Combined cycle dynamics

Author(s):  
F. M. Mansour ◽  
A. M. Abdul Aziz ◽  
S. M. Abdel-Ghany ◽  
H. M. El-shaer

A mathematical model describing the dynamic behaviour of each major component of the combined cycle is presented. The formulae are deduced from continuity, momentum, energy, and state equations. Partial differential equations (PDEs) are discretized to algebraic equations by using the implicit backward-central finite difference scheme and then solved by iteration. Explicit-Euler's integration method is applied to other differential equations (DEs). A multi-element control system is implemented to investigate its effect on the combined cycle's dynamic response. The simulation results are compared with the design and steady-state operational data of the unit number 4 in Cairo South Combined Cycle Power Plant, showing good agreement. The dynamic results prove the effectiveness of the multi-element control strategy to control the combined cycle plant with fast settling time, neglected steady-state error, and moderate overshoot or undershoot while assuring a stable operation under sudden changes of load.

Author(s):  
H A Arafa ◽  
M Rizk

This paper deals with an analytical and experimental assessment of the flow force effects on electrohydraulic servo-valve steady state characteristics. The system mathematical model is derived, and special consideration is given to non-linearity of the feedback wire stiffness and magnetic saturation of the armature. The ‘spool hydraulic stiffness’ is defined and expressed in terms of the servo-valve parameters and supply pressure to allow clear interpretation of the nature of flow force effects. Experimental results of spool displacement decrement due to flow force versus net displacement are in good agreement with the predicted performance in a wide range of input current up to almost full magnetic saturation. The results provide evidence, on an alternative basis, of the non-linear feedback behaviour. Correlation is also made between flow force and limits of stable operation, and an expression is derived for the maximum allowable supply pressure.


Author(s):  
Xiaomo Jiang ◽  
Eduardo Mendoza ◽  
TsungPo Lin

Condition monitoring and diagnostics of a combined cycle gas turbine power plant has become an important tool to improve its availability, reliability, and performance. However, there are two major challenges in the diagnostics of performance degradation and anomaly in a single shaft combined cycle power plant. First, since the gas turbine and steam turbine in such a plant share a common generator, each turbine’s contribution to the total plant power output is not directly measured, but must be accurately estimated to identify the possible causes of plant level degradation. Second, multivariate operational data instrumented from a power plant need to be used in the plant model calibration, power splitting and degradation diagnostics. Sensor data always contains some degree of uncertainty. This adds to the difficulty of both estimation of gas turbine to steam turbine power split and degradation diagnostics. This paper presents an integrated probabilistic methodology for accurate power splitting and the degradation diagnostics of a single shaft combined cycle plant, accounting for uncertainties in the measured data. The method integrates the Bayesian inference approach, thermodynamic physics modeling, and sensed operational data seamlessly. The physics-based thermodynamic heat balance model is first established to model the power plant components and their thermodynamic relationships. The model is calibrated to model the plant performance at the design conditions of its main components. The calibrated model is then employed to simulate the plant performance at various operating conditions. A Bayesian inference method is next developed to determine the power split between the gas turbine and the steam turbine by comparing the measured and expected power outputs at different operation conditions, considering uncertainties in multiple measured variables. The calibrated model and calculated power split are further applied to pinpoint the possible causes at individual components resulting in the plant level degradation. The proposed methodology is demonstrated using operational data from a real-world single shaft combined cycle power plant with a known degradation issue. This study provides an effective probabilistic methodology to accurately split the power for degradation diagnostics of a single shaft combined cycle plant, addressing the uncertainties in multiple measured variables.


2015 ◽  
Vol 53 (5) ◽  
pp. 545-552
Author(s):  
Shin Hyuk Kim ◽  
Lee Si Hwang ◽  
Yong Jin Joo ◽  
Sang Uk Lee ◽  
Byung Mo Shon ◽  
...  

Author(s):  
Ahmed A. Shabana ◽  
Ahmed K. Aboubakr ◽  
Lifen Ding

In this investigation, a new three-dimensional nonlinear train car coupler model that takes into account the geometric nonlinearity due to the coupler and car body displacements is developed. The proposed nonlinear coupler model allows for arbitrary three-dimensional motion of the car bodies and captures kinematic degrees of freedom that are not captured using existing simpler models. The coupler kinematic equations are expressed in terms of the car body coordinates, as well as the relative coordinates of the coupler with respect to the car body. The virtual work is used to obtain expressions for the generalized forces associated with the car body and coupler coordinates. By assuming the inertia of the coupler components negligible compared to the inertia of the car body, the system coordinates are partitioned into two distinct sets: inertial and noninertial coordinates. The inertial coordinates that describe the car motion have inertia forces associated with them. The noninertial coupler coordinates; on the other hand, describe the coupler kinematics and have no inertia forces associated with them. The use of the principle of virtual work leads to a coupled system of differential and algebraic equations expressed in terms of the inertial and noninertial coordinates. The differential equations, which depend on the coupler noninertial coordinates, govern the motion of the train cars; whereas the algebraic force equations are the result of the quasi-static equilibrium conditions of the massless coupler components. Given the inertial coordinates and velocities, the quasi-static coupler algebraic force equations are solved iteratively for the noninertial coordinates using a Newton–Raphson algorithm. This approach leads to significant reduction in the numbers of state equations, system inertial coordinates, and constraint equations; and allows avoiding a system of stiff differential equations that can arise because of the relatively small coupler mass. The use of the concept of the noninertial coordinates and the resulting differential/algebraic equations obtained in this study is demonstrated using the knuckle coupler, which is widely used in North America. Numerical results of simple train models are presented in order to demonstrate the use of the formulation developed in this paper.


1999 ◽  
Vol 123 (1) ◽  
pp. 251-254 ◽  
Author(s):  
J. Bausa ◽  
G. Tsatsaronis

In the first part of this study, a general method for solving dynamic optimization problems has been presented: the dynamic process model, consisting of first-order ordinary differential equations (ODEs) and algebraic equations, is discretized over the time horizon using well established methods for the solution of ODEs. The discretized system is then treated as large-scale non-linear parameter optimization problem. This transformation is implemented in a user-friendly software package. An application of this software is demonstrated in the present paper by optimizing the process of rapid load-increase in a single-pressure combined-cycle power plant. The power plant is described with a simplified model that consists of 18 first order ordinary differential equations and 67 algebraic equations. For this model a time-optimal operation associated with a load increase from 50 percent to 75 percent of base load is calculated by considering given restrictions on some temperature gradients.


BioResources ◽  
2020 ◽  
Vol 15 (3) ◽  
pp. 7079-7099
Author(s):  
Jianying Chen ◽  
Guojing He ◽  
Xiaodong (Alice) Wang ◽  
Jiejun Wang ◽  
Jin Yi ◽  
...  

Timber-concrete composite beams are a new type of structural element that is environmentally friendly. The structural efficiency of this kind of beam highly depends on the stiffness of the interlayer connection. The structural efficiency of the composite was evaluated by experimental and theoretical investigations performed on the relative horizontal slip and vertical uplift along the interlayer between composite’s timber and concrete slab. Differential equations were established based on a theoretical analysis of combination effects of interlayer slip and vertical uplift, by using deformation theory of elastics. Subsequently, the differential equations were solved and the magnitude of uplift force at the interlayer was obtained. It was concluded that the theoretical calculations were in good agreement with the results of experimentation.


2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.


2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.


2020 ◽  
Vol 7 (1) ◽  
pp. 48-55 ◽  
Author(s):  
Bolat Duissenbekov ◽  
Abduhalyk Tokmuratov ◽  
Nurlan Zhangabay ◽  
Zhenis Orazbayev ◽  
Baisbay Yerimbetov ◽  
...  

AbstractThe study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables, i.e., stiffness surface and through-thickness stiffness. Differential equations under consideration were evaluated in the form of algebraic equations with the finite element method. For a reinforced shell, a system of 98 equations on a 8×8 grid was established, which was next solved with the approximation method from the nonlinear plasticity theory. A test case involved computing a 1×1 shallow shell taking into account the nonlinear properties of concrete. With nonlinear equations for the concrete creep taken as constitutive, equations for the quasi-static shell motion under constant load were derived. The resultant equations were written in a differential form and the problem of solving these differential equations was then reduced to the solving of the Cauchy problem. The numerical solution to this problem allows describing the stress-strain state of the shell at each point of the shell grid within a specified time interval.


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