Nuclear power plant steam turbine—Modeling for model based control purposes

The nature of the processes taking place in a nuclear power plant (NPP) steam turbine is the reason why their modeling is very difficult, especially when the model is intended to be used for on-line optimal model based process control over a wide range of operating conditions, caused by changing electrical power demand e.g. when combined heat and power mode of work is utilized. The paper presents three nonlinear models of NPP steam turbine, which are: the static model, and two dynamic versions, detailed and simplified. As the input variables, the models use the valve opening degree and the steam flow properties: mass flow rate, pressure and temperature. The models enable to get access to many internal variables describing process within the turbine. They can be treated as the output or state variables. In order to verify and validate the models, data from the WWER-440/213 reactor and the 4 CK 465 turbine were utilized as the benchmark. The performed simulations have shown good accordance of the static and dynamic models with the benchmark data in steady state conditions. The dynamic models also demonstrated good behavior in transient conditions. The models were analyzed in terms of computational load and accuracy over a wide range of varying inputs and for different numerical calculation parameters, especially time step values. It was found that the detailed dynamic model, due to its complexity and the resultant long calculation time, is not applicable in advanced control methods, e.g. model predictive control. However, the introduced simplifications significantly decreased the computational load, which enables to use the simplified model for on-line control.     

Unique temperature distribution and explicit efficiency formula for one-dimensional thermoelectric generators under constant Seebeck coefficients

A thermoelectric generator converts a temperature difference into electrical energy. Its energy conversion efficiency is determined by the steady-state temperature distribution inside the generator. By assuming the thermoelectric material in the generator has a temperature-independent Seebeck coefficient and the generator is one-dimensional, we show that the second-order integro-differential equation describing the inside temperature distribution has a unique solution for any given ratio of external load resistance to the internal resistance. Hence the efficiency is well defined. Furthermore, we show the efficiency has an explicit formula in terms of the temperature-dependent thermal conductivity and electrical resistivity of the thermoelectric material. On the contrary, the integro-differential equation may have multiple solutions if an external load resistance value is given instead of the external-load-to-internal resistance ratio.     

Influence of turbulence on the performance of a laboratory scale HAWT

The oncoming wind to horizontal axis wind turbines (HAWT) may change its speed and direction stochastically in time. Hence, turbine blades are exposed to flows both with fluctuating angle of attack and fluctuating yaw angles. The modern wind turbines are reacting to those changes by pitch angle and torque control not only to exploit as much power as possible but also stabilize energy production and prevent any damage of the turbine. However, time scales of wind fluctuations and sudden changes of wind properties can be very short and with very high in amplitude. In the present study we focus on the influence of turbulence on the performance of a HAWT. Main motivation of the investigations is to figure out best strategies for the aerodynamic design of the blades operating under turbulent conditions. A laboratory scale HAWT and a performance measurement set-up are employed to measure the influence of the oncoming wind. The tests are conducted in the closed loop wind tunnel of our institute. The test section of the tunnel is 1.87 m in width, 1.4 m in height and 2 m in length. The rotor blades are specially designed and optimized for this wind tunnel and the generator used. The turbulence is generated by two static squared mesh grids; fine and coarse one. Hence, two mainly different turbulence scales are obtained. In addition, the distance between the wind-turbine and the grid is adjusted to have additional sub-turbulence scales for each grid. The turbulence is nearly isotropic and decays in the flow direction. The developments of Taylor's micro scale (λ_g) and integral scale (L_g) of the turbulence in the flow direction at various incoming wind velocities (8−16 m/s) are measured. Hence, the facility allows to expose the wind-turbine to turbulence with various energy and length scale content. Those measurements are conducted with hot-wire anemometry in the absence of the wind-turbine. Upstream and downstream turbulence intensities (TI) distributions are measured to give insight on the surrounding free stream and turbine wake interaction and how can different turbulence eddies scales contribute in the influence of the performance of the turbine. Performance measurements are conducted with and without turbulence and the results are compared. The study shows that the higher the turbulence, the more the power extracted by the turbine. This is due to the higher interaction of large eddies with the turbine wake and with the boundary layer, which helps to keeping it attached. Furthermore, higher TI's help in suppressing the tip vortex, thus, reduce turbine tip losses. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic modelling of once-through subcritical steam generator for solar applications

This brief paper outlines a nonlinear dynamic model of a once-through subcritical steam generator for solar thermal plants. The purpose of the model is to describe the overall system performance and component interaction with sufficient accuracy for controller design, rather than to describe the microscopic details occuring within the steam generator. The model equations are arranged in state-space form to facilitate digital simulation and control system design. The modelling methodology is an extension of the earlier work of Ray and Bowman.     

Homogeneous/Heterogeneous Condensation in Transonic Steam Turbine Stages Including Rotor/Stator Interaction

In this numerical investigation we simulate condensing flows typical for the last stages in low pressure steam turbines of large power plants. The main fluid dynamical characteristics are unsteadiness, high free stream turbulence, complex rotor/stator interaction and metastable conditions of the working fluid, leading to partial phase transition and polydispersed two‐phase flow in the transonic regime. Here we focus on a model for simulation of the condensation process which includes simultaneous homogeneous and heterogeneous nucleation. This model is applied to a turbine stage, consisting of one rotor and one stator. We found that the reduction of thermodynamic nonequilibrium by natural or artificial seeding with heterogeneous nuclei can reduce the thermodynamic losses, but after exceeding a certain limit the efficiency may be lower compared with pure homogeneous condensation.     

Mathematical modeling of a steam generator for sensor fault detection

A dynamic model for a nuclear power plant steam generator (vertical, preheated, U-tube recirculation-type) is formulated as a sixth-order nonlinear system. The model integrates nodal mass and energy balances for the primary water, the U-tube metal and the secondary water and steam. The downcomer flow is determined by a static balance of momentum. The mathematical system is solved using transient input data from the Philippsburg 2 (FRG) nuclear power plant. The results of the calculation are compared with actual measured values. The proposed model provides a low-cost tool for the automatic control and simulation of the steam generating process. The “parity-space” algorithm is used to demonstrate the applicability of the mathematical model for sensor fault detection and identification purposes. This technique provides a powerful means of generating temporal analytic redundancy between sensor signals. It demonstrates good detection rates of sensor errors using relatively few steps of scanning time and allows the reconfiguration of faulty signals.     

Modelling and Optimization of Cogeneration Plants

Cogeneration plants have a long tradition in Germany and are used to transfrom a given energy into various destination energies, e.g. natural gas into mechanical, electrical and heat energy. In this paper a cogeneration plant composed of several components like gas turbines, waste heat boilers, steam turbines, etc, is modelled in steady state. The thermo-dynamic behaviour of the plant is determined by a set of measured data, which is used to adopt the mathematical model to the real plant. By defining a suitable objective function incorporating e.g. emission trading, an appropriate NLP-solver can be used to solve the generated model which includes several nonlinear constraints. Solutions for different environmental and business conditions are presented, to demonstrate the enormous potential of the proposed method for energy suppliers. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An interval-valued hesitant fuzzy multigranulation rough set over two universes model for steam turbine fault diagnosis

In the field of mechanical engineering, steam turbine fault diagnosis is a difficult task for mechanical engineers who are confronted with challenges in dealing with copious amounts of uncertain information. Different mechanical engineers may have their own opinions about the system fault knowledge base that differs slightly from other mechanical engineers. Thus, to solve the problems presented by uncertain data analysis and group decision-making in steam turbine fault diagnosis, we propose a new rough set model that combines interval-valued hesitant fuzzy sets with multigranulation rough sets over two universes, called an interval-valued hesitant fuzzy multigranulation rough set over two universes. In the multigranulation framework, both basic definitions and some important properties of the proposed model are presented. Then, we develop a general approach to steam turbine fault diagnosis by using the proposed model. Lastly, an illustrative example is provided to verify the established approach and demonstrate its validity and applicability.     

Wavelet neural network based on islanding detection via inverter‐based DG

In this article, a passive neurowavelet based on islanding detection technique for grid‐connected inverter‐based distributed generation has been developed. Connecting distributed generator to the distribution network has many benefits such as increasing the capacity of the grid and enhancing the power quality. However, it gives rise to many problems. This is mainly due to the fact that distribution networks are designed without any generation units at that level. Hence, integrating distributed generators into the existing distribution network is not problem‐free. Unintentional islanding is one of the encountered problems. Islanding is the situation where the distribution system containing both distributed generator and loads is separated from the main grid as a result of many reasons such as electrical faults and their subsequent switching incidents, equipment failures, or preplanned switching events like maintenance. The proposed method utilizes and combines wavelet analysis and artificial neural network to detect islanding. Discrete wavelet transform is capable of decomposing the signals into different frequency bands. It can be utilized in extracting discriminative features from the acquired voltage signals. Passive schemes have a large nondetection zone (NDZ) and concern has been raised on active method due to its degrading power quality effect. The main emphasis of the proposed scheme is to reduce the NDZ to as close as possible and to keep the output power quality unchanged. The simulations results, performed by MATLAB/Simulink, shows that the proposed method has a small NDZ. Also, this method is capable of detecting islanding accurately within the minimum standard time. © 2014 Wiley Periodicals, Inc. Complexity 21: 309–324, 2015     

Modelling and long-term simulation of a heat recovery steam generator

Developing accurate non-linear dynamical models for heat recovery steam generator (HRSG) units is presented in this article. The common non-linear autoregressive with exogenous input (NARX) system topology was employed to develop the neuro-fuzzy models based on the experimental data taken during field experiments. In this structure, the non-linear behaviours of the HRSG unit can be characterized through interpolation of local linear models associated with different operating regions via fuzzy inference mechanism. The operating regimes were recognized by applying a genetic algorithm-based fuzzy clustering technique to the prepared data sets. The structures of the fuzzy models are defined with respect to the obtained optimal cluster centres and the corresponding membership functions. The parameters of fuzzy rules were adjusted by recursive least-squares estimation method to fit the model responses to real data. The performances of developed models were evaluated by performing a comparison between the model responses and the responses of the real plant. In addition, the stability of the developed models was assessed by perturbing the model inputs from the nominal values. This guarantees the long-term simulation capabilities of the developed models. A comparison between the responses of the corresponding models and the models obtained from some recent modelling approaches was performed to show the advantages of the developed models. The results show the accuracy and reliability of the developed models at transient and steady-state conditions.     

Multivariable adaptive variable structure disturbance rejection control for DFIG system

A novel variable structure and disturbance rejection control strategy for a wind turbines equipped with a double fed induction generator based on stator‐flux‐oriented vector control is presented. According to estimation of maximum power operation points of wind turbine under stochastic wind velocity profiles and tracking them using traditional offline gain, scheduling and innovative adaptive online method is necessary. To demonstrate the effectiveness of the proposed control strategy, the estimation of maximum operating power point of wind turbine and tracking it under stochastic wind velocity profiles has been considered as a test case. Simulation results show the validity of the proposed technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 50–62, 2016     

Locating series FACTS devices for multi-objective congestion management improving voltage and transient stability

Transmission congestion management is a vital task in electricity markets. Series FACTS devices can be used as effective tools to relieve congestion mostly employing Optimal Power Flow based methods, in which total cost as the objective function is minimized. However, power system stability may be deteriorated after relieving congestion using traditional methods leading to a vulnerable power system against disturbances. In this paper, a multi-objective framework is proposed for congestion management where three competing objective functions including total operating cost, voltage and transient stability margins are simultaneously optimized. This leads to an economical and robust operating point where enough levels of voltage and transient security are included. The proposed method optimally locates and sizes series FACTS devices on the most congested branches determined by a priority list based on Locational Marginal Prices. Individual sets of Pareto solutions, resulted from solving multi-objective congestion management for each location of FACTS devices, are merged together to create the comprehensive Pareto set. Results of testing the proposed method on the well-known New-England test system are discussed in details and confirm efficiency of the proposed method.     

An algorithmic approach for maintenance management based on advanced state space systems and harmonic regressions

Point mechanisms are special track elements which failures results in delays and increased operating costs. In some cases such failures cause fatalities. A new robust algorithm for fault detection of point mechanisms is developed. It detects faults by comparing what can be considered the ‘normal’ or ‘expected’ shape of some signal with respect to the actual shape observed as new data become available. The expected shape is computed as a forecast of a combination of models. The proposed system deals with complicated features of the data in the case study, the main ones being the irregular sampling interval of the data and the time varying nature of the periodic behaviour. The system models are set up in a continuous-time framework and the system has been tested on a large dataset taken from a point mechanism operating on a commercial line.     

Transient amplification of maximum vibration amplitudes

Many low damped structures as turbine blades or drill strings are exposed to high dynamical loads causing high vibration amplitudes. These applications comprise sub-critical eigenfrequencies. Hereby, the lower eigenfrequencies have to be passed before reaching the operating point. Most investigations of vibration amplitudes caused by a resonance passage deal with the computation of single degree of freedom systems. Thereby, it has been shown that the stationary vibration response provides the highest possible amplitude. Further it can be stated that the maximum vibration response of the resonance passage decreases with an increasing sweep velocity [3]. Isolated modes of linear systems can be represented by single degree of freedom systems. Subsequently a mode shape can be described by the multiplication of the amplification function of the mode and the belonging eigenvector. There are only some recent works that deal with resonance passages of vicinal modes, e. g. [1]. In this paper the resonance passage of a three dimensional system with nearby modes is studied. To calculate the transient vibration response an analytical approach is used. It is shown that the maximum amplitude of the stationary vibration response is not the upper limit for the maximum amplitude of the resonance passage. Thus, the maximum amplitude may rise while the sweep velocity increases. Hence, regarding a multi degree of freedom system the maximum amplitude of the resonance passage can exceed the maximum amplitude of the stationary vibration response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于NARX神经网络方法的汽轮机转子关键部位应力预测

汽轮机启动过程中,对转子进行应力预测具有重要意义.为满足在线预测国产某350 MW超临界汽轮机转子关键部位应力的需要,提出了一种基于具有外部输入的非线性自回归(NARX)神经网络的应力预测方法.根据转子实际尺寸建立二维轴对称有限元模型,确定了相应的边界条件,并对有限元计算结果进行验证,得到了转子在冷启动工况下的温度场和应力场,确定了转子的危险点.再根据冷启动规则,构建了288个典型启动工况,并对每个启动工况分别进行有限元计算,获取了每个工况下机组运行参数以及转子危险点处应力的时间历程数据,进而建立了神经网络训练样本库,并使用NARX神经网络对危险点处应力进行预测.此基于NARX神经网络的预测方法可以准确预测出汽轮机转子危险点处的应力变化趋势,其预测值与有限元仿真结果吻合良好,可以满足转子应力在线预测的需求.     

Analysis of a viscous soft dielectric elastomer generator operating in an electrical circuit

Dielectric Elastomer Generators (DEGs) are able to convert mechanical work into electric energy. A soft dielectric elastomer generator can be modelled as a strain-dependent variable capacitor undergoing large viscoelastic deformation. In this work we analyze an electrical circuit for energy harvesting in which the DEG is stretched periodically by a source of mechanical work. Since these devices undergo a high number of electro-mechanical loading cycles at large deformation, it turns out that viscous effects must be carefully taken into account as they strongly affect the generator performance. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design of an active fault tolerant control system for a simulated industrial steam turbine

An active fault tolerant control (FTC) scheme is proposed in this paper to accommodate for an industrial steam turbine faults based on integration of a data-driven fault detection and diagnosis (FDD) module and an adaptive generalized predictive control (GPC) approach. The FDD module uses a fusion-based methodology to incorporate a multi-attribute feature via a support vector machine (SVM) and adaptive neuro-fuzzy inference system (ANFIS) classifiers. In the GPC formulation, an adaptive configuration of its internal model has been devised to capture the faulty model for the set of internal steam turbine faults. To handle the most challenging faults, however, the GPC control configuration is modified via its weighting factors to demand for satisfactory control recovery with less vigorous control actions. The proposed FTC scheme is hence able to systematically maintain early FDD with efficient fault accommodation against faults jeopardizing the steam turbine availability. Extensive simulation tests are conducted to explore the effectiveness of the proposed FTC performances in response to different categories of steam turbine fault scenarios.     

Real Gas Effects in Condensing Transonic Steam Flow

Considering the flow in the last stages of LP (low pressure) steam turbine the strong non‐linearity of the thermal parameters of state and the possibility of the two‐phase flow have to be taken into account in the numerical calculation of the flow field. In this paper a 3‐D numerical calculation of the steam condensing flow for the turbine geometry will be presented. The steam properties are described here on the basis of the IAPWS'97 formulation. The calculation of the condensation phenomenon allows one to determine the losses caused by the formation of the liquid phase and to predict the areas of erosion.