Optimal Multipurpose-Multireservoir Operation Model with Variable Productivity of Hydropower Plants

Optimal operation of a multipurpose multireservoir system in the Eastern Nile River Basin

“…See Tilmant and Kelman (2007) and Goor et al (2010) for a detailed explanation on how those parameters are derived from the primal and dual information available at the solution of the numerous one-stage optimization problems (7-15) at stage t + 1. The approximation of hydropower functionsP t are also stored as constraints:…”

“…The detailed methodology to calculate the convex hull approximation and the parameters ψ h , ω h and δ h is described by Goor et al (2010). The SDDP model is coded in MATLAB ® and relies on the open-source COIN-OR Linear Programming solver CLP (http://www.coin-or.org/projects/Clp.xml) to solve the onestage problem (7) to (15).…”

“…To remove this source of non-convexity, the hydropower production function is estimated by a convex hull approximation. The detailed methodology to calculate the convex hull approximation and the parameters is described by Goor et al (2010). The net benefit from the agricultural sector, denoted IR t , is the sum of the benefits obtained at each irrigation demand site d as a function of the volume of water y (d,p) t f that has been delivered to the crops p at that site d during the irrigation season:…”

A framework for incorporating ecological releases in single reservoir operation

“…The objectives of the study reported in this paper are to: (1) develop a reservoir operation framework for restoring the flow Notations J total days in the decision horizon s j end storage on day j I j reservoir inflow on day j x j downstream release on day j, assumed to be flowing through turbines ws j water supply release on day j sp j spillage on day j R j release for other purposes on day j s min minimum allowable storage s max maximum allowable storage P 1 monthly mean downstream flow P 2 1-day minimum flow P 3 3-day minimum flow P 4 7-day minimum flow P 5 3-day maximum flow P 6 7-day maximum flow h i j a binary variable associated with the ith ecological flow parameter on day j C a large positive number C ⁄ a large positive number q i 1 a binary variable associated with the ith ecological flow parameter, it is 1 if the ith ecological flow parameter is less than its low boundary, t arg et i min q i 2 a binary variable associated with the ith ecological flow parameter, it is 1 if the ith ecological flow parameter is larger than its upper boundary, t arg et i max }ws j releases for water supply on day j wd j daily domestic (industrial) water demand s j estimated average storage for day j r water supply satisfaction ratio st k breakpoints on the storage axis in the linearization of storage-head curve a k,j a real number between 0 and 1 associated with each breakpoint b k,j a binary variable associated with each interval on storage axis b 0,j , b K1,j two dummy binary variables associated with the two end points, both are 0 he j estimated monthly mean water elevation in the reservoir E j approximated daily hydropower generation f(st k ) the water head corresponds to a certain storage, st k , is provided to piecewise linearize the storage-head curve. q k break points on the release axis b l,j a binary variable associated with each interval on the elevation axis y l mid points of each interval on the elevation axis M a large positive number K 1 the number of breaking points (including two end points) in linearization of Storage-Elevation curve K 2 the number of breaking points (including two end points) in modeling of Energy-Elevation-StorageRelease relationship g allowable number of mis-hits E firm yield monthly firm energy requirement f ðq k ;ỹ l Þ daily hydropower generation corresponds to a break point q k on the release axis and midpointỹ l for the intervals on elevation axis regime to pre-impact conditions; (2) implement and test the framework using a daily reservoir operation model considering anthropogenic water needs and ecological flow releases; and (3) investigate the tradeoff between meeting anthropogenic water needs and ecological flow requirements.…”

Valuation of Multiple Hyro Reservoir Storage Systems in Competitive Electricity Markets

“…Moreover, Tilmant et al (2008) and Goor et al (2011) extend the subject to water resources planning and take irrigation issues into account. Thereby Pereira et al (1999), Tilmant et al (2008) and Goor et al (2011) apply stochastic dual dynamic programming (SDDP) on a cascaded multireservoir system. Applying SDDP to this scheduling problem avoids the curse of dimensionality occurring in dynamic optimization problems.…”