Currently research on joint operation of a large reservoir and its re-regulating reservoir focuses on either water quantity regulation or water head regulation. The accuracy of relevant models is in need of improvement if the influence of factors such as water flow hysteresis and the aftereffect of tail water level variation are taken into consideration. In this paper, given the actual production of Pankou-Xiaoxuan cascade hydropower stations that combines two operation modes (‘electricity to water’ and ‘water to electricity’), a coupling model of their short-term optimal operation is developed, which considers Xiaoxuan reservoir’s regulating effect on Pankou reservoir’s outflow volume and water head. Factors such as water flow hysteresis and the aftereffect of tail water level variation are also considered to enhance the model’s accuracy. The Backward Propagation (BP) neural network is employed for precise calculation of the downstream reservoir’s inflow and the upstream reservoir’s tail water level. Besides, we put forth Accompanying Progressive Optimality Algorithm (APOA) to solve the coupling model with aftereffect. An example is given to verify the scientificity of the proposed model and the advantages of APOA. Through analysis of the model calculation results, the optimal operation rules of the cascade reservoirs are obtained in terms of water quantity regulation and water head regulation, which can provide scientific reference for cascade reservoirs’ optimal operation.

In decision-making with interval numbers, there are problems such as how to reduce the loss of decision information to improve decision accuracy and the difficulty of using interval numbers for sorting. On the basis of fully considering the subjective and objective weights of indexes, the grey entropy method (GEM) is improved by taking advantage of the Mahalanobis-Taguchi System (MTS) in which the orthogonal design has few tests but much obtained information, and the Mahalanobis distance can reflect the correlation between indexes. Then, the signal-to-noise ratio is integrated with the improved degree of balance and approach, and a multi-dimensional interval number decision model based on MTS and GEM is put forth. This model is applied to selecting the optimal scheme of controlling the Pankou reservoir’s water level in flood season. Compared with the decision results of other methods, the optimal scheme selected by the proposed model can achieve greater benefits within an acceptable risk range and thus better coordinate the balance between risk and benefit, which verifies the feasibility and validity of the model.

To narrow the gap between theoretical research and practical application of short-term optimal reservoir power generation operation under uncertain conditions, a comprehensive study is conducted on the formulation, evaluation, and implementation of operation schemes throughout the entire procedure of optimal operation. Firstly, the three implementation modes of the optimal operation scheme are assessed with the post-evaluation method. After the optimal implementation mode is determined, the formulation and implementation of optimal operation schemes are improved by combining the advantages of conventional and optimal operation and using the concept of warning water level in operation rules. Finally, the Xiaoxuan Reservoir is taken as an example for simulation calculation under different operating conditions. The results show that the operation model integrated with operation rules has both the security of conventional operation and the profitability of optimal operation. The accordingly-formulated optimal operation schemes, when implemented with the output control mode, can provide valuable guidance for the actual operation of hydropower stations.

For reservoirs with combined storage capacity for flood control and beneficial purposes, there tends to be potential benefit loss when the flood control limited water level is used in medium and small floods. How to find the optimal water level scheme for profit-making and pursue the optimization of comprehensive benefits has always been a difficult problem in multi-objective reservoir optimal operation. Based on the principle of the maximum benefit obtained by the product conversion curve and the isorevenue line in microeconomics, taking flood control and power generation as two products of a reservoir, a multi-objective optimal operation scheme decision-making model is established to seek the highest water level scheme that can produce the maximum comprehensive benefits of flood control and power generation. A case study of the Three Gorges reservoir in the early flood season of a dry year shows that on the one hand, under the condition of deterministic inflow, the model can work out the optimal water level and the corresponding best equilibrium point for both flood control and power generation, and it can increase the total power output by 4.48% without reducing the flood control benefits; on the other hand, it can also obtain the dynamic control area of the maximum allowable water level for power generation considering inflow forecast error, which provides a theoretical reference for determining the starting water level in medium and small floods and utilizing flood resources.

In the short-term operation of the power generation of cascade reservoirs, uncertainty factors such as inflow forecast errors could cause various types of risks. The inflow to a downstream reservoir is not only affected by inflow forecast errors from upstream reservoirs but also the forecast errors associated with inflow to the stream segment between the reservoirs, such as from a tributary. The inflow forecast errors of different forecast periods may also be correlated. To address this multivariate problem, the inflow forecast error variables were jointly fitted in this study using the Gaussian mixture model (GMM) and a t-Copula function based on the analysis of the error distribution characteristics in different forecast periods. Therefore, a stochastic model that coupled with the GMM and t-Copula to calculate inflow forecast errors in multiple forecast periods was established. Furthermore, according to the simulation results of the stochastic model and the predicted runoff series, a set of simulated runoff processes were obtained. Then they were combined with the existing power generation plan to carry out the risk analysis for short-term operation of the power generation in a cascade reservoir. The approach was evaluated using the Jinguan cascade hydropower system within the Yalong River basin as a case study. For this case study, the risk analysis for short-term operation of the power generation was analyzed based on stochastic simulation of the inflow forecast errors; the results show the feasibility and effectiveness of the proposed methods.