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By K. D. W. Nandalal

Dynamic programming is a technique of fixing multi-stage difficulties within which judgements at one level develop into the stipulations governing the succeeding levels. it may be utilized to the administration of water reservoirs, permitting them to be operated extra successfully. this is often one of many few books committed exclusively to dynamic programming options utilized in reservoir administration. It offers the applicability of those suggestions and their limits at the operational research of reservoir platforms. The dynamic programming types provided during this booklet were utilized to reservoir platforms around the globe, aiding the reader to understand the applicability and boundaries of those versions. The publication additionally contains a version for the operation of a reservoir in the course of an emergency state of affairs. This quantity may be a invaluable connection with researchers in hydrology, water assets and engineering, in addition to pros in reservoir administration.

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Extra resources for Dynamic Programming Based Operation of Reservoirs: Applicability and Limits (International Hydrology Series)

Example text

75 (turbines þ generators þ transmission). Reservoir storages and releases are assumed to be the state variables and decision variables, respectively. This maximization is subject to constraints on reservoir storages and releases. Storage constraints and release constraints are identical with those for the single-reservoir case (Eq. 3 and Eq. 4). State transformation equations, which are expressed by the principle of continuity, are as follows. For the upstream reservoir, S1;jþ1 ¼ S1;j þ I1;j À E1;j À R1;j À O1;j : (2:8) For the downstream reservoir, S2;jþ1 ¼ S2;j þ I2;j À E2;j À R2;j þ R1;j þ O1;j À O2;j : (2:9) For the run-of-the-river plant, R3;j ¼ R2;j þ I3;j þ O2;j À O3;j : (2:10) Where Ei,j ¼ evaporation from reservoir i during period j, i ¼ 1, 2 (106 m3), Ii,j ¼ incremental inflow to reservoir i during period j, i ¼ 1, 2 (106 m3), I3,j ¼ incremental inflow to runoff river plant (106 m3), Oi,j ¼ spill from reservoir i during period j, i ¼ 1, 2 (106 m3), O3,j ¼ spill over run-of-the-river plant (106 m3), Ri,j ¼ release from reservoir i during period j, i ¼ 1, 2 (106 m3), R3,j ¼ release through run-of-the-river plant (106 m3), and Si,j ¼ storage of reservoir i at beginning of period j, i ¼ 1, 2 (106 m3).

RMAXi;j and i ¼ 1; 2; j ¼ 1; 2; . . ; T; Si;j SMAXi;j ; Ri;j ¼ RMAXi;j ; when Ri;j ! RMAXi;j ; i ¼ 1; 2; j ¼ 1; 2; . . ; T; Oi;j ¼ 0:0; when Ri;j RMAXi;j ; i ¼ 1; 2; j ¼ 1; 2; . . ; T; (3:16) The storage of the reservoirs during any stage must be within the limits of minimum and maximum live storage capacity. SMAXi;j ; (3:15) SMAXi;jþ1 STORAGE CONSTRAINT Si;j (3:14) and Si;jþ1 SMINi;j (3:13) i ¼ 1; 2; j ¼ 1; 2; . . ; T; (3:10) where SMINi,j ¼ minimum storage of reservoir i at beginning of period j (106 m3), and SMAXi,j ¼ maximum storage of reservoir i at beginning of period j (106 m3).

Due to the characteristics of the Markov sequential decision process, after a large number of iterations of the recursive relation (Eq. 5) the ‘‘steady state’’ for each period in successive years will finally be reached. It is independent of the initial state. There are two criteria marking convergence of the steady state: (i) stabilization of the policy; and (ii) stabilization of the expected annual increment of the objective values. 6. However, experimental evidence shows that often the second criterion of convergence cannot be achieved.

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