \frac{f_i}{f_{i 0}}$                 (3)

where, R is the universal gas constant, T is the thermodynamic temperature, n_i is the mole number of the i-th dissolved gas, f_i is the actual fugacity of the gas, and f_i0 is the fugacity of the gas under standard state. A fugacity coefficient is introduced to correct the non-ideality of water, and model coefficients are optimized in combination with water quality parameters such as water hardness and pH value in Guizhou. Finally, the three component exergies are integrated to establish the exergy inventory of hydraulic engineering in Southwest China, and the calculation boundaries and parameter selection standards of each component exergy are clarified.

Based on the above refined component-level exergy model, this study further optimizes the construction method of the system exergy flow network diagram. The core innovation lies in integrating graph theory with the unit coupling characteristics of hydraulic engineering in Southwest China to achieve accurate visualization of exergy flow transfer and loss paths. Reservoirs, water conveyance pipelines, turbines, generators, and other units are abstracted as thermodynamic nodes, and the input exergy, output exergy, and exergy loss attributes of each node are defined. According to the layout characteristics of cascade hydropower stations and cross-regional water conveyance pipelines in Guizhou, a node coupling coefficient is newly introduced to quantify the exergy flow interaction effect among cascade units. Exergy flow is defined as the edge of the network graph, and an exergy flow quality coefficient is introduced to distinguish the utilization value of different types of exergy. The calculation formula is:

$\omega=\frac{E_{ {use }}}{E_{ {total }}}$              (4)

where, E_use is the effectively usable exergy flow, and E_total is the total exergy flow. Through this coefficient, the transfer efficiency of each exergy flow is labeled, intuitively revealing the conversion paths and loss links of mechanical exergy, thermal exergy, and chemical exergy in the system. Based on the exergy flow network diagram, a system exergy flow topology matrix is constructed. The matrix elements represent the proportion of exergy flow between nodes and can quickly locate key units and weak connection paths of exergy losses in hydraulic engineering projects in Guizhou, providing quantitative and visual core support for subsequent system structural diagnosis and optimization. Compared with traditional exergy flow network diagrams, its adaptability to the structural characteristics of hydraulic engineering in Southwest China and diagnostic accuracy are significantly improved. Figure 1 shows the graph-theory-based exergy flow network topology model of the hydraulic engineering system.

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2.2 Construction of multi-level exergy efficiency evaluation index system

In view of the core limitation that traditional exergy efficiency evaluation only focuses on single equipment and cannot quantify process exergy losses and structural exergy losses, this study constructs a three-level exergy efficiency evaluation index system of “equipment–process–system”. The core innovation lies in breaking through a single evaluation dimension and introducing two new indicators, namely process exergy loss intensity (PELI) and structural exergy loss contribution degree (SELC), so as to achieve accurate quantification of the thermodynamic perfection degree and system structural characteristics of hydraulic engineering. It adapts to the operational characteristics of hydraulic engineering in Southwest China, which feature large differences in unit scale and complex structures. All indicator designs strictly follow the disciplinary norms of thermodynamic system evaluation. The system construction is based on exergy balance theory, abandoning the dependence of traditional indicators on output scale and absolute exergy loss values, and emphasizing the correlation between indicators and system structure as well as energy conversion processes, thereby providing accurate evaluation support for subsequent system exergy loss diagnosis and structural optimization. Figure 2 shows the correlation diagram of the “equipment–process–system” multi-level exergy efficiency evaluation index system.

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Figure 2. Correlation diagram of the “equipment–process–system” multi-level exergy efficiency evaluation index system

This study proposes PELI for the first time to quantify the thermodynamic perfection degree of each energy conversion process in hydraulic engineering. The core innovation lies in eliminating the interference of output scale on exergy loss evaluation and accurately capturing the low-efficiency characteristics of “small-flow, high-loss” processes such as small mountain water conveyance pipelines and auxiliary electromechanical equipment in Southwest China. Its core calculation formula is:

$P E L I=\frac{E_{ {lass\_proc }}}{E_{ {use\_proc }}}$                (5)

where, PELI is the PELI, E_loss,proc is the total exergy loss of a certain energy conversion process, and E_use,proc is the effective output exergy of that process. Compared with traditional exergy efficiency, this indicator does not depend on the process output scale and can achieve horizontal comparison of energy conversion processes of different scales and types. For example, the exergy loss characteristics of hydraulic conversion processes of small mountain water conveyance pipelines and large turbines can be directly quantified and compared. Parameter calibration adopts long-term operational data from typical hydraulic engineering projects in Guizhou Province in Southwest China. By measuring the exergy loss and effective output exergy of different types of energy conversion processes and applying statistical fitting methods, reasonable PELI threshold values are calibrated, and PELI evaluation standards for different types of hydraulic engineering such as hydropower stations and pumping stations are clarified. Three evaluation levels, namely low efficiency, medium efficiency, and high efficiency, are defined to ensure the adaptability and operability of the indicator for engineering scenarios in Southwest China.

To accurately quantify the impact of system structural layout on total exergy loss, this study proposes SELC, breaking through the traditional evaluation mode of “ranking by absolute exergy loss value”. It can accurately locate weak connection paths in the system characterized by “low exergy loss but high contribution” and adapts to the complex structural characteristics of cascade hydropower stations and cross-regional water conveyance pipelines in Southwest China. Its core calculation is based on the system exergy flow topology matrix and combined with matrix operations and graph theory methods. The calculation formula is:

$S E L C_i=\frac{E_{l o s s, i} \cdot \omega_i}{\sum_{i=1}^n E_{l o s s, i} \cdot \omega_i}$                (6)

where, SELC_i is the SELC degree of the i-th unit or connection path, E_loss,i is the exergy loss value of that unit or path, ω_i is the connection weight of that unit or path, and n is the total number of system units and connection paths. In the calculation process, a system exergy loss contribution matrix is constructed, in which row vectors represent the exergy loss values of each unit/path and column vectors represent their connection weights. Through matrix normalization operations, SELC values are obtained to ensure normalization and comparability of the results. A key exergy loss threshold is introduced. When the SELC value exceeds the threshold, it is identified as a key exergy loss unit/path. This method can accurately identify weak links such as water conveyance connections between cascade hydropower stations and matching connections between electromechanical equipment and the power grid, providing precise targets for structural optimization and solving the problem that traditional evaluation methods cannot locate structural-level exergy loss bottlenecks.

To ensure the scientificity, rationality, and practicality of the evaluation index system, this study conducts indicator validation and weight allocation based on thermodynamic theory and adopts the entropy weight method to construct an indicator weight allocation model, adapting to the fluctuation characteristics of operational data of hydraulic engineering in Southwest China. First, based on the first and second laws of thermodynamics, the consistency of the newly introduced indicators with exergy balance theory is verified, and the physical meaning and value range of PELI and SELC are clarified to ensure the theoretical rigor of indicator design. Second, the relationships among indicators at different levels are analyzed to eliminate indicator redundancy, and a hierarchical correlation model of “equipment level–process level–system level” is constructed. Finally, the entropy weight method is used to quantify the weights of each indicator. The weight allocation is entirely based on measured operational data from typical hydraulic engineering projects in Guizhou Province in Southwest China, abandoning the limitations of traditional subjective weighting methods, and ensuring that the index system can truly reflect the exergy loss characteristics and structural features of hydraulic engineering in Southwest China, thereby providing scientific and reliable evaluation support for subsequent system exergy loss diagnosis and optimization.

2.3 System structural vulnerability analysis method based on exergy flow diagnosis

In view of the core limitation that existing studies cannot associate system structural characteristics with exergy losses and have difficulty diagnosing structural weak points, this study proposes a system structural vulnerability analysis method based on exergy flow diagnosis. The core logic is to integrate thermodynamic system topology theory with exergy flow analysis technology, introduce two key parameters, namely structural coefficient and connection coefficient, and construct an exergy flow supply–demand mismatch degree model, so as to realize quantitative characterization of the influence of system structure on exergy efficiency and accurately identify structural weak links. This method is specifically adapted to the complex structural characteristics of cascade coupling and multi-unit linkage in hydraulic engineering in Southwest China. It breaks through the limitation of traditional vulnerability analysis that only focuses on equipment performance, associates structural layout and unit matching relationships with exergy losses, and forms a complete analysis system of “coefficient quantification–mismatch diagnosis–vulnerability identification–optimization orientation”, providing targeted support for system structural optimization. All technical designs strictly follow thermodynamic disciplinary norms and the operational characteristics of engineering in Southwest China.

To quantify the restriction degree of system topology on exergy efficiency, this study defines the structural coefficient, breaking through the disconnection between traditional topology analysis and exergy efficiency evaluation, and focusing on adapting to the layout characteristics of cascade hydraulic engineering in Southwest China. The structural coefficient characterizes the restriction of system topology on the theoretical maximum exergy efficiency, with a value range of 0–1. The closer the value is to 1, the smaller the restriction of structure on exergy efficiency and the higher the thermodynamic perfection degree. Its core calculation formula is derived based on the topology matrix constructed from the system exergy flow network diagram, integrating key parameters such as the number of units, the number of connection paths, and the proportion of energy feedback. At the same time, according to the series and parallel layout characteristics of cascade hydropower stations in Southwest China, a cascade coupling coefficient is added for correction. The final calculation formula is:

$S C=\frac{\eta_{e x, a c t}}{\eta_{e x, max }} \cdot \alpha \cdot \frac{N_c}{N_t} \cdot \beta$                (7)

where, SC is the structural coefficient, η_ex,act is the actual system exergy efficiency, η_ex,max is the theoretical maximum system exergy efficiency, α is the cascade coupling coefficient, N_c is the number of effective energy feedback paths, N_t is the total number of connection paths, and β is the topology balance coefficient. The core innovation of this coefficient lies in realizing the direct association between topology and exergy efficiency. By quantifying the cumulative impact of unreasonable series–parallel structures and the absence of energy feedback paths on exergy losses, it can accurately determine whether the layout of cascade hydropower stations in mountainous areas of Southwest China leads to cumulative exergy losses, solving the problem that traditional methods cannot quantify the impact of structural layout on exergy efficiency.

To accurately identify additional exergy losses caused by exergy flow matching defects between units, this study defines the connection coefficient and constructs an exergy flow supply–demand mismatch degree model, breaking through the limitation of traditional matching analysis that only focuses on parameter phenomena and adapting to common operational problems in hydraulic engineering in Southwest China such as “oversized unit driving small load” and “throttling regulation”. The connection coefficient quantifies the matching degree of exergy flow between units, covering the matching relationships among water flow and unit design parameters, transmission and transformation capacity, and energy conversion and storage units. Its value range is 0–1. The closer the value is to 1, the higher the matching degree and the smaller the additional exergy loss. Its calculation takes the exergy flow supply–demand mismatch degree as the core, and the derivation process incorporates the matching deviation between unit input exergy and output exergy. At the same time, a regulation correction coefficient is introduced to quantify additional exergy losses caused by unreasonable operation modes. The corrected calculation formula is:

$C C=\left(1-\frac{\left|E_{ {in }, i}-E_{ {out }, j}\right|}{\max \left(E_{ {in }, i}, E_{ {out }, j}\right)}\right) \cdot \gamma$               (8)

where, CC is the connection coefficient, E_in,i is the input exergy of the i-th unit, E_out,j is the output exergy of the j-th associated unit, and γ is the operation regulation correction coefficient. The technical breakthrough of this coefficient lies in its ability to accurately capture core problems in hydraulic engineering in Southwest China, such as mismatch between unit design parameters and mountainous inflow, and mismatch between transmission and transformation capacity and unit output exergy, and to quantify the additional exergy losses caused by these problems, providing quantitative support for optimization of unit connection relationships.

Based on the above two key coefficients, this study constructs a system structural vulnerability assessment process, integrating the structural coefficient, connection coefficient, and the SELC proposed earlier to form a multi-indicator collaborative vulnerability diagnosis system. At the same time, considering the operational environmental characteristics of mountainous terrain and heavy rainfall and floods in Southwest China, the pertinence and accuracy of vulnerability identification are improved. The core innovation of the assessment process lies in adopting the control variable method to conduct sensitivity analysis. By keeping other parameters unchanged and independently simulating the degradation of exergy performance of key units or failure of connection paths, the sensitivity change of overall system exergy efficiency is calculated, and the magnitude of efficiency decline is determined. Combined with measured data from typical hydraulic engineering projects in Southwest China, vulnerability thresholds for each indicator are set. When the structural coefficient is lower than the threshold, the connection coefficient is lower than the threshold, or the SELC is higher than the threshold, and the decline magnitude of system exergy efficiency exceeds the set standard, the unit or path is identified as a structural vulnerable point. For the identified vulnerable points, combined with the terrain, climate, and other operational environmental characteristics of engineering projects in Southwest China, the formation causes and evolution mechanisms are analyzed in depth. Different types of inducing factors such as terrain constraints, unreasonable layout, and equipment matching deviation are distinguished. Finally, targeted optimization suggestions such as unit layout adjustment, equipment upgrading, and connection path reconstruction are proposed, realizing the precise connection between vulnerability diagnosis and structural optimization and ensuring the engineering practicality and operability of the analysis results. Figure 3 presents the system vulnerability diagnosis flowchart based on structural coefficient and connection coefficient.

Figure 3. System vulnerability diagnosis flowchart based on structural coefficient and connection coefficient

2.4 Multi-objective collaborative optimization model coupling exergy–economic–environmental factors and dynamic dispatch strategy

In view of the core limitation that traditional hydraulic engineering optimization models only focus on single exergy efficiency, do not incorporate structural characteristics, and lack multi-benefit coordination, this study constructs a multi-objective collaborative optimization model coupling exergy–economic–environmental factors. The core breakthrough lies in introducing structural decision variables, realizing the transition from operation parameter optimization to coordinated optimization of system structure and operation. It adapts to the operational characteristics of hydraulic engineering in Southwest China with large inflow fluctuations and complex structures. At the same time, combined with dynamic exergy analysis technology, an Model Predictive Control (MPC)-based real-time dispatch strategy is developed to solve the problem that traditional static dispatch cannot adapt to temporal variations, forming a complete technical system of “static optimization–dynamic dispatch–effect verification”, taking into account thermodynamic theoretical rigor and engineering practicality.

The core innovation of the model lies in the dual-dimension design of decision variables, breaking through the limitation of existing models that only focus on operation parameters, and constructing a collaborative optimization decision system of “operation parameters–structural variables”. Operation parameter variables are set around the temporal variation characteristics of inflow in Southwest China, covering core parameters such as reservoir water level, unit combination, guide vane opening, and water conveyance flow rate, ensuring that parameters adapt to the significant differences between rainy and dry seasons in mountainous areas. Structural variables are the key innovation of this study, introducing parameters related to system structural modification, including local pipe network reconstruction schemes, selection and layout of new regenerative and energy recovery units, and electromechanical equipment upgrading parameters. Among them, pipe network reconstruction parameters include pipe diameter adjustment coefficient and material optimization coefficient; energy recovery unit parameters include selection coefficient and layout weight; electromechanical equipment upgrading parameters include capacity adjustment coefficient and efficiency optimization coefficient. Through the introduction of structural variables, the optimization model extends from “operation regulation” to “structural design–operation regulation”, accurately solving the problem of high exergy losses caused by unreasonable structures in hydraulic engineering in Southwest China.

The construction of objective functions follows the principle of “exergy as the core, economic and environmental coordination”. All three objectives incorporate the engineering characteristics of Southwest China and innovative design. The core formulas are as follows. The exergy objective takes minimization of total system exergy loss as the core, integrating the refined component-level exergy model constructed previously to quantify the total losses of mechanical exergy, thermal exergy, and chemical exergy. The objective function is:

$\min E_{ {loss }, { total }}=\sum E_{ {loss }, { mech }}+\sum E_{ {loss }, { th }}+\sum E_{ {loss }, { chem }}$               (9)

where, E_loss,total is the total system exergy loss, and E_loss,mech, E_loss,th, and E_loss,chem are the losses of mechanical exergy, thermal exergy, and chemical exergy, respectively. The economic objective takes minimization of annual total cost as the core, introducing exergy loss cost, converting exergy loss into equivalent power generation loss value, setting conversion coefficients according to electricity price policies in Southwest China, and incorporating a mountainous engineering operation and maintenance difficulty coefficient to correct operation and maintenance cost. The objective function is:

$\min C_{\text {total }}=C_{e x}+C_{i n v}+C_{o p}$                 (10)

where, C_total is the annual total cost, C_ex is the exergy loss cost, C_inv is the structural modification investment cost, and C_op is the operation and maintenance cost. The environmental objective is based on exergy life cycle assessment, focusing on key carbon emission links such as equipment manufacturing and energy consumption in hydraulic engineering in Southwest China, aiming to minimize cumulative exergy resource consumption and carbon emissions. The function is:

$\min \left(E_{r e s}+\mathrm{CO}_2\right)$                (11)

where, E_res is cumulative exergy resource consumption, and CO₂ is carbon emissions. Constraint conditions cover five categories: exergy balance, hydraulic, structural, economic, and environmental constraints, adapting to the thermodynamic and hydraulic characteristics of engineering in Southwest China.

The optimization algorithm adopts the Non-dominated Sorting Genetic Algorithm III (NSGA-III algorithm). In view of the complex characteristics of the model with multiple variables, multiple constraints, and nonlinearity, this study introduces a surrogate model to simplify calculation and improve optimization efficiency. At the same time, considering the fluctuation characteristics of operational data of hydraulic engineering in Southwest China, the crossover probability and mutation probability of the algorithm are optimized to solve the problems of slow convergence and unstable optimization results in traditional algorithms. The surrogate model selects a radial basis function neural network, trained based on measured data from typical hydraulic engineering projects in Guizhou Province in Southwest China, accurately fitting the nonlinear relationship between objective functions and decision variables, replacing complex hydraulic and thermodynamic simulation calculations, and greatly reducing computational cost. In the process of algorithm improvement, the crossover probability adopts an adaptive adjustment strategy, dynamically optimized with iteration times, and the mutation probability introduces a data fluctuation coefficient correction to ensure that the algorithm can adapt to the fluctuation characteristics of parameters such as inflow and load demand. Finally, efficient solution of multi-objective optimization is achieved, obtaining the Pareto optimal solution set and providing diversified choices for engineering decision-making.

To adapt to the temporal fluctuation characteristics of inflow and load in Southwest China and break through the limitation of traditional static dispatch, this study conducts dynamic exergy analysis and develops an MPC-based real-time exergy optimization dispatch strategy. The core innovation of dynamic exergy analysis lies in proposing the concept of dynamic exergy efficiency and calculating the system exergy efficiency at each time interval. The formula is:

$\eta_{e x, d y n}=\frac{E_{w i r, d y n}}{E_{i n, d y n}}$                (12)

Figure 4. Schematic diagram of dynamic exergy optimization dispatch strategy based on Long Short-Term Memory (LSTM) prediction and Model Predictive Control (MPC) rolling