Similar articles

Abstract: The simulation of a high-temperature gas-cooled reactor pebble-bed module (HTR-PM) plant is discussed. This lumped parameter model has the form of a set differential algebraic equations (DAEs) that include stiff equations to model point neutron kinetics. The nested approach is the most common method to solve DAE, but this approach is very expensive and time-consuming due to inner iterations. This paper deals with an alternative approach in which a simultaneous solution method is used. The DAEs are discretized over a time horizon using collocation on finite elements, and Radau collocation points are applied. The resulting nonlinear algebraic equations can be solved by existing solvers. The discrete algorithm is discussed in detail; both accuracy and stability issues are considered. Finally, the simulation results are presented to validate the efficiency and accuracy of the simultaneous approach that takes much less time than the nested one.

[1]Antonio, F.T., Biegler, L.T., Enrique, S.V.G., 2005. Dynamic optimization of HIPS open-loop unstable polymerization. Industrial and Engineering Chemical Research, 44(8):2659-2674.

[2]Ascher, U.M., Petzold, L.R., 1998. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Society for Industrial and Applied Mathematics, Philadelphia, USA.

[3]Betts, J.T., 2001. Practical Methods for Optimal Control Using Nonlinear Programming. SIAM, Philadelphia, USA.

[4]Biegler, L.T., 2007. An overview of simultaneous strategies for dynamic optimization. Chemical Engineering and Processing: Process Intensification, 46(11):1043-1053.

[5]Biegler, L.T., Zavala, V., 2009. Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization. Computers & Chemical Engineering, 33(3):575-582.

[6]Biegler, L.T., Cervantes, A.M., Wächter, A., 2002. Advances in simultaneous strategies for dynamic process optimization. Chemical Engineering Science, 57(4):575-593.

[7]Breitenecker, F., Popper, N., 2009. Classification and Evaluation of Features in Advanced Simulators. Proceedings MATHMOD Vienna, p.1445-1467.

[8]Cai, Z., 2005. Nuclear Power Reactor Neutron Dynamics. National Defense Industry Press, Beijing, p.154-177 (in Chinese).

[9]Cervantes, A., Biegler, L.T., 1999. Optimization Strategies for Dynamic Systems. Kluwer Academic Publishers, Kluwer.

[10]Chen, Y., Shao, Z., Qian, J., Wang, K., 2010. Global versus local orthogonal collocation in simultaneous approach. CIESC Journal, 61(2):384-391 (in Chinese).

[11]Colonna, P., van Putten, H., 2007. Dynamic modeling of steam power cycles: Part I—Modeling paradigm and validation. Applied Thermal Engineering, 27(2-3):467-480.

[12]Dong, Z., Huang, X., Feng, J., Zhang, L., 2009. Dynamic model for control system design and simulation of a low temperature nuclear reactor. Nuclear Engineering and Design, 239(10):2141-2151.

[13]Feehery, W.F., Banga, J.R., Barton, P.I., 1995. A Novel Approach to Dynamic Optimization of ODE and DAE Systems as High Index Problems. AIChE Annual Meeting, Miami Beach, FL, USA.

[14]Haire, E., Wanner, G., 2006. Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems (2nd Ed.). Science Press, Springer-Verlag, Berlin, Heidelberg, Germany.

[15]Hangos, K.M., Cameron, I.T., 2001. Process Modelling and Model Analysis. Academic Press, San Diego, CA, USA.

[16]Kameswaran, S., Biegler, L., 2006. Simultaneous dynamic optimization strategies: Recent advances and challenges. Computers & Chemical Engineering, 30(10-12):1560-1575.

[17]Li, H., Huang, X., Zhang, L., 2008a. A lumped parameter dynamic model of the helical coiled once-through steam generator with movable boundaries. Nuclear Engineering and Design, 238(7):1657-1663.

[18]Li, H., Huang, X., Zhang, L., 2008b. Operation and control simulation of a modular high temperature gas cooled reactor nuclear power plant. IEEE Transactions on Nuclear Science, 55(4):2357-2365.

[19]Li, H., Huang, X., Zhang, L., 2008c. A simplified mathematical dynamic model of the HTR-10 high temperature gas-cooled reactor with control system design purposes. Annals of Nuclear Energy, 35(9):1642-1651.

[20]Lv, C., 2002. System Simulation and Modelling on Large Power Unit. Tsinghua University Press, Beijing, China, p.208-222 (in Chinese).

[21]Ni, W., 1996. Some Problems on Thermal Power System Modelling and Control. Science Press, Beijing, China, p.186-200 (in Chinese).

[22]Robbins, C., Hoggett-Jones, C., 2002. Modular simulation software for modelling the impacts of alternative spent fuel management practices in the nuclear power industry. Simulation Modelling Practice and Theory, 10(3-4):153-168.

[23]Shen, J., Tang, T., 2006. Spectral and High-Order Methods with Applications. Science Press, Beijing, China (in Chinese).

[24]Shirazi, S., Mousavi, A., Aghanajafi, C., Sadoughi, S., Sharifloo, N., 2010. Design, construction and simulation of a multipurpose system for precision movement of control rods in nuclear reactors. Annals of Nuclear Energy, 37(12):1659-1665.

[25]Tobias, J., Biegler, L.T., Wächter, A., 2003. Dynamic optimization of the Tennessee Eastman process using the OptControlCentre. Computers & Chemical Engineering, 27(11):1513-1531.