# Performance optimization of engineering systems with particular reference to dry-cooled power plants

Thesis (PhD (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 1995.

Thesis

Computer simulation programs were developed for the analysis of dry-cooling systems for power plant applications. Both forced draft direct condensing air"cooled condensers and hyperbolic natural draft indirect dry-cooling towers are considered. The results of a considerable amount of theoretical and experimental work are taken into account to model all the physical phenomena ofthese systems, to formu1ate the problems in formal mathematical terms and to design and apply suitable computational algorithms to solve these problems effectively and reliably. The dry-cooling systems are characterized by equation-based models. These equations are simultaneously solved by a specially designed constrained nonlinear least squares algorithm to determine the performance characteristics of the dry-cooling systems under fixed prescnoed operating conditions, or under varying operating conditions when coupled to a turbo-generator set. The solution procedure is very fast and effective. A capital and operating cost estimation procedure, based on information obtained from dry-cooling system component manufacturers and the literature, is proposed. Analytical functions express the annual cost in terms ofthe various geometrical and operating parameters ofthe dry-cooling systems. The simu1ation and the cost estimation procedures were coupled to a constrained nonlinear programming code which enable the design of minimum cost dry-cooling systems at fixed prescribed operating conditions, or dry-cooling systems which minimize the ratio of total annual cost to the annual net power output of the corresponding turbo-generator set. Since prevailing atmospheric conditions, especially the ambient temperature, influence the performance of dry-cooling systems, wide fluctuations in turbine back pressure occur. Therefore, in the latter case the optimal design is based on the annual mean hourly frequency ofambient temperatures, rather than a fixed value. The equation-based models and the optimization problems are simultaneously solved along an infeasible path (infeasible path integrated approach). The optimization model takes into consideration all the parameters that may affect the capital and operating cost of the dry-cooling systems and does not prescribe any limits, other than those absolutely essential due to practical limitations and to simulate the systems effectively. The influence that changes ofthe constraint limits and some problem parameters have on the optinmm solution, are evaluated (sensitivity analysis). The Sequential Quadratic Programming (SQP) method is used as the basis in implementing nonlinear optimization techniques to solve the cost minimirnti~n problems. A stable dual active set algorithm for convex quadratic programming (QP) problems is implemented that makes use of the special features ofthe QP subproblems associated with the SQP methods. TIrls QP algorithm is also used as part of the algorithm that solves the constrained nonlinear least squares problem This particular implementation of the SQP method proved to be very reliable and efficient when applied to the optimization problems based on the infeasible path integrated approach. However, as the nonlinear optimization problems become large, storage requirements for the Hessian matrix and computational expense of solving large quadratic programming (QP) subproblems become prohibitive. To overcome these difficulties, a reduced Hessian SQP decomposition strategy with coordinate bases was implemented. This method exploits the low dimensionality of the subspace of independent decision variables. The performance of this SQP decomposition is further improved by exploiting the mathematical structure of the engineering model, for example the block diagonal structure ofthe Jacobian matrix. Reductions ofbetween 50-90% in the total CPU time are obtained compared to conventional SQP optimization methods. However, more function and gradient evaluations are used by this decomposition strategy. The computer programs were extensively tested on various optimization problems and provide fast and effective means to determine practical trends in the manufacturing and construction of costoptimal dry-cooling systems, as well as their optimal performance and operating conditions in power plant applications. The dissertation shows that, through the proper application of powerful optimization strategies and careful tailoring of the well constructed optimization model, direct optimization of complex models does not need to be time consuming and difficult. Reconnnendations for further research are made.

Imported from http://etd.sun.ac.za April 2010.