The fast startup and load-increasing process of power plants is a complex task involving several restrictions that have to be fulfilled simultaneously. An important restriction is the maximum allowed thermal stress of the steam generator pipes and the steam turbines caused by temperature gradients. In this paper the startup process is treated as a dynamic optimization problem. Any appropriate objective function can be used in this optimization problem. Examples include the minimization of fuel consumption or the minimization of the time required to reach the desired load. The maximum allowable temperature and pressure gradients in major plant components appear as additional constraints. In this paper a general method for solving these problems is 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. Thus, the continuous dynamic optimization problem is transformed into a large-scale non-linear parameter optimization problem with up to 20,000 optimization parameters and constraints. Such parameter optimization problems can be solved with appropriate sequential quadratic programming (SQP) methods that have become available lately. An application of this method is presented in the second part of this study by optimizing the process of rapid load increase in a single-pressure combined-cycle power plant on the basis of a simplified model.

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ZnO nanocrystals with various shapes (see Figure) have been synthesized via non‐hydrolytic ester elimination sol–gel reactions between zinc acetate and 1,12‐dodecanediol. Uniform anisotropic cone‐shaped, hexagonal cone‐shaped, and rod‐shaped ZnO nanocrystals have been synthesized using various surfactants.

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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.