Turbine thermal performance and energy efficiency evaluation method and system based on hybrid modeling

Abstract

The application discloses a steam turbine thermodynamic performance and energy efficiency evaluation method and system based on hybrid modeling, relates to the technical field of energy efficiency evaluation, and solves the technical problem that the existing technology has a large approximation in processing variable working condition and a complex thermodynamic system, and the calculation precision is limited; real-time operation data of a steam turbine and a working flow network are acquired; a mechanism model of the steam turbine is constructed according to the working flow network of the steam turbine; a dynamic prediction model of exhaust enthalpy and cylinder efficiency is constructed according to the mechanism model; the thermodynamic performance and energy efficiency indexes are analyzed based on the real-time operation data of the steam turbine; not only the steady-state characteristics can be reflected, but also dynamic transient effects such as metal heat accumulation under variable working conditions can be captured, and the exhaust enthalpy and cylinder efficiency can be accurately predicted.

Description

Technical Field

[0001] This application belongs to the field of energy efficiency assessment, specifically a method and system for assessing the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling. Background Technology

[0002] A steam turbine is a rotary power machine that converts the thermal energy of steam into mechanical energy. It is a type of prime mover, and its core principle is to use high-temperature, high-pressure steam to drive turbine blades, thereby outputting mechanical work to power generators, compressors, pumps, and other equipment. Evaluating the thermodynamic performance and energy efficiency of steam turbines offers numerous significant benefits. From an economic perspective, accurate evaluation allows for precise control of turbine operating efficiency, timely identification of energy-intensive processes, and targeted optimization to reduce fuel consumption, lower operating costs, and improve corporate economic efficiency. From a technical perspective, evaluation provides in-depth understanding of the internal thermodynamic processes of the steam turbine, offering a scientific basis for equipment improvement and upgrades, supporting the development of more efficient steam turbine technologies, and driving technological progress in the industry. From an environmental perspective, efficient steam turbine operation reduces energy waste and pollutant emissions, aligning with energy conservation and emission reduction requirements. Furthermore, regular evaluations can identify potential faults early, enabling timely maintenance and repairs, preventing unplanned downtime, ensuring stable and reliable turbine operation, and extending equipment lifespan.

[0003] In the existing technology, the thermodynamic performance evaluation of steam turbines mainly adopts the mechanism modeling method. By establishing a system model of the steam turbine flow path and thermodynamic system through the working principle of the steam turbine and thermodynamic equations, the thermodynamic performance of the steam turbine can be evaluated. However, when dealing with variable operating conditions and complex thermodynamic systems, the mechanism model often has large approximations, and the calculation accuracy is limited.

[0004] This application provides a method and system for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling, in order to solve the above-mentioned technical problems. Summary of the Invention

[0005] This application aims to solve at least one of the technical problems existing in the prior art; to this end, this application proposes a method and system for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling, which is used to solve the technical problem that the mechanism model often has large approximations and limited calculation accuracy when dealing with variable operating conditions and complex thermodynamic systems.

[0006] To achieve the above objectives, the first aspect of this application provides a method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling, including: Obtain real-time operating data of the steam turbine and its workflow to the network; A mechanistic model of the steam turbine is constructed based on the turbine's working flow network; A dynamic prediction model for exhaust enthalpy and cylinder efficiency was constructed based on the mechanistic model. Analysis of thermodynamic performance and energy efficiency indicators based on real-time operating data of steam turbines.

[0007] Preferably, the step of constructing the turbine's mechanistic model based on the turbine's working flow network includes: Obtain the working flow network of the steam engine; divide the steam turbine into several stages along the steam flow direction; and treat the high-pressure cylinder, intermediate-pressure cylinder, and low-pressure cylinder as a calculation segment; each stage consists of one stationary blade and one moving blade; A unipolar energy conversion model is established; the reaction degree of steam in the moving blade is calculated based on the reaction degree analysis function; the expression of the reaction degree analysis function is: ;in, This is the actual enthalpy of steam as it leaves the stationary blade and enters the moving blade. This is the actual enthalpy of the steam after it leaves the moving blade; The stagnation enthalpy of the steam before the stage; The relationship between pressure and flow rate under varying operating conditions is analyzed using the Vlugel formula; the expression of the Vlugel formula is: ;in, The steam mass flow rate through this stage group; The mass flow rate of steam passing through the same stage group under varying operating conditions; The absolute pressure of the steam before the stage; The absolute pressure of steam before the same stage group under varying operating conditions; This refers to the absolute pressure of the steam after the stage; The absolute pressure of steam after the same stage group under varying operating conditions; The absolute temperature of the steam before the stage; The absolute temperature of the steam before the stage under varying operating conditions; The sum of the cycle work at each stage is converted into mechanical work at the shaft end, and the power parameters and rotor motion equations are analyzed; among which, the power parameters include: total internal power and shaft end power; The expression for the total internal power is: ;in, This refers to the steam mass flow rate; For the total series; For the effective enthalpy drop of the j-th level; The expression for the shaft end power is: ;in, Mechanical loss; The expression for the rotor motion equation is as follows: ;in, It is the moment of inertia; Angular velocity; This represents the load torque.

[0008] Preferably, the establishment of the unipolar energy conversion model includes: Based on the approximate isentropic expansion of steam in the stationary blades, the theoretical outlet velocity is analyzed; the expression for the theoretical outlet velocity is: ;in, The enthalpy of vapor stagnation at the inlet of the still leaf; This represents the ideal enthalpy value when the quotient expands to the point of export pressure. Based on formula Calculate the actual export speed; where, The stationary blade velocity coefficient; based on the formula Calculate nozzle loss; As steam enters the moving blades, the change in relative velocity generates a circumferential force acting on the blades; the work done per unit mass of steam on the turbine circumference is calculated based on the Euler turbine equation; the expression of the Euler turbine equation is: ;in, The circumferential velocity at the average diameter of the blade is expressed as: ; and The circumferential component of the absolute velocity of import and export Based on formula Calculate the relative velocity at the blade exit; where, The velocity coefficient of the moving blade; This is the theoretical relative exit speed; Based on formula Calculate blade loss; based on formula Calculate the residual velocity loss; where, The absolute velocity at the exit of the moving blade; Analyze the effective enthalpy drop and efficiency of the single-stage; the ideal usable enthalpy drop of the stage is: The effective enthalpy drop of the stage is: The efficiency of the stage is: .

[0009] Preferably, the step of constructing a dynamic prediction model for exhaust enthalpy and cylinder efficiency based on the mechanistic model includes: The steam turbine is modeled separately as a high-pressure cylinder, an intermediate-pressure cylinder, and a low-pressure cylinder; for each cylinder, the enthalpy value after isentropic expansion is calculated based on the steam properties; the enthalpy value calculation formula is as follows: ;in, ; The specific entropy of the steam inlet; This refers to the inlet steam pressure; Intake air temperature; This refers to the exhaust pressure; A dynamic differential equation for metal wall temperature and a cylinder energy conservation equation are constructed. The dynamic differential equation for metal wall temperature and the cylinder energy conservation equation are integrated and trained with an artificial intelligence model to obtain a dynamic prediction model.

[0010] Preferably, the construction of the dynamic differential equation for the metal wall temperature includes: The average steam temperature is analyzed based on the relationship between cylinder metal temperature and convective heat transfer between steam and metal; the formula for calculating the average steam temperature is as follows: ;in, This refers to the exhaust steam temperature. Based on formula The analysis yielded the metal heat balance equation; in which, Equivalent metallic mass; Specific heat of metals; The heat transfer coefficient; For heat exchange area; Discretizing the metal heat balance equation yields the dynamic differential equation for the metal wall temperature: .

[0011] Preferably, the construction of the cylinder energy conservation equation includes: Based on formula Analyze the energy balance equation on the steam side of the cylinder control unit; where... This refers to the output shaft power of the cylinder. For the specific enthalpy of steam; Enthalpy of vapor output; ; The rate of change of the internal energy of the metal; This refers to the steam mass flow rate; After rearranging the energy balance equation, the dynamic exhaust enthalpy is obtained as follows: ;when When the dynamic exhaust enthalpy is higher, it is lower than the steady-state value; conversely, it is higher than the steady-state value. (Based on the formula...) Calculate the cylinder efficiency value.

[0012] Preferably, the integration and training of the dynamic differential equation of metal wall temperature and the cylinder energy conservation equation with the artificial intelligence model includes: Retrieve the dynamic differential equation of metal wall temperature and the energy conservation equation for each cylinder; obtain historical measurement values ​​and parameter vectors at several historical moments; the historical measurement values ​​include: steam mass flow rate, inlet steam pressure, inlet steam temperature, outlet steam pressure, and cylinder output shaft power; the parameter vectors include: heat transfer coefficient, heat transfer area, equivalent metal mass, metal specific heat, and efficiency correction coefficient. The number of layers and the time series model framework of the fully connected network are selected; the metal wall temperature dynamic differential equation, the energy conservation equation and the number of layers and the time series model framework of the fully connected network are integrated to construct the initial model; Historical measurements are used as input to the model, and error values ​​are used as output. The historical measurements and error values ​​are integrated into training data. The training data is then divided into training set, validation set, and test set according to a set ratio. The initial model is trained using the training set, and its internal parameters are adjusted using the validation set. The trained initial model is then tested using the test set to obtain test metrics. Obtain the range of indicators. If all test indicators are within the range, mark the initial model as a dynamic prediction model; otherwise, retrain the initial model.

[0013] Preferably, the analysis of thermodynamic performance and energy efficiency indicators based on real-time operating data of the steam turbine includes: Retrieve real-time operating data of the steam turbine; the real-time operating data includes: steam mass flow rate, inlet steam pressure, inlet steam temperature, outlet steam pressure, and cylinder output shaft power; Real-time operating data is input into the dynamic prediction model to obtain the corresponding parameter vector; the parameter vector is input into the turbine's mechanism model to obtain the theoretical cylinder efficiency; the theoretical cylinder efficiency is multiplied by the efficiency correction coefficient to obtain the predicted actual cylinder efficiency; the energy conversion of the turbine is evaluated based on the predicted actual cylinder efficiency.

[0014] Preferably, the evaluation of the turbine's energy conversion based on the predicted actual cylinder efficiency includes: Retrieve the predicted actual cylinder efficiency; obtain the efficiency evaluation table; match the predicted actual cylinder efficiency with the efficiency evaluation table to obtain the turbine's energy conversion level; where the energy conversion level includes: low, medium, and high; When the turbine's energy conversion level is medium, an abnormal alarm signal is generated, and the turbine is maintained and repaired; when the turbine's energy conversion level is low, a fault alarm signal is generated, and the turbine is stopped from operating.

[0015] The second aspect of this application provides a steam turbine thermodynamic performance and energy efficiency evaluation system based on hybrid modeling, including: a data acquisition module, a model building module, and a data analysis module; The data acquisition module is used to acquire real-time operating data of the steam turbine and the workflow network; The model building module is used to build a mechanistic model of the steam turbine based on the turbine's working flow network; and to build a dynamic prediction model of exhaust enthalpy and cylinder efficiency based on the mechanistic model. The data analysis module is used to analyze the thermal performance and energy efficiency indicators based on the real-time operating data of the steam turbine.

[0016] Compared with the prior art, the beneficial effects of this application are: 1. This application constructs a workflow network to divide cylinder segments and stages, establishing a complete mechanistic model including the Flueger formula, Euler turbine equation, and rotor motion equation, fully reflecting the actual energy conversion physical processes inside the steam turbine. Based on this, a dynamic differential equation for metal wall temperature and a cylinder energy conservation equation are introduced and integrated with a fully connected network and a time-series model framework for training. This allows the model to not only reflect steady-state characteristics but also capture dynamic transient effects such as metal heat storage under varying operating conditions, thereby accurately predicting exhaust enthalpy and cylinder efficiency, overcoming the limitations of traditional pure mechanistic models or pure data-driven models.

[0017] 2. This application achieves online quantitative evaluation of the turbine energy conversion process by inputting real-time operating data into a dynamic prediction model to obtain parameter vectors, then combining this with a mechanistic model to calculate the theoretical cylinder efficiency and multiplying it by an efficiency correction coefficient. The system categorizes energy conversion levels into low, medium, and high based on the efficiency evaluation table and automatically triggers corresponding alarm and handling strategies: a medium level generates an abnormal alarm signal to prompt maintenance and repair; a low level generates a fault alarm signal and forces a shutdown. This effectively avoids economic losses and safety hazards caused by equipment operating with defects or severely degraded efficiency, significantly improving the intelligent operation and maintenance level of power plants. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram illustrating the overall steps of the method described in this application; Figure 2 This is a schematic diagram of the system module connection structure of this application. Detailed Implementation

[0020] The technical solutions of this application will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0021] Example 1: Please see Figure 1 The first aspect of this application provides a method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling, including: S101. Obtain real-time operating data of the steam turbine and the workflow network.

[0022] Specifically, real-time operational data can be various process parameters collected online from the power plant's distributed control system (DCS), such as main steam pressure, main steam temperature, reheat steam temperature, extraction steam pressure and temperature at each stage, condenser vacuum, and the unit's real-time power generation. This data reflects the turbine's current operating condition. The working flow network describes the complete flow path of steam after it exits the boiler, sequentially passing through the high-pressure main steam valve, high-pressure regulating valve, high-pressure cylinder, intermediate reheater, intermediate-pressure main steam valve, intermediate-pressure regulating valve, intermediate-pressure cylinder, connecting pipe, and finally entering the low-pressure cylinder to perform work before the exhaust steam is discharged into the condenser. Obtaining an accurate working flow network is the structural foundation for subsequent physical model construction; it defines the boundaries and control volumes of each stage group and each cylinder. The data acquisition frequency can be configured as needed, such as once per second or every few seconds, to meet the requirements of dynamic process monitoring.

[0023] S102. Construct a mechanistic model of the steam turbine based on the working flow network of the steam turbine.

[0024] The core of this step is to establish a white-box model that faithfully reflects the physical nature of energy conversion in the flow path of a steam turbine, utilizing fundamental principles of thermodynamics, fluid mechanics, and rotor dynamics. Based on the clearly defined steam flow direction in the previous steps, we divide the steam turbine into several stages along the steam flow direction, and model the high-pressure cylinder, intermediate-pressure cylinder, and low-pressure cylinder as a separate computational segment. This mechanistic model analyzes the single-stage work process by establishing isentropic expansion of the stationary blades, the velocity triangle of the moving blades, and the Euler turbine equation, and introduces the Flueger formula to describe the coupling relationship between flow rate and pressure under varying operating conditions. Finally, the model can calculate the effective enthalpy drop of each stage, sum them up, subtract mechanical losses to obtain the shaft-end power, and then correlate the power with speed and load through the rotor motion equation. The fundamental purpose of constructing the mechanistic model is to provide a solid physical consistency guarantee for the entire evaluation system, ensuring that the model's output conforms to basic physical laws under any operating condition and does not contain fundamental errors such as violations of the second law of thermodynamics.

[0025] S103. Construct a dynamic prediction model for exhaust enthalpy and cylinder efficiency based on the mechanism model.

[0026] Specifically, while mechanistic models are physically robust, their fixed assumptions and parameters often lead to decreased computational accuracy when dealing with transient processes such as heat storage and release in the cylinder metal during rapid load changes. Therefore, this step introduces a description of the dynamic process based on the mechanistic model. Specifically, it first models the turbine separately for high-, medium-, and low-pressure cylinders, and calculates the ideal enthalpy of isentropic expansion for each cylinder based on the standards of the International Association for the Properties of Water and Steam (IAPWS). Next, it constructs two key dynamic equations: one is the dynamic differential equation for metal wall temperature, used to quantify the time-varying law of metal temperature with average steam temperature; the other is the cylinder energy conservation equation, which couples the rate of change of internal metal energy with the inlet and outlet energy of steam. These two equations are cleverly integrated into an artificial intelligence model framework, trained using historical operating data, to obtain a dynamic prediction model. This hybrid model retains the mechanistic framework while gaining the ability to learn dynamic biases, correction coefficients, and physical parameters that are difficult to measure directly from the data, thereby accurately predicting the dynamic exhaust enthalpy and cylinder efficiency with time-varying characteristics.

[0027] S104. Analysis of thermodynamic performance and energy efficiency indicators based on real-time operating data of steam turbines.

[0028] Specifically, after obtaining the offline-trained dynamic prediction model, this step deploys it online. We input the real-time operating data collected in S101 into the dynamic prediction model constructed in S103. The model quickly infers a set of key parameter vectors, such as the efficiency correction coefficient and heat transfer coefficient. Subsequently, these parameters are fed back into the mechanistic model constructed in S102. The mechanistic model performs secondary calculations to obtain the theoretical cylinder efficiency, and then uses the correction coefficient to calculate the final predicted actual cylinder efficiency. This analysis path tightly integrates the flexibility of data-driven approaches with the reliability of mechanistic models, achieving accurate online calculation of energy efficiency indicators. Ultimately, the system can evaluate the energy conversion status of the turbine based on this real-time energy efficiency data and map continuous efficiency values ​​to discrete energy efficiency levels, providing a basis for subsequent alarm or optimization operations.

[0029] Example 2: Based on step S102 in Example 1, the construction process of the turbine mechanism model is further refined. This construction process can be decomposed into several parts: the division of stages and cylinder sections, the establishment of a single-stage energy conversion model, the introduction of variable operating condition characteristics, and the connection of the whole machine energy transfer chain, thus forming a self-consistent and rigorous physical model system from micro to macro.

[0030] Obtain the working flow network of the steam engine; divide the steam turbine into several stages along the steam flow direction; and treat the high-pressure cylinder, intermediate-pressure cylinder, and low-pressure cylinder as a calculation segment; wherein, each stage consists of one stationary blade and one moving blade.

[0031] Specifically, the high-pressure, intermediate-pressure, and low-pressure cylinders each contain multiple stages of blades. Each stage consists of a stationary blade (or nozzle) and a following moving blade, forming a basic working unit. The reason for segmenting the cylinders and refining the internal structure to the "stage" level is that different cylinders have vastly different steam parameter ranges, metal quality, and structural dimensions, resulting in varying heat storage capacities and response speeds. Without this segmented modeling, using a single lumped model to represent the entire turbine would fail to accurately describe the dynamic changes in the high-pressure cylinder exhaust temperature and intermediate-pressure cylinder inlet temperature under partial load conditions due to the reheater and metal walls, nor would it describe the unique characteristics of the low-pressure cylinder operating in the wet steam region. By adopting this segmented, staged, and structured modeling approach, it's like building a system with a series of modular building blocks, preserving crucial physical details while avoiding an uncontrollable explosion of computational complexity.

[0032] A unipolar energy conversion model is established; the reaction degree of steam in the moving blade is calculated based on the reaction degree analysis function; the expression of the reaction degree analysis function is: ;in, This is the actual enthalpy of steam as it leaves the stationary blade and enters the moving blade. This is the actual enthalpy of the steam after it leaves the moving blade; The stagnation enthalpy of the steam before the stage.

[0033] From a physical perspective, the reaction degree typically ranges from 0 to 1. If the reaction degree is 0, it means that the enthalpy drop of the steam occurs entirely in the stationary blades, and there is no further decrease in pressure or enthalpy in the moving blade passage; this is usually called a pure impulse stage. If the reaction degree is greater than 0, it indicates that a portion of the enthalpy drop is distributed to the moving blades. When the steam flows through the moving blades, not only does the direction of the relative velocity change, but its magnitude also increases due to continued expansion; this is usually called a reaction stage. In design, the reaction degree is a key parameter affecting blade profile, stage efficiency, and axial thrust. Introducing this calculation is not simply applying an empirical constant, but rather enabling the model to dynamically adjust the enthalpy drop distribution ratio based on changes in the inlet steam temperature and pressure of each stage when analyzing variable operating conditions, thus more realistically reflecting efficiency changes.

[0034] Based on the approximate isentropic expansion of steam in the stationary blades, the theoretical outlet velocity is analyzed; the expression for the theoretical outlet velocity is: ;in, The enthalpy of vapor stagnation at the inlet of the still leaf; This is the ideal enthalpy value when the quotient expands to the point of export pressure.

[0035] This represents the ideal state that steam can achieve assuming no friction or eddy current losses. However, in reality, steam inevitably experiences losses as it flows through the stator blade passage; based on the formula... Calculate the actual export velocity; obtain a more realistic actual export velocity, where, The stationary blade velocity coefficient is typically less than 1, and its specific value is influenced by factors such as blade surface roughness and channel geometry. The irreversible energy loss due to friction and other factors, i.e., nozzle loss, is expressed in the formula... Calculate nozzle loss.

[0036] Furthermore, after leaving the stationary blades, the steam enters the high-speed rotating moving blades. Since the moving blades themselves are in motion, the relative velocity of the steam relative to the moving blades differs from its absolute velocity as viewed from absolute space; these two velocity-velocity triangles are formed. According to the principle of angular momentum, the relative velocity deflects and changes as it flows through the moving blade passage, thus generating a circumferential force acting on the blades. To calculate the work done per unit mass of steam, this embodiment introduces the Euler turbine equation. The expression for this equation is: ,in, It is the circumferential velocity at the average diameter of the blade (which can be obtained by...). (obtained) and This is the component of the absolute velocity of steam entering and leaving the rotor blades in the circumferential direction. This equation directly reveals the source of the work done on the rotor's circumference from a mechanical perspective; it is equal to the mechanical energy transferred to the rotor by the steam due to the change in angular momentum before and after the high-speed rotating blades. This is the most crucial bridge connecting thermodynamics and rotor dynamics.

[0037] Energy losses within the blades are also significant. To calculate these losses, we first need to know the actual relative velocity at the blade exit. This can be done using a formula... Calculations are performed, in which, It is the blade velocity coefficient. This assumes a theoretical relative exit velocity under isentropic flow conditions. Therefore, the blade losses caused by friction and vortices within the blade can be calculated using the formula... The exact figure is calculated. Furthermore, the steam itself possesses a considerable absolute velocity when it leaves the moving blades. This portion of kinetic energy cannot be utilized by the blades of this stage; it will be used by the next stage or ultimately wasted as exhaust loss, constituting residual velocity loss. Therefore, we can now fully analyze the effective enthalpy drop and efficiency of a single-stage. The ideal enthalpy drop of a stage can be expressed as... This represents the total energy that steam can release under ideal conditions without any irreversible loss; and the effective enthalpy drop of the stage is equal to the work done around the wheel calculated by the aforementioned Euler turbine equation, which is... The stage efficiency can be obtained by dividing the effective enthalpy drop by the ideal available enthalpy drop. In the fields of control and simulation, this series of formulas is sometimes collectively referred to as the economic evaluation algorithm for a given level. Its core lies in constructing a complete causal chain from inlet parameters and geometric dimensions to work capacity and efficiency. With this foundation, when evaluating variable operating conditions, it becomes clear whether the decrease in efficiency is due to an increase in residual velocity loss caused by a change in the speed ratio, or due to shock waves or flow separation losses caused by changes in reaction degree resulting from steam deviating from the design point.

[0038] After constructing the unipolar energy conversion model step by step, a key question arises: how are the pressures and flow rates redistributed at each stage of the turbine when the operating conditions change? This directly determines the steam inlet and outlet states of each stage, thus affecting the effective enthalpy drop of each stage and the overall power output. To efficiently and accurately address this issue, this embodiment uses the Flügger formula to analyze the relationship between stage pressure and flow rate under varying operating conditions. The expression of this formula is: ,in and These represent the steam mass flow rates through the same stage group under the baseline and variable operating conditions, respectively. , This represents absolute pressure before the class group. , For the absolute pressure after the class group, , The absolute temperature before the stage group.

[0039] Here, it's important to explain why we chose the Freuger formula, an analytical method based on the overall pressure ratio of the stage, instead of the traditional method that requires detailed iterative calculations under varying operating conditions, starting from the first stage. Traditional methods require assuming that the reaction degree and velocity coefficient of each stage change very little under varying operating conditions, and then iteratively solving for the pressure, temperature, and enthalpy drop of each stage from the first stage. When there are many stages, this closed-loop iteration is not only computationally intensive but also highly susceptible to amplification of small assumptions at one stage as they propagate downstream, leading to complete distortion of the exhaust state calculations for the last few stages. The Freuger formula, on the other hand, is essentially an approximate relationship derived from continuous flow and the thermodynamics of open systems. It directly establishes the coupling between the total flow rate of the stage, the total pressure before and after the stage, and the temperature, completely avoiding the forced assumptions of constant reaction degree for each stage within the group. This is analogous to not needing to calculate the opening of each tap to estimate the total water flow, but instead being able to quickly and accurately determine flow rate changes by measuring the pressure difference between the inlet and outlet pipes. It is this characteristic of being able to quickly assess the flow-pressure coupling relationship without needing detailed parameters at each level that gives this model its unique efficiency and robustness in calculations under varying operating conditions over a wide load range.

[0040] After determining the pressure and enthalpy drop distribution at each stage under varying operating conditions using the methods described above, the final step in modeling the entire machine is to string together these scattered "periodic work" pearls into a power transfer chain from heat to machinery. We convert the sum of the periodic work at each stage into shaft-end mechanical work and analyze the power parameters and rotor motion equations. The power parameters mainly involve the total internal power and shaft-end power. The total internal power is the sum of the mechanical work done by the steam on the moving blades, derived from... Calculation, here Represents steam mass flow rate. For the total series, This refers to the effective enthalpy drop we've already calculated for stage j. This represents the total amount of steam thermal energy converted into mechanical energy, but not all of it can be transmitted through the coupling. Shaft end power. , among them This represents the frictional losses of the supporting bearings and the mechanical losses consumed by auxiliary equipment such as the main oil pump. Ultimately, this power acts on the rotor, forming a dynamic torque balance. Rotor motion equation This is the mathematical description of this equilibrium, where J is the moment of inertia. Angular velocity, The electromagnetic resistance load torque applied to the generator. During steady-state operation, the turbine's driving torque balances the load torque, angular acceleration is zero, and rotational speed is constant. However, if changes in grid load commands cause a sudden change in the load torque T_{l}, or changes in steam parameters lead to a change in total internal power... In the event of a sudden change, the rotor's moment of inertia J will exert its physical inertia effect, smoothing out power fluctuations through instantaneous changes in rotational speed, thus establishing a complete electromechanical transient chain from the steam turbine's inlet regulation command to the grid frequency response. By accumulating unipolar enthalpy drop to total internal power, then subtracting losses to obtain shaft-end power, and finally arriving at the rotor motion equation that determines the rotational speed change, this embodiment constructs a seamless, physically self-consistent thermo-mechanical energy transfer chain from microscopic energy conversion to macroscopic mechanical transmission. This also lays a solid physical framework for subsequent embodiments to introduce dynamic response of metal wall temperature and accurately correct exhaust enthalpy and cylinder efficiency under transient operating conditions.

[0041] Example 3: In the previous embodiment, we described the process of constructing a complete mechanistic model of the turbine's flow path, from a single stage to the entire unit. However, when the turbine operates under a wide range of varying loads, a steady-state mechanistic model alone is insufficient to accurately capture its transient thermodynamic characteristics, especially the real dynamic changes in exhaust enthalpy and cylinder efficiency. Therefore, this embodiment, based on the existing mechanistic model and continuing the cylinder-specific concept from Embodiment 2, further advances the turbine's evaluation capabilities, focusing on the introduction of cylinder-specific isentropic enthalpy calculation and dynamic modeling concepts.

[0042] In establishing a dynamic prediction model, the turbine must first be modeled separately for high-pressure, intermediate-pressure, and low-pressure cylinders. As mentioned earlier, the reason for this separate cylinder modeling, rather than using a lumped model of the entire unit, lies in the significant differences in physical properties and thermal environments between the different cylinders. Specifically, the high-pressure cylinder operates in the extreme high-temperature and high-pressure environment of the main steam, with thick cylinder walls and a large equivalent metal mass. Its enormous heat storage capacity is slowly released during load reduction, reheating the steam flowing through it. The intermediate-pressure cylinder receives steam from the intermediate reheater, and its parameter changes and heat storage characteristics are not synchronized with those of the high-pressure cylinder. The last few stages of the low-pressure cylinder operate in the wet steam region, with relatively low metal wall temperatures and a large structural size. If we don't treat each cylinder as an independent control entity and establish its energy and mass dynamic balance separately, it means forcibly averaging the dynamic parameters such as the metal heat storage effect and heat transfer coefficient changes among the three cylinders. Essentially, this obscures the primary and secondary contributions and temporal differences of each cylinder to the changing operating conditions, making it impossible to accurately depict the mismatch process where the high-pressure cylinder exhaust enthalpy drops sharply during the initial load reduction phase while the medium and low-pressure cylinder exhaust enthalpy remains stable. Therefore, modeling the high, medium, and low-pressure cylinders separately is the structural foundation for ensuring dynamic accuracy.

[0043] After establishing the framework for cylinder modeling, it is necessary to define an ideal baseline for the thermodynamic performance of each cylinder. For each cylinder, this embodiment calculates the enthalpy after isentropic expansion based on steam properties. The enthalpy calculation formula used in the calculation adopts the internationally recognized Industrial Standard for Thermodynamic Properties of Water and Water Steam (IAPWS), specifically expressed as follows: The inlet specific entropy is defined as follows: .here Represents the specific entropy of the incoming steam. The inlet steam pressure. For the steam inlet temperature, and This refers to the exhaust pressure. In simpler terms, it assumes that the steam expands within the cylinder under adiabatic conditions with no frictional loss, changing isentropically from the inlet pressure to the outlet pressure. The ideal enthalpy value is then found using the IAPWS standard steam gauge. This ideal exhaust enthalpy represents the lowest energy state of the steam under theoretically perfect work conditions and is a core component of the denominator in subsequent cylinder efficiency calculations. It's important to note that using the IAPWS standard to calculate the enthalpy-entropy relationship, compared to traditional fitting formulas, avoids physical errors when crossing critical or near-saturation lines, ensuring the absolute scientific rigidity of the underlying thermophysical properties of the mechanistic model across a wide load range.

[0044] However, this leads to a fundamental dilemma of pure mechanistic models. If we only focus on calculating the ideal isentropic enthalpy and directly extrapolate the exhaust enthalpy using steady-state assumptions, we arrive at a constant physical baseline. From the perspective of pure mechanistic models, the exhaust enthalpy here often depends only on the inlet and outlet pressure and temperature, failing to account for the exhaust enthalpy shift caused by changes in metal wall temperature. In reality, when the unit rapidly reduces load, the high-temperature metal cylinder wall releases heat to the steam, resulting in an actual exhaust enthalpy far exceeding the ideal isentropic enthalpy; conversely, when the load increases, the cold metal rapidly absorbs heat from the steam, causing the actual exhaust enthalpy to drop abnormally momentarily. The physical essence of this dynamic deficit is the instantaneous heat storage and release of the metal. If this is not described, the calculated cylinder efficiency will be severely distorted during the transition process, and may even cause transient value fluctuations exceeding the normal range, triggering false alarms. To address this issue, this embodiment starts from the physical source, constructing a dynamic differential equation for metal wall temperature and a cylinder energy conservation equation. By simultaneously solving these two equations, the changes in metal internal energy are captured in real time, correcting the steam energy balance. Finally, the dynamic differential equation for metal wall temperature and the cylinder energy conservation equation are integrated and trained with an artificial intelligence model to obtain a dynamic prediction model. The significance of introducing an artificial intelligence model lies in the fact that parameters such as equivalent metal mass and heat transfer coefficient in the differential equations are often difficult to obtain in real time or vary nonlinearly with operating conditions. In such cases, by using architectures such as fully connected networks or time-series models to learn the optimal representation of these parameters from massive historical data of the unit, system deviations caused by a single fixed parameter can be significantly eliminated.

[0045] Through the planning of this embodiment, the model system successfully transitioned from "steady-state stage and cylinder segment physical equations" to "dynamic energy balance and isentropic benchmark definition of cylinder segmentation." This not only explained the deep physical mechanism of cylinder segmentation modeling but also filled the blind spots of pure mechanistic models by introducing the concept of dynamic thermal balance. This paves the way for the detailed development of the specific discretization solution of the metal wall temperature equation, the derivation of the dynamic exhaust enthalpy formula for cylinder energy conservation, and the final deep integration and training with the artificial intelligence framework in subsequent embodiments.

[0046] Example 4: After introducing dynamic requirements and establishing the cylinder division principle in Example 3, this example specifically focuses on the core issue of dynamic changes in metal wall temperature, and constructs a dynamic differential equation for metal wall temperature that can be recursively calculated online.

[0047] First, the steam-side temperature conditions driving the change in metal wall temperature need to be determined. This embodiment analyzes the average steam temperature based on the relationship between cylinder metal temperature and convective heat transfer between steam and metal. A lumped approximation is introduced here, using the arithmetic mean of the inlet and outlet temperatures to estimate the average state of the steam inside the cylinder. Specifically, the formula for calculating the average steam temperature is as follows: , among them This represents the exhaust steam temperature. This approach, using the average inlet and outlet temperatures, is a lumped-data strategy widely validated in engineering practice. The reason this approach works, rather than deploying numerous virtual measuring points along the cylinder flow path to solve for detailed temperature distribution, is that with numerous turbine stages and extremely high steam velocities, the inlet and outlet parameters can already macroscopically capture the overall steam energy level. Pursuing accurate steam temperatures after each stage would require complex along-path thermodynamic calculations and iterations, which would lead to unacceptable computational costs and time delays in an online evaluation system requiring rapid response. Using this average temperature as the driving force for convective heat transfer between steam and metal, while ignoring some detailed changes along the path, essentially captures the most significant component of the thermal shock to the metal wall caused by the mainstream steam temperature change. This has proven to be an excellent compromise between ensuring dynamic accuracy and real-time computation.

[0048] After obtaining the average steam temperature, the next step is to establish the thermal equilibrium relationship between the steam and the metal. This embodiment uses the lumped parameter method, based on the formula... Analysis yields the metal heat balance equation. The physical essence of this equation is the energy conservation of the cylinder's metal components. The left side of the equation represents the heat stored or released by the metal per unit time due to temperature changes, while the right side represents the net heat transfer from the steam to the metal through convection. Represents equivalent metallic mass. Representing the specific heat of the metal, the product of these two parameters constitutes the heat capacity of the metal body. It is important to note that the equivalent metal mass is not the actual total physical mass of the cylinder, but rather the effective mass participating in the dynamic heat storage process. It is generally identified by combining the dimensions in the design drawings and actual operating data. For heavy structural parts that are not in direct contact with steam or have an extremely slow temperature response, their contribution to the rapid dynamic process can be ignored; therefore, the overall lifting weight of the cylinder should not be simply substituted into this value. Parameters It is the heat transfer coefficient. Both the heat transfer area and the heat transfer coefficient describe the convective heat transfer capacity per unit temperature difference between the steam and the metal wall. The lumped parameter itself is a complex time-varying parameter affected by steam flow rate, physical properties, and wall condition. In the subsequent hybrid modeling of this embodiment, it will be used as one of the key feature parameters for dynamic identification by the artificial intelligence model. The core essence of the lumped parameter method lies in its virtual compression of the metal, which originally had a temperature gradient distribution across the entire cylinder cross-section, into a uniform temperature distribution. The object is considered to have a much smaller internal thermal resistance than the convective thermal resistance between it and the steam. Compared to CFD methods, which often require the construction of fine three-dimensional meshes and iterative solutions to computational fluid dynamics differential equations, the lumped parameter method cleverly avoids solving complex partial differential equations. Its computational cost is almost negligible, yet it successfully and explicitly characterizes the dominant transient physical process of metal thermal storage.

[0049] After establishing the mathematically continuous form of the metal heat balance equation, it is necessary to discretize this equation in the time domain in order to truly deploy it in a digital control system for real-time computation. By discretizing it, the final recursive form of the dynamic differential equation for the metal wall temperature is obtained as follows: Here, the superscript (k) represents the current moment, and (k-1) represents the previous moment. The necessity of this discretization lies in the fact that the field control and monitoring systems operate with a certain sampling period and can only manipulate discrete data points. This recursive formula essentially uses a linear extrapolation of the temperature change rate from the previous moment over time to approximate the metal temperature at the current moment. From a physical perspective, as long as the sampling period we choose is much smaller than the inherent thermal time constant of the cylinder metal, for example, controlled on the order of seconds or milliseconds, then assuming that the temperature change rate remains constant within a step is perfectly acceptable, and the truncation error it introduces has a negligible impact on the overall dynamic performance evaluation.

[0050] Without real-time solution to this dynamic differential equation for metal wall temperature, the system will remain confined to steady-state or quasi-steady-state modeling assumptions. During rapid load changes, the significant heat storage and release effects of the cylinder metal will be completely ignored. This leads to a serious consequence: the calculated actual exhaust enthalpy is overestimated during load increases and underestimated during load decreases, resulting in severely distorted cylinder efficiency assessments during dynamic response and potentially missing potential equipment hazard signals caused by severe thermal shock. This embodiment, by constructing a lightweight, physically clear, and online recursive solution mathematical model, accurately addresses the shortcomings of pure mechanistic models in the field of dynamic thermal balance without excessive computational effort. It also paves the way for subsequent embodiments to derive the more crucial internal energy change rate term in the cylinder energy conservation equation.

[0051] Example 5: Based on the solution of the metal wall temperature change rate in Example 4, this example further derives the calculation formula of dynamic exhaust enthalpy by starting from the energy conservation on the steam side of the cylinder control body, and thereby obtains the dynamic cylinder efficiency, thus truly pushing the mechanism model from steady-state analysis to dynamic analysis that can describe the rapid load change process.

[0052] When constructing the cylinder energy conservation equation, each cylinder must first be considered as an open thermodynamic system, taking into account the energy accompanying steam inflow and outflow, the shaft work output by the system, and the changes in energy stored within the system. Based on the formula... Let's analyze the energy balance equation on the steam side of the cylinder control unit. In this equation, the left side... This represents the total enthalpy input that flows into the cylinder with steam per unit time. It is the steam mass flow rate. It is the specific enthalpy of the steam inlet; the first item on the right. This represents the enthalpy carried away by the steam as it flows out of the cylinder. This refers to the vapor enthalpy ratio we ultimately need to solve for. In dynamic estimation, it is not a constant but a variable that changes with time; the second term on the right... This refers to the output shaft power of the cylinder, which represents the energy that the steam converts into mechanical work within the cylinder and transfers to the rotor. Physically, it equals the sum of the wheel circumference work of each stage within that cylinder section in the previously established mechanistic model, minus the associated mechanical losses such as bearing friction. (The last item on the right...) That is the rate of change of the internal energy of the metal, from This term is the core output of the dynamic differential equation of metal wall temperature constructed in Example 4, which quantifies the heat absorbed or released by the cylinder metal body per unit time.

[0053] The physical essence of this equation is quite clear: the total energy of the steam entering the cylinder can only have three paths—either it remains in the steam and flows out of the cylinder, or it is converted into mechanical work and extracted, or it is used to heat or cool the cylinder metal itself. This is the specific manifestation of the first law of thermodynamics in the cylinder, an open control body. It is worth noting that in some traditional steady-state performance evaluation models, people habitually assume the rate of change of internal energy in the metal to be zero, which is equivalent to assuming that the metal temperature no longer changes with time, meaning that the cylinder is always in thermal equilibrium. This simplification is acceptable during the stable operation phase when the load remains constant for a long time, because the metal wall temperature has indeed stabilized and there is no longer significant heat transfer. However, once the unit begins to participate in grid peak shaving and rapidly adjusts or decreases the load, the lack of this term immediately exposes serious problems.

[0054] By rearranging the above energy balance equations, we can obtain an explicit formula for calculating the dynamic exhaust enthalpy. We will... Leaving it alone on one side of the equation, after simplification, it becomes... This formula intuitively reveals the three components that determine the actual exhaust enthalpy: the intake enthalpy provides an energy baseline; This item represents the actual mechanical work done by a unit mass of steam. This energy has been extracted and naturally cannot remain in the steam, so it must be deducted from the inlet enthalpy. The larger this deduction, the stronger the cylinder's work capacity, and the lower the exhaust enthalpy will be; while the last item... The most critical dynamic correction term is the one that directly reflects the instantaneous impact of the cylinder metal heat storage or release process on the exhaust enthalpy.

[0055] Here, we need to explain in detail why the dynamic exhaust enthalpy deviates from its steady-state value, and the direction and pattern of this deviation. When operating conditions change, such as when the unit is rapidly reducing load, the cylinder inlet steam temperature and pressure begin to decrease. The high-temperature cylinder metal is hotter than the steam flowing through it, therefore... The value is negative, indicating that the metal is releasing heat to the vapor. This correction term is also negative, but note the minus sign before it in the formula; therefore, this portion of heat release is actually included in the exhaust enthalpy, increasing it. In other words, the stored heat released by the metal additionally heats the steam, making the actual outflowing steam enthalpy significantly higher than the steady-state ideal value calculated solely based on inlet and outlet pressure and temperature. Conversely, during rapid load increases, the inlet steam temperature rises rapidly, while the cold metal urgently needs to absorb heat from the steam to warm up. The last term in the formula will cause the exhaust enthalpy to be lower than the steady-state estimate, because a significant portion of the steam energy is used to raise the temperature of the metal itself; the steam energy is "retained" within the cylinder metal. When When the load changes, the dynamic exhaust enthalpy is less than the steady-state value; conversely, it is greater than the steady-state value. This is precisely where this embodiment differs fundamentally from traditional methods—we can not only observe the cylinder efficiency rise and fall caused by load changes, but also see from the internal physical mechanism whether it is metal heat storage that delays the decrease in exhaust enthalpy, or metal heat release that boosts the instantaneous value of exhaust enthalpy, as well as the duration and magnitude of these dynamic processes.

[0056] The dynamic exhaust enthalpy with time-varying characteristics was obtained. Then, we can combine this with the isentropic expansion ideal exhaust enthalpy calculated in Example 3. Now we can finally evaluate the dynamic efficiency of the cylinder. Cylinder efficiency is calculated based on the formula... The numerator of this formula is the actual effective enthalpy drop, and the denominator is the theoretically maximum possible ideal isentropic enthalpy drop. The ratio of the two is the actual cylinder efficiency at the current transient moment. Due to the different metal heat storage states at different times, the exhaust enthalpy... and ideal exhaust enthalpy Each changes over time, therefore cylinder efficiency It also becomes a continuous time function, which can truly reflect the actual energy utilization rate of the steam turbine every second under drastic operating conditions such as deep peak shaving and primary frequency regulation.

[0057] This embodiment explicitly incorporates the rate of change of metal internal energy into the cylinder's energy balance, fully derives the analytical formula for dynamic exhaust enthalpy, and finally provides a method for calculating dynamic cylinder efficiency. This extends the evaluation capability of the mechanism model from steady state to dynamic analysis across the entire operating range, preventing others from circumventing the protection of the turbine's true dynamic energy efficiency state by simply assuming a fixed exhaust enthalpy or ignoring the metal heat storage effect.

[0058] Example 6: This embodiment, based on the previously established and solved dynamic differential equations of metal wall temperature and cylinder energy conservation equations, focuses on illustrating the integrated training process of deep fusion between physical models and artificial intelligence models. This is also the key to integrating prior knowledge and data-driven capabilities in the entire hybrid modeling system.

[0059] Before training, it is necessary to retrieve the dynamic differential equation of metal wall temperature and the energy conservation equation for each cylinder, and obtain historical measurements and parameter vectors at several historical moments. The historical measurements mainly include time-series processes that can be directly acquired through the power plant's DCS system, such as steam mass flow rate, inlet steam pressure, inlet steam temperature, outlet steam pressure, and cylinder output shaft power. The parameter vector includes physical quantities that are not easily measured directly or will drift slowly over time, such as heat transfer coefficient, heat transfer area, equivalent metal mass, metal specific heat, and efficiency correction coefficient. These parameters are treated as a whole vector because they are not completely independent. For example, the heat transfer coefficient and heat transfer area may change due to scaling or wear during actual operation, and the equivalent metal mass and metal specific heat jointly determine the time constant of the heat capacity. Estimating each parameter independently makes it difficult to guarantee that the combined result is physically consistent. Packaging them into a parameter vector and having the model identify them as a whole during a forward inference helps maintain the implicit physical constraints between the parameters.

[0060] In selecting the network architecture, this embodiment chooses a fully connected network with a specific number of layers and a time-series model framework. The fully connected network is responsible for constructing the complex nonlinear mapping from observables to non-observable parameters, making it suitable for handling multi-dimensional input-output feature spaces; here, it serves as the main framework for parameter identification. The time-series model framework chosen is one capable of handling long-sequence dependencies, such as a Long Short-Term Memory (LSTM) network or a gated recurrent unit (GRU). The fundamental reason for choosing this type of time-series model is that the metal wall temperature change and metal heat storage effect of the turbine have significant memory characteristics. The exhaust enthalpy at the current moment depends not only on the inlet and outlet parameters at this moment but also highly on the accumulated metal heat absorption and release processes of the unit load trajectory over the previous few minutes or even tens of minutes. Without such a gating mechanism that can capture long-term dependencies, the model would treat each load change as an independent, unrelated event. As a result, in scenarios with frequent small-amplitude load fluctuations, the prediction of dynamic exhaust enthalpy would exhibit significant phase lag or oscillation bias. Of course, the temporal model framework is not limited to the two structures mentioned above. Other neural network structures that can handle unequal long-duration sequences and have gating or self-attention mechanisms can also play a role in the fusion framework of this embodiment.

[0061] After determining the basic network units, the most crucial step is to fuse the dynamic differential equation of metal wall temperature, the energy conservation equation, the number of layers in the fully connected network, and the temporal model framework to construct the initial model. This fusion is not simply attaching physical formulas as pre- or post-modules to the network; rather, it employs specific strategies to make the physical equations an intrinsic component of the training and inference processes. From the practice of this embodiment, at least two fusion methods with independent defensive value exist, and either can be used individually or deployed in combination to form protection in depth. The first method is to use the physical equations as the final output constraint layer of the network. In the first half of the network, the fully connected network and the time-series model generate a set of parameter vector predictions based on the input time-series measurements, and also generate a preliminary estimate of the exhaust enthalpy at future times. However, at the output, the dynamic differential equation of metal wall temperature and the cylinder energy conservation equation intervene as an insurmountable mathematical module, applying a "physical penalty" or "physical calibration" to the network's output. That is, if the state variables predicted by the network violate the law of energy conservation or deviate too much from the recursive result of metal thermal equilibrium, the loss function will impose a significant physical penalty term, forcing the model to converge in the direction that satisfies physical laws during parameter updates. The advantage of this approach is that no matter how complex the internal structure of the model is, its final output must be verified by physical laws, eliminating the possibility of absurd results prohibited by the second law of thermodynamics under extreme conditions from a pure black-box model. The second approach is to input the intermediate state variables calculated by the physical equations as auxiliary features into the neural network. Specifically, at each sampling moment, the parameters corrected in the previous moment are substituted into the dynamic differential equation of the metal wall temperature to deduce the rate of change of the metal wall temperature and the rate of change of the metal internal energy at the current moment. These physically derived dynamic state variables are then concatenated with the time-series measurements to form an expanded feature vector, which is fed into the input layer of the fully connected network and the time-series model. In this way, the neural network "knows" from the beginning how the heat storage or release in the cylinder is changing. Its subsequent learning task is no longer blindly digging for physical laws from scratch, but rather performing residual correction and nonlinear refinement based on the physical intuition it already possesses. The advantage of this approach is that it significantly reduces the degrees of freedom that the neural network needs to fit, allowing it to focus its main learning capacity on secondary effects that are difficult to describe with explicit equations, thereby achieving high generalization accuracy with a limited amount of data.

[0062] After the structural fusion of the model is completed, supervised training is required. In this embodiment, historical measurements are used as the model input, and the error value is used as the model output. The error value here does not refer to the excessive deviation in the process, but rather to the residual between the preliminary calculation value of the physical equation and the actual operating record. For example, for a known historical moment, inputting the inlet steam pressure and temperature, exhaust steam pressure, steam flow rate, and shaft power into the physical equation, without considering dynamic correction, yields a steady-state exhaust enthalpy estimate. This estimate inevitably has an error compared to the actual exhaust enthalpy record at that moment. This error encapsulates all transient components that the mechanistic model fails to capture, such as the metal heat storage effect and the dynamic shift of the heat transfer coefficient. The design goal of the model is to learn how to predict the magnitude and direction of this error from the input time series. Using the error as the output, rather than directly having the model output the absolute value of the exhaust enthalpy, has the advantage that the principal components are handled by the physical equation, the model only needs to learn the residuals, the learning difficulty is greatly reduced, and it is less likely to exhibit outrageous deviations in the load range where training data is sparse. Next, historical measurements and error values ​​are integrated into training data, which is then divided into training, validation, and test sets according to a predetermined ratio. The training set is used to update the network's weights and bias parameters, allowing it to learn the error distribution pattern from historical samples. The validation set evaluates the model's generalization level at the end of each training cycle, guiding learning rate decay, early stopping strategies, and hyperparameter tuning to prevent overfitting—that is, the model memorizes noise details at specific moments but loses its grasp of the overall pattern. The test set is not involved in the training process at all; it is only used after the model training is complete to evaluate its real-world predictive ability under previously unseen historical conditions. This is the fundamental standard for verifying the model's practical value. The ratio between the three sets can typically be engineered, such as 6:2:2 or 7:1.5:1.5, as long as the training samples are sufficient and the validation and test sets cover a sufficiently wide range of operating conditions.

[0063] During training, the initial model is trained using the training set, and its internal parameters are adjusted using the validation set. The trained initial model is then tested using the test set to obtain test metrics. The metric range is determined; if all test metrics fall within the range, the initial model is labeled as a dynamic prediction model; otherwise, the initial model is retrained. These test metrics can cover multiple dimensions, such as the root mean square error of exhaust enthalpy prediction, the mean absolute percentage error of cylinder efficiency prediction, and the coefficient of determination. The metric range is pre-set based on the accuracy thresholds required by actual engineering conditions; for example, the absolute error of cylinder efficiency prediction is required to be within ±0.5%. Only when all selected test metrics fall within acceptable ranges is the model considered to have the ability to reliably extrapolate under unknown operating conditions. The fundamental value of this step lies in mitigating the extrapolation prediction risks common in pure black-box models. A purely data-driven model without any physical constraints may fit perfectly within the operating conditions covered by the training data. However, once the operating conditions exceed the historical data envelopment line—for example, if the load slips to a deep peak-shaving range never seen in historical data—the pure black-box model, lacking embedded understanding of physical laws, may suddenly diverge in its predictions or violate basic energy conservation, which is disastrous for online monitoring systems. This embodiment, by embedding physical equations into the model structure and training logic, and applying hard constraints using index ranges during the testing phase, effectively performs a double calibration of the model: it must possess both strong nonlinear fitting capabilities driven by data and be constantly constrained by physical laws. Therefore, even when faced with operating conditions never seen in the training set, its predictive behavior remains firmly constrained by physical baselines, exhibiting reliable physical interpretability and robust extrapolation security.

[0064] Example 7: Based on the model construction and offline training completed in the previous examples, this example puts the entire hybrid model system into real-time online operation, forming a complete closed loop from data collection to energy efficiency assessment to operation and maintenance decision-making.

[0065] After the online evaluation is initiated, the real-time operating data of the steam turbine is retrieved first. This real-time operating data specifically includes process parameters such as steam mass flow rate, inlet steam pressure, inlet steam temperature, outlet steam pressure, and cylinder output shaft power. These parameters are completely aligned in type with the historical measurements used for model training in Example 6. This is done to ensure that the data distribution faced by the model during the online inference phase remains statistically consistent with that during the training phase, avoiding accuracy drift caused by mismatches in feature dimensions or differences in units. In engineering implementation, the data acquisition frequency can typically be set at a level matching the refresh rate of the power plant's distributed control system, such as one set per second or one set every three seconds, with the specific frequency depending on the magnitude of the cylinder's thermal time constant. For units with thick high-pressure cylinder walls and high thermal inertia, an excessively high acquisition frequency will not provide additional effective information but will instead increase the burden of data transmission and processing. For units participating in primary frequency regulation and experiencing extremely rapid load changes, the sampling rate can be appropriately increased to capture the details of transient processes.

[0066] Real-time running data is input into the dynamic prediction model to obtain the corresponding parameter vector. This inference process is essentially a forward propagation calculation. After receiving the real-time data sequence from the current moment and the previous time window, the dynamic prediction model, composed of a fully connected network and a time series model, quickly outputs a set of parameter vectors under the action of the weights and activation functions of its internal layers. This parameter vector may include the heat transfer coefficient, heat transfer area, equivalent metal mass, metal specific heat, and efficiency correction coefficient identified during training in Example 6. It should be noted that the efficiency correction coefficient is not just a single global multiple for the final cylinder efficiency. In some implementations, it can be refined into an independent correction coefficient vector for each cylinder or even each stage group, which can more precisely compensate for the deviation in mechanism calculation caused by different flow conditions at different locations. Of course, if there are extreme requirements for calculation speed, only a centralized correction coefficient can be retained in the parameter vector as a compromise, and the model training process will automatically optimize the expressive power of this parameter.

[0067] Next, the parameter vector is input into the turbine's mechanistic model to obtain the theoretical cylinder efficiency. The theoretical cylinder efficiency refers to the initial efficiency benchmark calculated in the cylinder efficiency calculation formula described in Example 5, when all dynamic corrections and parameter adjustments are temporarily set to ideal states. At this point, the mechanistic model is no longer the fixed-parameter framework of the offline construction phase, but rather receives the latest heat transfer coefficients, equivalent metal mass, and other parameters from the dynamic prediction model. This allows its physical equations to be solved using parameters closest to the current physical state of the cylinder at every online moment. Therefore, the calculated theoretical cylinder efficiency is inherently more accurate than the fixed-parameter result of a pure mechanistic model. The theoretical cylinder efficiency is multiplied by the efficiency correction factor to obtain the predicted actual cylinder efficiency. The efficiency correction factor plays a final fine-tuning role here; its physical meaning can be understood as a concentrated compensation for secondary influencing factors not yet explicitly considered by the mechanistic model, such as profile changes caused by blade surface fouling and minor leakage variations. In terms of process, this calculation path, from real-time data to parameter vectors, and then to theoretical cylinder efficiency and actual cylinder efficiency, is a hybrid reasoning chain that uses a mechanistic model as the backbone and a data-driven model as a dynamic correction mechanism. This ensures that the efficiency values ​​do not violate the basic laws of thermodynamics and can track the real performance level under varying operating conditions in real time.

[0068] The energy conversion of the steam turbine is evaluated based on the predicted actual cylinder efficiency. The ultimate goal of online evaluation is not only to determine the level of an efficiency value, but more importantly, to translate this value into operational signals that maintenance personnel can directly understand and execute. To this end, this embodiment introduces a graded quantitative evaluation mechanism. The predicted actual cylinder efficiency is retrieved, an efficiency evaluation table is obtained, and the predicted actual cylinder efficiency is matched with the efficiency evaluation table to obtain the energy conversion level of the steam turbine. The energy conversion level here includes three grades: low, medium, and high. The efficiency evaluation table is a set of threshold ranges pre-set based on unit design parameters, historical operating statistics, and maintenance procedures. For example, for a typical cylinder, its design cylinder efficiency is approximately 92% near rated load conditions. Based on this, the energy conversion level can be set as follows: when the predicted actual cylinder efficiency is greater than or equal to 90%, the energy conversion level is considered high, indicating that the turbine's energy conversion status is good and it is operating within the normal economic range, requiring no intervention; when the actual cylinder efficiency is between 85% and 90%, the energy conversion level is considered medium, indicating that the turbine may have shown initial signs of deterioration such as slight scaling in the flow passage, increased blade surface roughness, or localized leakage. Although it can still operate, its economic efficiency has begun to decline; when the actual cylinder efficiency is below 85%, the energy conversion level is considered low. At this point, the energy conversion has deviated significantly from the normal level, possibly indicating serious blade damage, interstage seal failure, or rubbing between moving and stationary components, which could endanger equipment safety. Of course, these threshold figures are only given as an example. For turbines of different capacities and from different manufacturers, personalized thresholds can be set according to their performance guarantee values ​​and historical maintenance curves, without being limited by the above example values.

[0069] Mapping continuous cylinder efficiency values ​​to discrete level signals may seem simple, but it has significant engineering defensive value. If the system only outputs an efficiency trend curve, operators facing complex parameter changes on the large screen can easily miss early warning signals hidden in the slow degradation process due to distraction. However, by using a clear "high-medium-low" classification, it's like equipping the unit with a tireless digital energy efficiency sentinel. Any performance degradation that crosses the threshold will be immediately detected and explicitly announced in the form of a level signal. This avoids the management loophole of performance degradation continuing to worsen due to human negligence without any intervention.

[0070] When the turbine's energy conversion level is medium, an abnormal alarm signal is generated, prompting maintenance and repair of the turbine. The logic behind a medium-level abnormal alarm is not that the equipment has reached a dangerous level requiring immediate shutdown, but rather, based on the concept of preventative maintenance, it prompts maintenance personnel to perform flow cleaning of the cylinder, replace locally damaged valves, or inspect the shaft sealing system during the next planned troubleshooting window or off-peak hours. This aims to halt further deterioration and prevent a medium-level abnormality from worsening into a serious malfunction after several months of continuous operation. This strategy has significant economic value in power production management, allowing power generation companies to transform unplanned shutdowns into planned shutdowns, avoiding the high power losses and grid performance penalties resulting from forced emergency repairs during peak load periods. When the turbine's energy conversion level is low, a fault alarm signal is generated, stopping the turbine's operation. A low level means that the unit's energy conversion efficiency has collapsed below the permissible limit; continued operation could lead to catastrophic accidents such as blade breakage, shaft bending, or bearing burnout. At this point, the system automatically triggers the shutdown protection logic, sending a trip command to the turbine protection system via hard-wired connection or a safety-grade communication protocol. This rapidly closes the main steam valve and regulating valve, forcibly cutting off steam intake and compelling the unit to safely coast to a shutdown. It is important to note that the transition from the soft result of the algorithmic evaluation to the hard action of the shutdown protection involves a closed-loop transformation from the information domain to the physical domain. This is precisely the key aspect of the defensive protection in this embodiment. Simple efficiency calculations, if only displayed and not linked to equipment control, can be easily circumvented—infringers can simply claim their system only displays efficiency values ​​without executing shutdown actions to circumvent protection. However, this application directly maps the output of the evaluation logic to specific, differentiated unit control commands: one for targeted maintenance reminders, and the other for mandatory fault shutdown protection. This inseparably locks data, algorithms, and control into a closed-loop whole.

[0071] In another alternative implementation, the energy conversion level classification is not limited to three levels; it can be further subdivided into five levels: normal, warning, abnormal, severe, and dangerous, to match a more refined condition-based maintenance strategy. In scenarios with redundant unit configurations, low-level alarms may not necessarily result in a complete unit shutdown, but rather trigger automatic load limiting logic. For example, the unit load may be forcibly limited to below 50% of rated power to ensure equipment safety while still providing some output support. This is also a variation of directly controlling the turbine's operating status. In these variations, the causal relationship between the assessment results and specific equipment control actions remains complete and inseparable, also falling within the protection concept of this technical solution.

[0072] Please see Figure 2Another embodiment of this application provides a steam turbine thermodynamic performance and energy efficiency evaluation system based on hybrid modeling, including: a data acquisition module, a model building module and a data analysis module; The data acquisition module is used to acquire real-time operating data of the steam turbine and the workflow network; The model building module is used to build a mechanistic model of the steam turbine based on the turbine's working flow network; and to build a dynamic prediction model of exhaust enthalpy and cylinder efficiency based on the mechanistic model. The data analysis module is used to analyze the thermal performance and energy efficiency indicators based on the real-time operating data of the steam turbine.

[0073] Some of the data in the above formula are calculated by removing dimensions and taking their numerical values. The formula is the closest to the real situation obtained by software simulation of a large amount of collected data. The preset parameters and preset thresholds in the formula are set by those skilled in the art according to the actual situation or obtained through simulation of a large amount of data.

[0074] The working principle of this application is as follows: This application acquires real-time operating data and working flow network of the steam turbine; constructs a mechanism model of the steam turbine based on the working flow network; constructs a dynamic prediction model of exhaust enthalpy and cylinder efficiency based on the mechanism model; and analyzes the thermodynamic performance and energy efficiency indicators based on the real-time operating data of the steam turbine.

[0075] The above embodiments are only used to illustrate the technical methods of this application and are not intended to limit it. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of this application without departing from the spirit and scope of the technical methods of this application.

Claims

1. A method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling, characterized in that, include: Acquire real-time operating data of the steam turbine and its workflow to the network; A mechanistic model of the steam turbine is constructed based on the turbine's working flow network; A dynamic prediction model for exhaust enthalpy and cylinder efficiency was constructed based on the mechanistic model. Analysis of thermodynamic performance and energy efficiency indicators based on real-time operating data of steam turbines.

2. The method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling as described in claim 1, characterized in that, The construction of the turbine's mechanistic model based on the turbine's working flow network includes: Obtain the working flow network of the steam engine; divide the steam turbine into several stages along the steam flow direction; and treat the high-pressure cylinder, intermediate-pressure cylinder, and low-pressure cylinder as a calculation segment; each stage consists of one stationary blade and one moving blade; A unipolar energy conversion model is established; the reaction degree of steam in the moving blade is calculated based on the reaction degree analysis function; the expression of the reaction degree analysis function is: ;in, This is the actual enthalpy of steam as it leaves the stationary blade and enters the moving blade. This is the actual enthalpy of the steam after it leaves the moving blade; The stagnation enthalpy of the steam before the stage; The relationship between pressure and flow rate under varying operating conditions is analyzed using the Vlugel formula; the expression of the Vlugel formula is: ;in, The steam mass flow rate through this stage group; The mass flow rate of steam passing through the same stage group under varying operating conditions; The absolute pressure of the steam before the stage; The absolute pressure of steam before the same stage group under varying operating conditions; This refers to the absolute pressure of the steam after the stage; The absolute pressure of steam after the same stage group under varying operating conditions; The absolute temperature of the steam before the stage; The absolute temperature of the steam before the stage under varying operating conditions; The sum of the cycle work at each stage is converted into mechanical work at the shaft end, and the power parameters and rotor motion equations are analyzed; among which, the power parameters include: total internal power and shaft end power; The expression for the total internal power is: ;in, This refers to the steam mass flow rate; For the total series; For the effective enthalpy drop of the j-th level; The expression for the shaft end power is: ;in, Mechanical loss; The expression for the rotor motion equation is as follows: ;in, It is the moment of inertia; Angular velocity; This represents the load torque.

3. The method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling as described in claim 2, characterized in that, The establishment of the unipolar energy conversion model includes: Based on the approximate isentropic expansion of steam in the stationary blades, the theoretical outlet velocity is analyzed; the expression for the theoretical outlet velocity is: ;in, The enthalpy of vapor stagnation at the inlet of the still leaf; This represents the ideal enthalpy value when the quotient expands to the point of export pressure. Based on formula Calculate the actual export speed; where, The stationary blade velocity coefficient; based on the formula Calculate nozzle loss; As steam enters the moving blades, the change in relative velocity generates a circumferential force acting on the blades; the work done per unit mass of steam on the turbine circumference is calculated based on the Euler turbine equation; the expression of the Euler turbine equation is: ;in, The circumferential velocity at the average diameter of the blade is expressed as: ; and The circumferential component of the absolute velocity of import and export Based on formula Calculate the relative velocity at the blade exit; where, The velocity coefficient of the moving blade; This is the theoretical relative exit speed; Based on formula Calculate blade loss; based on formula Calculate the residual velocity loss; where, The absolute velocity at the exit of the moving blade; Analyze the effective enthalpy drop and efficiency of the single-stage; the ideal usable enthalpy drop of the stage is: The effective enthalpy drop of the stage is: The efficiency of the stage is: .

4. The method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling as described in claim 1, characterized in that, The dynamic prediction model for exhaust enthalpy and cylinder efficiency constructed based on the mechanistic model includes: The steam turbine is modeled separately as a high-pressure cylinder, an intermediate-pressure cylinder, and a low-pressure cylinder; for each cylinder, the enthalpy value after isentropic expansion is calculated based on the steam properties; the enthalpy value calculation formula is as follows: ;in, ; The specific entropy of the steam inlet; This refers to the inlet steam pressure; Intake air temperature; This refers to the exhaust pressure; A dynamic differential equation for metal wall temperature and a cylinder energy conservation equation are constructed. The dynamic differential equation for metal wall temperature and the cylinder energy conservation equation are integrated and trained with an artificial intelligence model to obtain a dynamic prediction model.

5. The method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling as described in claim 4, characterized in that, The construction of the dynamic differential equation for the metal wall temperature includes: The average steam temperature is analyzed based on the relationship between cylinder metal temperature and convective heat transfer between steam and metal; the formula for calculating the average steam temperature is as follows: ;in, This refers to the exhaust steam temperature. Based on formula The analysis yielded the metal heat balance equation; in which, Equivalent metallic mass; Specific heat of metals; The heat transfer coefficient; For heat exchange area; Discretizing the metal heat balance equation yields the dynamic differential equation for the metal wall temperature: .

6. The method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling according to claim 4, characterized in that, The construction of the cylinder energy conservation equation includes: Based on formula Analyze the energy balance equation on the steam side of the cylinder control unit; where... This refers to the output shaft power of the cylinder. For the specific enthalpy of steam; Enthalpy of vapor output; ; The rate of change of the internal energy of the metal; This refers to the steam mass flow rate; After rearranging the energy balance equation, the dynamic exhaust enthalpy is obtained as follows: ;when When the dynamic exhaust enthalpy is higher, it is lower than the steady-state value; conversely, it is higher than the steady-state value. (Based on the formula...) Calculate the cylinder efficiency value.

7. The method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling according to claim 4, characterized in that, The process of integrating and training the dynamic differential equation of metal wall temperature and the cylinder energy conservation equation with an artificial intelligence model includes: Retrieve the dynamic differential equation of metal wall temperature and the energy conservation equation for each cylinder; obtain historical measurement values ​​and parameter vectors at several historical moments; the historical measurement values ​​include: steam mass flow rate, inlet steam pressure, inlet steam temperature, outlet steam pressure, and cylinder output shaft power; the parameter vectors include: heat transfer coefficient, heat transfer area, equivalent metal mass, metal specific heat, and efficiency correction coefficient. The number of layers and the time series model framework of the fully connected network are selected; the metal wall temperature dynamic differential equation, the energy conservation equation and the number of layers and the time series model framework of the fully connected network are integrated to construct the initial model; Historical measurements are used as input to the model, and error values ​​are used as output. The historical measurements and error values ​​are integrated into training data. The training data is then divided into training set, validation set, and test set according to a set ratio. The initial model is trained using the training set, and its internal parameters are adjusted using the validation set. The trained initial model is then tested using the test set to obtain test metrics. Obtain the range of indicators. If all test indicators are within the range, mark the initial model as a dynamic prediction model; otherwise, retrain the initial model.

8. The method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling according to claim 1, characterized in that, The analysis of thermodynamic performance and energy efficiency indicators based on real-time operating data of the steam turbine includes: Retrieve real-time operating data of the steam turbine; the real-time operating data includes: steam mass flow rate, inlet steam pressure, inlet steam temperature, outlet steam pressure, and cylinder output shaft power; Real-time operating data is input into the dynamic prediction model to obtain the corresponding parameter vector; the parameter vector is input into the turbine's mechanism model to obtain the theoretical cylinder efficiency; the theoretical cylinder efficiency is multiplied by the efficiency correction coefficient to obtain the predicted actual cylinder efficiency; the energy conversion of the turbine is evaluated based on the predicted actual cylinder efficiency.

9. The method for evaluating the thermodynamic performance and energy efficiency of steam turbines based on hybrid modeling as described in claim 8, characterized in that, The evaluation of the turbine's energy conversion based on the predicted actual cylinder efficiency includes: Retrieve the predicted actual cylinder efficiency; obtain the efficiency evaluation table; match the predicted actual cylinder efficiency with the efficiency evaluation table to obtain the turbine's energy conversion level; where the energy conversion level includes: low, medium and high; When the turbine's energy conversion level is medium, an abnormal alarm signal is generated, and the turbine is maintained and repaired; when the turbine's energy conversion level is low, a fault alarm signal is generated, and the turbine is stopped from operating.

10. A steam turbine thermodynamic performance and energy efficiency evaluation system based on hybrid modeling, applied to the steam turbine thermodynamic performance and energy efficiency evaluation method based on hybrid modeling as described in any one of claims 1-9, characterized in that, include: Data acquisition module, model building module, and data analysis module; The data acquisition module is used to acquire real-time operating data of the steam turbine and the workflow network; The model building module is used to build a mechanistic model of the steam turbine based on the turbine's working flow network; and to build a dynamic prediction model of exhaust enthalpy and cylinder efficiency based on the mechanistic model. The data analysis module is used to analyze the thermal performance and energy efficiency indicators based on the real-time operating data of the steam turbine.

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