The perennial storage water level (PL), the water level at the end of wet season (WL), and the water level at the end of dry season (DL) are three critical water levels for multiyear regulating storage (MRS) reservoirs. Nevertheless, the three critical water levels have not been paid enough attention, and there is no general method that calculates them in light of developing regulating rules for MRS reservoirs. In order to address the issue, three-parameter regulation (TPR) rules based on the coordination between the intra- and interannual regulation effects of MRS reservoirs are presented. Specifically, a long-term optimal scheduling (LTOS) model is built for maximizing the multiyear average hydropower output (MAHO) of a multireservoir system. The TPR rules are a linear form of rule with three regulation parameters (annual, storage, and release regulation parameters), and use the cuckoo search (CS) algorithm to solve the LTOS model with three regulation parameters as the decision variables. The approach of utilizing the CS algorithm to solve the LTOS model with the WL and DL as the decision variables is abbreviated as the OPT approach. Moreover, the multiple linear regression (MLR) rules and the artificial neural network (ANN) rules are derived from the OPT approach-based water-level processes. The multireservoir system at the upstream of Yellow River (UYR) with two MRS reservoirs, Longyangxia (Long) and Liujiaxia (Liu) reservoirs, is taken as a case study, where the TPR rules are compared with the OPT approach, the MLR rules, and the ANN rules. The results show that for the UYR multireservoir system, (1) the TPR rules-based MAHO is about 0.3% (0.93 × 108
kW∙h) more than the OPT approach-based MAHO under the historical inflow condition, and the elapsed time of the TPR rules is only half of that of the OPT approach; (2) the TPR rules-based MAHO is about 0.79 × 108
kW∙h more than the MLR/ANN rules-based MAHO under the historical inflow condition, and the TPR rules can realize 0.1–0.4% MAHO more than the MLR and ANN rules when the reservoir inflow increases or reduces by 10%. According to the annual regulation parameter, the PLs of Long and Liu reservoirs are 2572.3 m and 1695.2 m, respectively. Therefore, the TPR rules are an easy-to-obtain and adaptable LTOS rule, which could reasonably and efficiently to determine the three critical water levels for MRS reservoirs.
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