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Using the artificial neural network to control the steam turbine heating process
Applied Thermal Engineering 108 (2016) 204–210
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Using the artificial neural network to control the steam turbine heating process Grzegorz Nowak ⇑, Andrzej Rusin Institute of Power Engineering and Turbomachinery, Silesian University of Technology, ul. Konarskiego 18, 44-100 Gliwice, Poland
h i g h l i g h t s Inverse Artificial Neural Network has a potential to control the start-up process of a steam turbine. Two serial neural networks made it possible to model the rotor stress based of steam parameters. An ANN with feedback enables transient stress modelling with good accuracy.
a r t i c l e
i n f o
Article history: Received 12 October 2015 Revised 31 March 2016 Accepted 18 July 2016 Available online 19 July 2016 Keywords: ANN Steam turbine Optimization Start-up
a b s t r a c t Due to the significant share of renewable energy sources (RES) – wind farms in particular – in the power sector of many countries, power generation systems become sensitive to variable weather conditions. Under unfavourable changes in weather, ensuring required energy supplies involves hasty start-ups of conventional steam power units whose operation should be characterized by higher and higher flexibility. Controlling the process of power engineering machinery operation requires fast predictive models that will make it possible to analyse many parallel scenarios and select the most favourable one. This approach is employed by the algorithm for the inverse neural network control presented in this paper. Based on the current thermal state of the turbine casing, the algorithm controls the steam temperature at the turbine inlet to keep both the start-up rate and the safety of the machine at the allowable level. The method used herein is based on two artificial neural networks (ANN) working in series. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Monitoring the stress state in power machinery components is an important aspect of supervising their safety. The knowledge of the stress state at any moment of operation makes it possible to assess the hazard posed by on-going processes, such as fatigue and creep, as well as the brittle cracking hazard. Therefore, the safety of operation requires determination of stresses in real time to allow an immediate response on part of the control system to the operating situation that arises [11]. This is of special importance considering the increasing share of RES-based power in national energy generation systems. In many countries wind farms have a considerable share in electricity generation. The problem is that obtaining energy from wind is a highly unpredictable process, and a sudden change in weather conditions may result in a power shortage in the system. In order to compensate for these shortages, a rather fast start-up of a conventional power unit is required. This, ⇑ Corresponding author. E-mail address: [email protected] (G. Nowak). http://dx.doi.org/10.1016/j.applthermaleng.2016.07.129 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
however, may have an unfavourable impact on the durability and reliability of the power unit elements, steam turbines in the first place. Therefore, conventional power units have to be characterized by very high, unprecedented flexibility, which means the capacity for frequent start-ups and shutdowns as well as for operation under variable thermal loads. In recent years, the application of the Artificial Neural Network (ANN) algorithm has been more and more common in cases that require an immediate assessment of diagnostic signals. The ANN metamodel is a universal approximator of the function of several variables and constitutes a nonlinear model of a given process making it possible to obtain a response to set input parameters [7,8]. The problem of monitoring the gas turbine set operation is discussed in Fast’s PhD dissertation [3], which shows the use of the ANN as a diagnostic tool. The neural network task was to classify diagnostic signals for the purposes of the gas turbine technical state assessment. At the same time, Fast and Palme published an article [4] showing the possibility of using the ANN to evaluate the operating conditions of a gas-steam combined heat & power plant. Each of the thermal cycle main elements (the heat recovery
G. Nowak, A. Rusin / Applied Thermal Engineering 108 (2016) 204–210
steam generator, the steam boiler, the gas turbine and the steam turbine) was modelled using a separate neural network. The networks were then combined into a single monitoring system. The diagnostics of the gas turbine failures was analysed by the authors of [10] using what is referred to as the extreme learning machine, which in fact is a neural network variant with a single hidden layer. The tool suitability was evaluated based on experimental data obtained for the gas turbine set gear under controlled conditions. Similar applications are presented by the authors of [5]. This time, however, in relation to the steam turbine operation safety and reliability. In this case, the neural network is used to assess the durability of the rotor blades. An interesting thing here is the inversion of the ANN algorithm to obtain desired input parameters for set output values. Thus, for a set level of durability, a certain value of the vibratory stress is determined which then constitutes one of 6 input data values. The presented calculations prove that the algorithm actually operates and it does so with high accuracy. The same computational technique was used in [2]. This time, to assess and determine the optimum operating parameters of a compressor. Based on a few measured thermodynamic parameters and setting the required level of the compressor efficiency, the necessary drop in the air temperature in the cooler was looked for. Such an application of the ANN is an example of the possibility of using it to control a given process. Other applications of artificial intelligence are presented in the paper written by Huang et al. [6], where the network is used to model the temperature inside an airport building based on the weather data and parameters of the building air-conditioning system operation. Moreover, the system was extended to predict the temperature using weather forecasts, the number of passengers and the time of the heating-cooling system operation or standby. Several variants of the number of historical data supplying the neural network were also tested in the study. The precision of the authors’ anticipations is at the level of 85–90%. The authors of [14] used the ANN to model selected operating parameters of a hybrid ground exchanger in a heat pump system. Based on the measurement of a few temperatures in different points of the cycle, the temperature of the medium flowing into the exchanger was predicted. Another example of the ANN application can be found in [1]. This time, in relation to the electric power system. Using a neural network, the authors establish the safety of the electric power system for different variants of the system operation and determine the need to take specific action. A neural network developed in this manner is a tool that assists the making of operating decisions. This work shows an attempt to use the ANN to control the steam turbine operation. The problem, however, is the complexity of such a task. In reality, several parameters without a strong direct correlation have to be taken into account. Therefore, this paper shows a possibility of controlling the steam turbine start-up process by changing the steam temperature at the turbine inlet, keeping the thermal stress at an allowable level at the same time. Since the thermal stress depends on the element temperature and the computations are made for the turbine rotor, the rotor temperature has to be assessed based on possible measurements. The idea is to solve the problem by using two ANN’s, where one is responsible for the temperature evaluation and the other – for the maximum stress control. The reason for which the approach based on two separate ANN’s is adopted results from the initial need for the rotor temperature evaluation (as the quantity cannot be measured) based on the casing temperature, and not on the modelled thermal stress.
2. The principle of the ANN operation The ANN operation is based on mimicking the human brain functions and the ANN component elements are artificial neurons
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that represent nerve cells whose task is to process input signals into output ones by means of simple mathematical operations. The network is composed of neurons arranged in layers and linked to each other to ensure the input-output flow of information [8]. A diagram of a typical neural network with a unidirectional information flow from the input to the output layer is presented in Fig. 1. Each neuron in layer ‘‘i” is linked to all neurons of the neighbouring layer, transmitting the signal from the (i 1) layer to the (i + 1) layer by means of what is referred to as the activation function. Because the input signals for a given neuron come from all neurons of the previous layer and because in fact their excitation strength varies, the signals in the ANN are burdened with weights whose task is to control the level of the signal reaching the neuron. A difference in the signal level has an effect on the neuron different activation and, consequently, on the signals transmitted further on.
3. The model of thermal stress determination Modelling stresses in components of the power engineering equipment and machinery is usually realized with Finite Element Method (FEM). However, such simulations to directly monitor the operating conditions and to control the start-up processes involves acting in real time. In other words, the supervision system has to provide rapid answers to questions concerning for example the maximum stress values at current parameters of the power unit operation. For this reason, the input parameters of the stress determination metamodel must be measuring quantities that have a direct impact on the strength state of the elements under analysis. In the case of the turbine internal casing, the factors deciding about the stress state are the casing current temperature field (thermal gradients) and the value of the steam pressure in the flow system. For the rotor, apart from its thermal state – also the rotational speed value, which decides about the level of mass loads. Because the rotor material temperature is not measured in the industrial practice (due to the character of the rotor operation), a decision was made to model the rotor stress state based on characteristic temperatures of the casing material. Consequently, appropriate measuring quantities were selected: the casing metal temperatures in selected areas and the steam pressure in the turbine inlet chamber; for the rotor, additionally, the rotational speed. In real systems such measurements are usually possible. The metal temperature was measured at deliberately selected points where the difference in temperature during the start-up process corresponded well to the curve illustrating changes in the maximum stress values in the element. In the case of the HP part internal casing the areas are shown in Fig. 2. One of these points (A) is the joint of the steam inlet connector pipe and the casing inlet chamber, which is located in the area of maximum unsteady-state stresses. The point is situated on the casing inner surface. Due to the very intense heat exchange in this area (very high heat transfer coefficients, heating on both sides of the joint), the measurement of the casing metal temperature is almost equivalent to the temperature measurement performed inside the turbine inlet chamber. The other metal temperature measuring point (B) is located in the front sealing area on the same radius as point A, shifted however by 200 mm in the axial direction. This means that it is distanced by about 100 mm from the nearest heating surface – the surface of the steam spiral inlet chamber. Determination of the rotor maximum stress values based on the casing temperature measurements presented above proved unsatisfactory. This was probably the effect of the lack of an unequivocal correlation between maximum stresses in the rotor and changes in temperature in the indicated points of the casing. Therefore, a
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Input data
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Fig. 1. Flowchart of the artificial neural network.
In this case, the output information generated by the network becomes the input data for the next step. The effect is that, apart from current forcing parameters, there is also information about the value of the system response in the previous time step [10,12,13]. Due to that, the ANN computational code was appropriately modified to reconstruct stresses in the turbine elements, taking account of the feedback mentioned above. The tests of the algorithm prepared in this way confirmed its effectiveness in determining stresses. This can be observed particularly in the case of reconstruction of the turbine rotor stresses based on temperatures measured in the casing. Measuring temperature in one element (where measurements can be performed) leads to stress determination in another. Based on the presented results, it can be seen that the network with feedback not only maps the modelled quantity more accurately but it is also less sensitive to local oscillations in parameters occurring at the start-up initial stage. The difference between the FEM computations and the ANN is about 3% for the maximum stress, and reaches up to 20% after the start-up parameters reach their nominal values. Since in terms of operation the most important thing is the initial part, up to the stress maximum, the ANN model seems to model the stress very well.
5. Predictive model
Fig. 2. Internal casing model with marked measuring points.
search was started for ‘‘better” locations for the temperature measurement that would point to such a correlation. As shown in Fig. 3, the area where the maximum stresses occur in the rotor is the corner of the first relief chamber [9]. This is an area located in the rotor inlet part, where large temperature gradients arise during the start-up. The gradient in the rotor axial direction is the most dominant one, especially at the start-up initial stage. Many simulations were performed to find this particular location for the measurements, which allows precise determination of stresses based on the measure casing temperature values. The measuring points are marked in Fig. 4. They are located near the casing pitch plane at a different depth. Point A is almost on the inner surface, whereas point B is situated 60 mm away from the surface. The subsequent simulations carried out for the casing proved that the newly found points also correlated well with the maximum stress component in the casing and therefore they were used to model the stress state both in the casing and in the rotor (see Figs. 6 and 7).
4. Modelling thermal stresses using the ANN Dedicated software, which was the ANN algorithm implementation, was written for the analysed problem of determining thermal stresses in the steam turbine main elements during transient phases of the machine operation. The model input data were measuring quantities usually available in any turbine operation control system. The output information was the current value of the maximum stress. In the course of further investigations it was found that, due to the importance of the history of changes in parameters describing the turbine elements behaviour in transient stages of operation, a recurrent network (i.e. a network with feedback) would be a more suitable neural network structure (Fig. 5).
The main goal of this work was to create a predictive model for the steam turbine operation control based on the ANN. In this case, the model consisted of both the turbine casing and rotor, for which an effort was made to provide such a heating process (start-up) that the maximum stress should be kept at the allowable level. The stress state is in relation to the thermal field within the component. Therefore, information is needed about the component thermal field, and on this basis the maximum stress can be evaluated. In practice, it is usually done by means of temperature measurements and the correlation developed between those temperatures and stresses. The problem is that the thermal stress within the rotor depends on its thermal field, which is not measured. A decision was made, then, to model the rotor temperature based on the temperature of the turbine casing. The correlation was built via an ANN, which as a result provided data for another ANN responsible for stress computations. In this way, the inverse problem is based on a two-step ANN modelling procedure – the thermal and the stress one. The above metamodel using the ANN with feedback was next implemented to create a predictive model whose task was to determine the history of changes in the steam temperature at the turbine inlet at set external limitations. The limitations were the allowable level of maximum stresses in an element on the one hand, and the maximum rate of the live steam temperature increment on the other. In this situation, the task of the algorithm was to run the start-up process with the maximum rate of the temperature growth without compromising the maximum stress criterion. Because thermal stresses, which are the main component of total stresses occurring in the thermal turbine elements, are a function of the element temperature field, it was necessary to simulate temperature in selected points of the element based on changes in the live steam temperature and then to determine stresses based on the temperature of the element material. The developed algorithm was thus composed of two serially connected neural networks, one of which was used to model temperature in selected points of the element, while the other – to model stresses. The initial phase of the development of the metamodel for the transient stress state determination was to find input quantities that would be in a direct relation to the stresses being determined.
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Fig. 3. Von mises stress field in the rotor.
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Fig. 4. Internal casing model with marked final measuring points.
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Fig. 5. Flowchart of an artificial neural network with feedback.
In order to make such a metamodel a suitable tool of stress assessment in real operating conditions, the input quantities should reflect current operating conditions and be, at the same time, the quantities of the measurement. The developed ANN algorithm was tested based on a series of numerical simulations of start-up processes worked out for a hypothetical high-power steam turbine. The results of the FEM numerical simulations were the network learning data. The simulations were carried out for 7 start-ups (3 from the cold state, 3 from the warm state and 1 from the hot state), and additionally – for different steam-metal initial differences. Fig. 8 presents curves illustrating changes in the casing metal temperature in point A during the start-ups under analysis. The curves marked with solid lines were used as the neural network learning data; the start-up shown with a dashed line was used to verify the quality of the network operation and was not included in the set of the learning data.
The network learning process was based on the back propagation algorithm [8]. consisting in minimizing the error function generated by the network (Fig. 9). Variable learning coefficients were also used. Owing to that, better convergence can be obtained and the network learning process can be accelerated. The input data in the form of standardized start-up parameters were processed by the network into a single output value. On the other hand, the system response is known as the effect of the turbine start-up numerical simulations performed earlier. The algorithm thus compares the outcome of the network operation to the anticipated result and aims at minimizing the differences between the two. Fig. 10 presents a comparison of temperatures in two selected points of the casing which are used as the basis to determine stresses in the turbine rotor and casing. The curves obtained from the FEM modelling are marked with dashed lines. In the case analysed herein, they are treated as benchmark histories. The curves generated by the neural network are plotted using solid lines. Good agreement between the two approaches can be noticed here, which suggests that a network with this type of preparation and learning is suitable for the performance of the set task. The same procedure was adopted in the case of the network responsible for the reconstruction of maximum stresses. Here, the network modelled a single component of the principal stress state. The analysis of the stress state of the modelled elements indicates that the maximum stress and strain values in the casing depend almost entirely on the minimum principal stress component (r3), whereas components r1 and r2 are responsible for maximum stresses in the rotor. It is these very quantities that are determined by means of the network. Because two stress state components have to be modelled in the rotor, a decision was made to use two separate specialized neural networks to determine one stress state component each. The other principal stress components have values with hardly any effect on the element stress and strain state and therefore they are omitted in the calculations. Nevertheless, the adopted approach makes it possible to find the total stress state tensor by determining each stress state component by means of a dedicated neural network.
6. Control of the start-up process The prepared artificial neural network algorithm was used to optimize the curve illustrating changes in the steam temperature at the turbine inlet during start-up. The algorithm operation (Fig. 11) is based on prediction of a single time step of the steam temperature in the turbine flow system (Tsi) at a set level of allowable stresses (rall). In order to serve this purpose, the computational algorithm was modified so that, at the network set output value (r), the input temperature could be corrected to keep the stress values below the maximum allowable stress level. It was also assumed
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Fig. 8. Curves illustrating changes in the casing metal temperature in point A during start-ups.
that the change in the steam temperature (steam temperature in the next step Tis) must not exceed the value set by the user (Tsmax). If both these conditions were satisfied, the values obtained at the output were the steam temperature to be set and the maximum stress resulting therefrom. In order to solve the task, a set of input data
had to be selected. Considering our extensive experience in thermo-mechanical stress simulations in steam turbines, a decision was made to choose the fundamental start-up parameters: steam inlet pressure (ps), rotor revolutions (n) and steam temperature (Ts). Since the stress state depends on the current thermal field, two metal temperatures are also taken into account (TA and TB) (Fig. 4). The transient character of the start-up is taken into
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Fig. 12. Temperature and principal stress curves for the original and optimized start-up for the casing.
Fig. 11. Flowchart of the predictive algorithm operation.
consideration by introducing information about the temperature distribution in the previous time step. All the input data are given in Fig. 11, where the superscript shows the current (i) and previous (i 1) time step. The great number of performed tests determined the thermal ANN structure (6–25–11–3), which consists of two hidden layers. The prepared algorithm workflow starts with computations, on the basis of input data, of two characteristic metal temperatures (TA and TB) using the ‘‘ANN Thermal”. These temperatures and the remaining input data (mentioned above) provide information for stress evaluation within the ‘‘ANN Stress”. The structure of this ANN consists of 3 hidden layers with the following numbers of neurons: 9–7–4–3–1. At this stage, the obtained stress value is compared with the allowable limit and if it is within the acceptable range the input steam temperature is increased by a small value (DT). The temperature is increased until one of two specified conditions is violated – the maximum stress condition or the maximum temperature rise within a single time step. If one of the conditions is met, the input steam temperature is taken as the predicted one. The performed simulations made it possible to obtain a new curve illustrating changes in the steam temperature at the turbine inlet. The dashed lines in Figs. 12 and 13 illustrate curves of the steam temperature at the turbine inlet (black) and of the resulting
Fig. 13. Temperature and principal stress curves for the original and optimized start-up for the rotor.
maximum principal stress components (red1) for the original start-up. Solutions for two different start-ups are presented to show the functioning of the developed algorithm. In the case of the casing, the start-up was originally carried out from the cold state with the average rate of the steam temperature increment of 2 K/min; in the case of the rotor, the presented start-up was carried out from the warm state with the same average temperature increment rate of 2 K/min. The solid lines in the charts are used to mark the corrected curve of stress values (red), limited to the allowable level (in this case – 450 MPa for the casing, 140 MPa for the rotor) and the optimized curve illustrating the history of temperature values corresponding to them (black). It can be noticed that at the startup initial stage the optimized temperature is characterized by a higher rate of growth compared to the original start-up, which continues until the allowable stress level is reached. From that moment on, the temperature increment rate slows down so that the set stress
1 For interpretation of color in Figs. 12 and 13, the reader is referred to the web version of this article.
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level should be maintained. In the original start-up there is a continuous rise in temperature, which results in exceeding the allowable stress values.
Development in the framework of Contract SP/E/1/67484/10 – Strategic Research Programme – Advanced technologies for obtaining energy: Development of a technology for highly efficient zero-emission coal-fired power units integrated with CO2 capture.
7. Conclusions References The strict requirements concerning the flexibility of the steam turbine operation create a need for reasonable control of the unsteady-state operation processes. This means that changes in the thermal state of the machine main elements have to be introduced as fast as possible, but without compromising safety requirements or the turbine durability. The examples presented above are just an indication of the possibility of using the artificial neural network to control the start-up process because in reality the turbine start-up requires controlling a greater number of parameters such as the steam pressure, the steam mass flow and the rotor revolutions. The constrained number of input parameters made it possible to get results with an error of about 20%, so it seems that it is possible to expand the algorithm with more data to make it more accurate. Additionally, the availability of measurement data from the operation history allows the creation of an ANN algorithm that will determine anticipated values of start-up parameters based on set limitations. These values, in turn, can serve the purpose of the operation control. Due to its very short computation time (milliseconds), the algorithm can work with very short sampling times, which is its essential advantage. However, attention should be drawn to the fact that in order to make the algorithm capable of generalizing results, i.e. of correctly predicting the system response to the set input functions of a varied (but physically possible) character, a lot of learning data (from many start-ups performed from different initial states and in different manners) are required. Acknowledgements The results presented in this paper were obtained from research work co-financed by the Polish National Centre of Research and
[1] A. Al-Masri, M. Ab Kadirb, H. Hizamb, N. Mariun, Simulation of an adaptive artificial neural network for power system security enhancement including control action, Appl. Soft Comput. 23 (2015) 1–11. [2] O. Cortés, G. Urquiza, J.A. Hernández, Optimization of operating conditions for compressor performance by means of neural network inverse, Appl. Energy 86 (2009) 2487–2493, http://dx.doi.org/10.1016/j.apenergy.2009.03.001. [3] M. Fast, Artificial Neural Networks for Gas Turbine Monitoring PhD dissertation, Lund University, Sweden, 2010. [4] M. Fast, T. Palme, Application of artificial neural networks to the condition monitoring and diagnosis of a combined heat and power plant, Energy 35 (2010) 1114–1120, http://dx.doi.org/10.1016/j.energy.2009.06.005. [5] Y. Hamzaoui, J. Rodríguez, J. Hernandez, V. Salazar, Optimization of operating conditions for steam turbine using an artificial neural network inverse, Appl. Therm. Eng. 75 (2015) 648–657. [6] Hao Huang, Lei Chen, Hu Eric, A neural network-based multizone modelling approach for predictive control system design in commercial buildings, Energy Build. (2015), http://dx.doi.org/10.1016/j.enbuild.2015.03.045. [7] M.S. Kan, A. Tan, J. Mathew, A review on prognostic techniques for nonstationary and non-linear rotating systems, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.02.016. [8] N. Karayiannis, A. Venetsanopoulos, Artificial Neural Networks: Learning Algorithms, Performance Evaluation, and Applications, Kluwer Academic Publishers, 1993. [9] G. Nowak, A. Rusin, Shape and operation optimization of a supercritical steam turbine rotor, Energy Convers. Manage. 74 (2013) 417–425. [10] Pak Kin Wong, Zhixin Yang, ChiMan Vong, Jianhua Zhong, Real-time fault diagnosis for gas turbine generator systems using extreme learning machine, Neurocomputing 128 (2014) 249–257. [11] A. Rusin, G. Nowak, M. Lipka, Practical algorithms for online thermal stress calculations and heating process control, J. Therm. Stress. 37 (11) (2014). [12] M. Sainlez, G. Heyen, Recurrent neural network prediction of steam production in a Kraft recovery boiler, Comput. Aid. Chem. Eng. 29 (2011) 1784–1788. [13] F.A. Soares, E. Flôres, C. Cabacinha, G. Carrijo, A. Paschoarelli Veiga, Recursive diameter prediction and volume calculation of eucalyptus trees using Multilayer Perceptron Networks, Comput. Electron. Agric. 78 (1) (2011) 19–27. [14] G. Wenjie, W. Jinbo, W. Shengwei, Performance analysis of hybrid ground source heat pump systems based on ANN predictive control, Appl. Energy 136 (2014) 1138–1144.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Using the artificial neural network to control the steam turbine heating process Grzegorz Nowak ⇑, Andrzej Rusin Institute of Power Engineering and Turbomachinery, Silesian University of Technology, ul. Konarskiego 18, 44-100 Gliwice, Poland
h i g h l i g h t s Inverse Artificial Neural Network has a potential to control the start-up process of a steam turbine. Two serial neural networks made it possible to model the rotor stress based of steam parameters. An ANN with feedback enables transient stress modelling with good accuracy.
a r t i c l e
i n f o
Article history: Received 12 October 2015 Revised 31 March 2016 Accepted 18 July 2016 Available online 19 July 2016 Keywords: ANN Steam turbine Optimization Start-up
a b s t r a c t Due to the significant share of renewable energy sources (RES) – wind farms in particular – in the power sector of many countries, power generation systems become sensitive to variable weather conditions. Under unfavourable changes in weather, ensuring required energy supplies involves hasty start-ups of conventional steam power units whose operation should be characterized by higher and higher flexibility. Controlling the process of power engineering machinery operation requires fast predictive models that will make it possible to analyse many parallel scenarios and select the most favourable one. This approach is employed by the algorithm for the inverse neural network control presented in this paper. Based on the current thermal state of the turbine casing, the algorithm controls the steam temperature at the turbine inlet to keep both the start-up rate and the safety of the machine at the allowable level. The method used herein is based on two artificial neural networks (ANN) working in series. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Monitoring the stress state in power machinery components is an important aspect of supervising their safety. The knowledge of the stress state at any moment of operation makes it possible to assess the hazard posed by on-going processes, such as fatigue and creep, as well as the brittle cracking hazard. Therefore, the safety of operation requires determination of stresses in real time to allow an immediate response on part of the control system to the operating situation that arises [11]. This is of special importance considering the increasing share of RES-based power in national energy generation systems. In many countries wind farms have a considerable share in electricity generation. The problem is that obtaining energy from wind is a highly unpredictable process, and a sudden change in weather conditions may result in a power shortage in the system. In order to compensate for these shortages, a rather fast start-up of a conventional power unit is required. This, ⇑ Corresponding author. E-mail address: [email protected] (G. Nowak). http://dx.doi.org/10.1016/j.applthermaleng.2016.07.129 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
however, may have an unfavourable impact on the durability and reliability of the power unit elements, steam turbines in the first place. Therefore, conventional power units have to be characterized by very high, unprecedented flexibility, which means the capacity for frequent start-ups and shutdowns as well as for operation under variable thermal loads. In recent years, the application of the Artificial Neural Network (ANN) algorithm has been more and more common in cases that require an immediate assessment of diagnostic signals. The ANN metamodel is a universal approximator of the function of several variables and constitutes a nonlinear model of a given process making it possible to obtain a response to set input parameters [7,8]. The problem of monitoring the gas turbine set operation is discussed in Fast’s PhD dissertation [3], which shows the use of the ANN as a diagnostic tool. The neural network task was to classify diagnostic signals for the purposes of the gas turbine technical state assessment. At the same time, Fast and Palme published an article [4] showing the possibility of using the ANN to evaluate the operating conditions of a gas-steam combined heat & power plant. Each of the thermal cycle main elements (the heat recovery
G. Nowak, A. Rusin / Applied Thermal Engineering 108 (2016) 204–210
steam generator, the steam boiler, the gas turbine and the steam turbine) was modelled using a separate neural network. The networks were then combined into a single monitoring system. The diagnostics of the gas turbine failures was analysed by the authors of [10] using what is referred to as the extreme learning machine, which in fact is a neural network variant with a single hidden layer. The tool suitability was evaluated based on experimental data obtained for the gas turbine set gear under controlled conditions. Similar applications are presented by the authors of [5]. This time, however, in relation to the steam turbine operation safety and reliability. In this case, the neural network is used to assess the durability of the rotor blades. An interesting thing here is the inversion of the ANN algorithm to obtain desired input parameters for set output values. Thus, for a set level of durability, a certain value of the vibratory stress is determined which then constitutes one of 6 input data values. The presented calculations prove that the algorithm actually operates and it does so with high accuracy. The same computational technique was used in [2]. This time, to assess and determine the optimum operating parameters of a compressor. Based on a few measured thermodynamic parameters and setting the required level of the compressor efficiency, the necessary drop in the air temperature in the cooler was looked for. Such an application of the ANN is an example of the possibility of using it to control a given process. Other applications of artificial intelligence are presented in the paper written by Huang et al. [6], where the network is used to model the temperature inside an airport building based on the weather data and parameters of the building air-conditioning system operation. Moreover, the system was extended to predict the temperature using weather forecasts, the number of passengers and the time of the heating-cooling system operation or standby. Several variants of the number of historical data supplying the neural network were also tested in the study. The precision of the authors’ anticipations is at the level of 85–90%. The authors of [14] used the ANN to model selected operating parameters of a hybrid ground exchanger in a heat pump system. Based on the measurement of a few temperatures in different points of the cycle, the temperature of the medium flowing into the exchanger was predicted. Another example of the ANN application can be found in [1]. This time, in relation to the electric power system. Using a neural network, the authors establish the safety of the electric power system for different variants of the system operation and determine the need to take specific action. A neural network developed in this manner is a tool that assists the making of operating decisions. This work shows an attempt to use the ANN to control the steam turbine operation. The problem, however, is the complexity of such a task. In reality, several parameters without a strong direct correlation have to be taken into account. Therefore, this paper shows a possibility of controlling the steam turbine start-up process by changing the steam temperature at the turbine inlet, keeping the thermal stress at an allowable level at the same time. Since the thermal stress depends on the element temperature and the computations are made for the turbine rotor, the rotor temperature has to be assessed based on possible measurements. The idea is to solve the problem by using two ANN’s, where one is responsible for the temperature evaluation and the other – for the maximum stress control. The reason for which the approach based on two separate ANN’s is adopted results from the initial need for the rotor temperature evaluation (as the quantity cannot be measured) based on the casing temperature, and not on the modelled thermal stress.
2. The principle of the ANN operation The ANN operation is based on mimicking the human brain functions and the ANN component elements are artificial neurons
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that represent nerve cells whose task is to process input signals into output ones by means of simple mathematical operations. The network is composed of neurons arranged in layers and linked to each other to ensure the input-output flow of information [8]. A diagram of a typical neural network with a unidirectional information flow from the input to the output layer is presented in Fig. 1. Each neuron in layer ‘‘i” is linked to all neurons of the neighbouring layer, transmitting the signal from the (i 1) layer to the (i + 1) layer by means of what is referred to as the activation function. Because the input signals for a given neuron come from all neurons of the previous layer and because in fact their excitation strength varies, the signals in the ANN are burdened with weights whose task is to control the level of the signal reaching the neuron. A difference in the signal level has an effect on the neuron different activation and, consequently, on the signals transmitted further on.
3. The model of thermal stress determination Modelling stresses in components of the power engineering equipment and machinery is usually realized with Finite Element Method (FEM). However, such simulations to directly monitor the operating conditions and to control the start-up processes involves acting in real time. In other words, the supervision system has to provide rapid answers to questions concerning for example the maximum stress values at current parameters of the power unit operation. For this reason, the input parameters of the stress determination metamodel must be measuring quantities that have a direct impact on the strength state of the elements under analysis. In the case of the turbine internal casing, the factors deciding about the stress state are the casing current temperature field (thermal gradients) and the value of the steam pressure in the flow system. For the rotor, apart from its thermal state – also the rotational speed value, which decides about the level of mass loads. Because the rotor material temperature is not measured in the industrial practice (due to the character of the rotor operation), a decision was made to model the rotor stress state based on characteristic temperatures of the casing material. Consequently, appropriate measuring quantities were selected: the casing metal temperatures in selected areas and the steam pressure in the turbine inlet chamber; for the rotor, additionally, the rotational speed. In real systems such measurements are usually possible. The metal temperature was measured at deliberately selected points where the difference in temperature during the start-up process corresponded well to the curve illustrating changes in the maximum stress values in the element. In the case of the HP part internal casing the areas are shown in Fig. 2. One of these points (A) is the joint of the steam inlet connector pipe and the casing inlet chamber, which is located in the area of maximum unsteady-state stresses. The point is situated on the casing inner surface. Due to the very intense heat exchange in this area (very high heat transfer coefficients, heating on both sides of the joint), the measurement of the casing metal temperature is almost equivalent to the temperature measurement performed inside the turbine inlet chamber. The other metal temperature measuring point (B) is located in the front sealing area on the same radius as point A, shifted however by 200 mm in the axial direction. This means that it is distanced by about 100 mm from the nearest heating surface – the surface of the steam spiral inlet chamber. Determination of the rotor maximum stress values based on the casing temperature measurements presented above proved unsatisfactory. This was probably the effect of the lack of an unequivocal correlation between maximum stresses in the rotor and changes in temperature in the indicated points of the casing. Therefore, a
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In this case, the output information generated by the network becomes the input data for the next step. The effect is that, apart from current forcing parameters, there is also information about the value of the system response in the previous time step [10,12,13]. Due to that, the ANN computational code was appropriately modified to reconstruct stresses in the turbine elements, taking account of the feedback mentioned above. The tests of the algorithm prepared in this way confirmed its effectiveness in determining stresses. This can be observed particularly in the case of reconstruction of the turbine rotor stresses based on temperatures measured in the casing. Measuring temperature in one element (where measurements can be performed) leads to stress determination in another. Based on the presented results, it can be seen that the network with feedback not only maps the modelled quantity more accurately but it is also less sensitive to local oscillations in parameters occurring at the start-up initial stage. The difference between the FEM computations and the ANN is about 3% for the maximum stress, and reaches up to 20% after the start-up parameters reach their nominal values. Since in terms of operation the most important thing is the initial part, up to the stress maximum, the ANN model seems to model the stress very well.
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Fig. 2. Internal casing model with marked measuring points.
search was started for ‘‘better” locations for the temperature measurement that would point to such a correlation. As shown in Fig. 3, the area where the maximum stresses occur in the rotor is the corner of the first relief chamber [9]. This is an area located in the rotor inlet part, where large temperature gradients arise during the start-up. The gradient in the rotor axial direction is the most dominant one, especially at the start-up initial stage. Many simulations were performed to find this particular location for the measurements, which allows precise determination of stresses based on the measure casing temperature values. The measuring points are marked in Fig. 4. They are located near the casing pitch plane at a different depth. Point A is almost on the inner surface, whereas point B is situated 60 mm away from the surface. The subsequent simulations carried out for the casing proved that the newly found points also correlated well with the maximum stress component in the casing and therefore they were used to model the stress state both in the casing and in the rotor (see Figs. 6 and 7).
4. Modelling thermal stresses using the ANN Dedicated software, which was the ANN algorithm implementation, was written for the analysed problem of determining thermal stresses in the steam turbine main elements during transient phases of the machine operation. The model input data were measuring quantities usually available in any turbine operation control system. The output information was the current value of the maximum stress. In the course of further investigations it was found that, due to the importance of the history of changes in parameters describing the turbine elements behaviour in transient stages of operation, a recurrent network (i.e. a network with feedback) would be a more suitable neural network structure (Fig. 5).
The main goal of this work was to create a predictive model for the steam turbine operation control based on the ANN. In this case, the model consisted of both the turbine casing and rotor, for which an effort was made to provide such a heating process (start-up) that the maximum stress should be kept at the allowable level. The stress state is in relation to the thermal field within the component. Therefore, information is needed about the component thermal field, and on this basis the maximum stress can be evaluated. In practice, it is usually done by means of temperature measurements and the correlation developed between those temperatures and stresses. The problem is that the thermal stress within the rotor depends on its thermal field, which is not measured. A decision was made, then, to model the rotor temperature based on the temperature of the turbine casing. The correlation was built via an ANN, which as a result provided data for another ANN responsible for stress computations. In this way, the inverse problem is based on a two-step ANN modelling procedure – the thermal and the stress one. The above metamodel using the ANN with feedback was next implemented to create a predictive model whose task was to determine the history of changes in the steam temperature at the turbine inlet at set external limitations. The limitations were the allowable level of maximum stresses in an element on the one hand, and the maximum rate of the live steam temperature increment on the other. In this situation, the task of the algorithm was to run the start-up process with the maximum rate of the temperature growth without compromising the maximum stress criterion. Because thermal stresses, which are the main component of total stresses occurring in the thermal turbine elements, are a function of the element temperature field, it was necessary to simulate temperature in selected points of the element based on changes in the live steam temperature and then to determine stresses based on the temperature of the element material. The developed algorithm was thus composed of two serially connected neural networks, one of which was used to model temperature in selected points of the element, while the other – to model stresses. The initial phase of the development of the metamodel for the transient stress state determination was to find input quantities that would be in a direct relation to the stresses being determined.
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Fig. 3. Von mises stress field in the rotor.
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Fig. 5. Flowchart of an artificial neural network with feedback.
In order to make such a metamodel a suitable tool of stress assessment in real operating conditions, the input quantities should reflect current operating conditions and be, at the same time, the quantities of the measurement. The developed ANN algorithm was tested based on a series of numerical simulations of start-up processes worked out for a hypothetical high-power steam turbine. The results of the FEM numerical simulations were the network learning data. The simulations were carried out for 7 start-ups (3 from the cold state, 3 from the warm state and 1 from the hot state), and additionally – for different steam-metal initial differences. Fig. 8 presents curves illustrating changes in the casing metal temperature in point A during the start-ups under analysis. The curves marked with solid lines were used as the neural network learning data; the start-up shown with a dashed line was used to verify the quality of the network operation and was not included in the set of the learning data.
The network learning process was based on the back propagation algorithm [8]. consisting in minimizing the error function generated by the network (Fig. 9). Variable learning coefficients were also used. Owing to that, better convergence can be obtained and the network learning process can be accelerated. The input data in the form of standardized start-up parameters were processed by the network into a single output value. On the other hand, the system response is known as the effect of the turbine start-up numerical simulations performed earlier. The algorithm thus compares the outcome of the network operation to the anticipated result and aims at minimizing the differences between the two. Fig. 10 presents a comparison of temperatures in two selected points of the casing which are used as the basis to determine stresses in the turbine rotor and casing. The curves obtained from the FEM modelling are marked with dashed lines. In the case analysed herein, they are treated as benchmark histories. The curves generated by the neural network are plotted using solid lines. Good agreement between the two approaches can be noticed here, which suggests that a network with this type of preparation and learning is suitable for the performance of the set task. The same procedure was adopted in the case of the network responsible for the reconstruction of maximum stresses. Here, the network modelled a single component of the principal stress state. The analysis of the stress state of the modelled elements indicates that the maximum stress and strain values in the casing depend almost entirely on the minimum principal stress component (r3), whereas components r1 and r2 are responsible for maximum stresses in the rotor. It is these very quantities that are determined by means of the network. Because two stress state components have to be modelled in the rotor, a decision was made to use two separate specialized neural networks to determine one stress state component each. The other principal stress components have values with hardly any effect on the element stress and strain state and therefore they are omitted in the calculations. Nevertheless, the adopted approach makes it possible to find the total stress state tensor by determining each stress state component by means of a dedicated neural network.
6. Control of the start-up process The prepared artificial neural network algorithm was used to optimize the curve illustrating changes in the steam temperature at the turbine inlet during start-up. The algorithm operation (Fig. 11) is based on prediction of a single time step of the steam temperature in the turbine flow system (Tsi) at a set level of allowable stresses (rall). In order to serve this purpose, the computational algorithm was modified so that, at the network set output value (r), the input temperature could be corrected to keep the stress values below the maximum allowable stress level. It was also assumed
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that the change in the steam temperature (steam temperature in the next step Tis) must not exceed the value set by the user (Tsmax). If both these conditions were satisfied, the values obtained at the output were the steam temperature to be set and the maximum stress resulting therefrom. In order to solve the task, a set of input data
had to be selected. Considering our extensive experience in thermo-mechanical stress simulations in steam turbines, a decision was made to choose the fundamental start-up parameters: steam inlet pressure (ps), rotor revolutions (n) and steam temperature (Ts). Since the stress state depends on the current thermal field, two metal temperatures are also taken into account (TA and TB) (Fig. 4). The transient character of the start-up is taken into
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consideration by introducing information about the temperature distribution in the previous time step. All the input data are given in Fig. 11, where the superscript shows the current (i) and previous (i 1) time step. The great number of performed tests determined the thermal ANN structure (6–25–11–3), which consists of two hidden layers. The prepared algorithm workflow starts with computations, on the basis of input data, of two characteristic metal temperatures (TA and TB) using the ‘‘ANN Thermal”. These temperatures and the remaining input data (mentioned above) provide information for stress evaluation within the ‘‘ANN Stress”. The structure of this ANN consists of 3 hidden layers with the following numbers of neurons: 9–7–4–3–1. At this stage, the obtained stress value is compared with the allowable limit and if it is within the acceptable range the input steam temperature is increased by a small value (DT). The temperature is increased until one of two specified conditions is violated – the maximum stress condition or the maximum temperature rise within a single time step. If one of the conditions is met, the input steam temperature is taken as the predicted one. The performed simulations made it possible to obtain a new curve illustrating changes in the steam temperature at the turbine inlet. The dashed lines in Figs. 12 and 13 illustrate curves of the steam temperature at the turbine inlet (black) and of the resulting
Fig. 13. Temperature and principal stress curves for the original and optimized start-up for the rotor.
maximum principal stress components (red1) for the original start-up. Solutions for two different start-ups are presented to show the functioning of the developed algorithm. In the case of the casing, the start-up was originally carried out from the cold state with the average rate of the steam temperature increment of 2 K/min; in the case of the rotor, the presented start-up was carried out from the warm state with the same average temperature increment rate of 2 K/min. The solid lines in the charts are used to mark the corrected curve of stress values (red), limited to the allowable level (in this case – 450 MPa for the casing, 140 MPa for the rotor) and the optimized curve illustrating the history of temperature values corresponding to them (black). It can be noticed that at the startup initial stage the optimized temperature is characterized by a higher rate of growth compared to the original start-up, which continues until the allowable stress level is reached. From that moment on, the temperature increment rate slows down so that the set stress
1 For interpretation of color in Figs. 12 and 13, the reader is referred to the web version of this article.
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level should be maintained. In the original start-up there is a continuous rise in temperature, which results in exceeding the allowable stress values.
Development in the framework of Contract SP/E/1/67484/10 – Strategic Research Programme – Advanced technologies for obtaining energy: Development of a technology for highly efficient zero-emission coal-fired power units integrated with CO2 capture.
7. Conclusions References The strict requirements concerning the flexibility of the steam turbine operation create a need for reasonable control of the unsteady-state operation processes. This means that changes in the thermal state of the machine main elements have to be introduced as fast as possible, but without compromising safety requirements or the turbine durability. The examples presented above are just an indication of the possibility of using the artificial neural network to control the start-up process because in reality the turbine start-up requires controlling a greater number of parameters such as the steam pressure, the steam mass flow and the rotor revolutions. The constrained number of input parameters made it possible to get results with an error of about 20%, so it seems that it is possible to expand the algorithm with more data to make it more accurate. Additionally, the availability of measurement data from the operation history allows the creation of an ANN algorithm that will determine anticipated values of start-up parameters based on set limitations. These values, in turn, can serve the purpose of the operation control. Due to its very short computation time (milliseconds), the algorithm can work with very short sampling times, which is its essential advantage. However, attention should be drawn to the fact that in order to make the algorithm capable of generalizing results, i.e. of correctly predicting the system response to the set input functions of a varied (but physically possible) character, a lot of learning data (from many start-ups performed from different initial states and in different manners) are required. Acknowledgements The results presented in this paper were obtained from research work co-financed by the Polish National Centre of Research and
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