Algorithms for Optimizing Hydropower System Operation

Abstract

Successive linear programming, an optimal control algorithm, and a combination of linear programming and dynamic programming (LP‐DP) are employed to optimize the operation of multireservoir hydrosystems given a deterministic inflow forecast. The algorithm maximize the value of energy produced at on‐peak and off‐peak rates, plus the estimated value of water remaining in storage at the end of the 12‐month planning period. The LP‐DP algorithm is clearly dominated: it takes longer to find a solution and produces significantly less hydropower than the other two procedures. Successive linear programming (SLP) appears to find the global maximum and is easily implemented. For simple systems the optimal control algorithm finds the optimum in about one fifth the time required by SLP but is harder to implement. Computing costs for a two‐reservoir, 12‐month deterministic problem averaged about seven cents per run using optimal control and 37 cents using successive linear programming.

Capacity optimization of hydropower storage projects using particle swarm optimization algorithm

“…Successive linear programming (SLP) (Yeh et al 1979;Grygier & Stedinger 1985) and sequential quadratic programming (SQP) (Powell 1983;Marino & Loaiciga 1985;Diaz & Fontane 1989) Minimizing the cost of design and operation of a hydropower dam reservoir system may be formulated as a nonlinear optimization problem. In this problem, hydraulic, hydrologic and physical equations simulate the proper performance of the system under different design and/or operational conditions.…”

Optimizing profits from hydroelectricity production

“…In equation (22), a cost for spinning is incurred when a unit offers 10S reserve without producing electricity at the same time. Furthermore, equations (23) to (26) state that a cost is incurred when the unit needs a start-up. Thus, this cost is added when there is some production at the current period p (y E d,u,p = 1) but no production at the previous period p − 1 (y E d,u,p−1 = 0).…”

“…Thus, this cost is added when there is some production at the current period p (y E d,u,p = 1) but no production at the previous period p − 1 (y E d,u,p−1 = 0). Note that equation (23) assumes that there is no production before period 1 (i.e., at period 0). Note also that equations (25) and (26) are not mandatory as the optimization process minimizes the start-up costs.…”

“…This section describes how non linear water head effects can be evaluated using a successive linear programming method that is often reported in the literature on water management [3,18,23,51]. The method starts from the initial solution obtained by solving the original model.…”

Chance-constrained optimal control for multireservoir system optimization and risk analysis

“…Computational effort and storage requirements were shown to increase linearly with the state dimension of the problem, thereby permitting ef®cient application to large-scale systems. While these applications overcome dif®culties in incorporating state-space constraints through use of penalty terms, Grygier and Stedinger (1985) attempted to directly include state variable constraints in the OCT problem without resorting to penalty terms. This results in complex corner or jump optimality conditions that are dif®cult to evaluate for large-scale systems.…”