Determination of Normal Operating Heights of Reservoirs in a Network Using Non-linear Reservoir Method
M. K. A. Abdulrahman *
Department of Mathematics, Universiti Teknologi Malaysia, Malaysia and Department of Maths., Stats., and Computer Science, Kaduna Polytechnic, Nigeria
A. A. Moh’d Ismail
Department of Mathematics, Universiti Teknologi Malaysia, Malaysia
Sie Long Kek
Department of Mathematics, Universiti Tun Hussein Onn, Malaysia
*Author to whom correspondence should be addressed.
Abstract
In reservoir modeling, making the steady-state policy of the flood control is a challenging task. In this paper, the normal operating heights of a reservoir network is discussed. Initially, the coupled tank system is employed to model the reservoir network. At the equilibrium state, the normal operating heights are then derived analytically. As the linearization is taken, the associated Jacobian matrix, which is a diagonally dominant tridiagonal matrix with negative diagonal entries, is obtained. Because of the negative eigenvalues of this matrix, the stability condition of the reservoir network can be made. For illustration, the different rain rates are used to calculate the surface area of the reservoir and the corresponding normal operating heights of the reservoir are then determined. The result obtained shows the stability of the reservoir. In conclusion, the approach discussed is efficient to the decision making on the stability of a reservoir network.
Keywords: Reservoir network, coupled tank system, tridiagonal matrix, flood control, steady state