Electric Power Systems Research 76 (2006) 404–412 Parameterisation effect on the behaviour of a head-dependent hydro chain using a nonlinear model J.P.S. Catal˜ ao a,∗ , S.J.P.S. Mariano a , V.M.F. Mendes b , L.A.F.M. Ferreira c a Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha, Portugal b Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Em´ ıdio Navarro, 1950-062 Lisbon, Portugal c Department of Electrical Engineering and Computers, Instituto Superior T´ ecnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal Received 5 March 2005; received in revised form 13 July 2005; accepted 1 September 2005 Available online 3 October 2005 Abstract This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain. We use a method based on nonlinear programming (NLP), namely quadratic programming, to consider hydroelectric power generation a function of water discharge and of the head. The method has been applied successfully to solve a test case based on a realistic cascaded hydro system with a negligible computational time requirement and is also applied to show that the role played by reservoirs in the hydro chain do not depend only on their relative position. As a new contribution to earlier studies, which presented reservoir operation rules mainly for medium and long-term planning procedures, we show that the physical data defining hydro chain parameters used in the nonlinear model have an effect on the STHS, implying different optimal storage trajectories for the reservoirs accordingly not only with their position in the hydro chain but also with the new parameterisation defining the data for the hydro system. Moreover, considering head dependency in the hydroelectric power generation, usually neglected for hydro plants with a large storage capacity, provides a better short-term management of the conversion of the potential energy available in the reservoirs into electric energy, which represents a major advantage for the hydroelectric utilities in a competitive electricity market. © 2005 Elsevier B.V. All rights reserved. Keywords: Short-term hydro scheduling (STHS); Nonlinear programming (NLP); Cascaded reservoirs; Variable head 1. Introduction In this paper, the short-term hydro scheduling (STHS) prob- lem of a head-dependent hydro chain is considered. Hydro plants with a small storage capacity are known as run-of-the-river. Typ- ically, run-of-the-river hydro plants are considered to operate under stationary conditions with constant head and at the maxi- mum water level in the reservoirs, corresponding by design to the optimum efficiency operating point. However, it is often desir- able to change this policy, thus incurring into head changes. The operating efficiency is sensitive to the head–head change effect. Significant loss of efficiency can occur in operating hydro plants away from their most efficient operating point. Thus, hydroelectric power generation has to be considered as a ∗ Corresponding author. E-mail addresses: catalao@ubi.pt (J.P.S. Catal˜ ao), sm@ubi.pt (S.J.P.S. Mar- iano), vfmendes@isel.pt (V.M.F. Mendes), lmf@ist.utl.pt (L.A.F.M. Ferreira). function of water discharge and also of the head in order to avoid this loss of efficiency, that is, in order to take in account the head change effect. In a run-of-the-river cascaded hydraulic configuration an upstream reservoir highly influences the operation of the next downstream reservoir. The latter reservoir also influences the upstream plant by its effect on the tail water elevation and effective head [1]. Actually, the cascaded hydraulic configuration coupled with the nonlinear head change effect, augments the problem dimension and the complexity, but they should be considered because they are important for the most advantage management of the conversion of the potential energy available in the reservoirs into electric energy. In a competitive electricity market, the most advantageous management of the conversion of the potential energy available in the reservoirs into electric energy is not only a major advantage for the hydroelectric utilities, but also is essential for the welfare, development and the economic progress of our society. This is because hydroelectric energy can be regarded as a renewable 0378-7796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2005.09.002