Multi-Stage Dynamic Programming Method for Short-Term Cascade Reservoirs Optimal Operation with Flow Attenuation

Considering water propagation impact in short-term optimal operation of cascade reservoirs using Nested Progressive Optimality Algorithm

Effects of reservoir cascades on diversity, distribution, and abundance of fish assemblages in three Neotropical basins.

Alpine hydropower reservoirs play a crucial role in the energy system as a source of renewable energy and energy storage, as well as in water management mitigating the impacts of extreme events and augmenting freshwater availability. The effective operation of hydropower reservoirs requires knowledge of the expected inflows, and the inflows prediction methods usually require the historical series of observed inflows. The reservoir inflow is often estimated because it is hardly measurable due to its spatial distribution along the reservoir sides. However, traditional methods such as the Simple Water Balance for estimating inflows can yield fluctuating and potentially negative results due to errors in water level measurement and stage-storage relationships. This study focuses on the estimation of inflow to ten reservoirs belonging to three different hydropower cascade systems situated in the Italian Alps. Two new methodologies to estimate reservoir inflow are proposed. The first (Optimized Inflow Estimation from Water Balance, OIEWB) consists of an optimization-based method and extends a known literature optimization technique to cascade reservoirs. In particular, the OIEWB method estimates the inflows to cascade reservoirs solving a bi-objective optimization problem aiming to minimize both the differences between consecutive inflow and the differences between observed and estimated water levels. It also includes an automatic calibration of the weight of the objectives according to the physical characteristics of each reservoir, avoiding any a priori calibration. The second (Filtered Inflow Estimation from Water Balance, FIEWB) consists of a low-pass filter shaped as a piecewise linear function whose slope is defined, again, by the physical characteristics of each reservoir. The low-pass filter is applied to the SWB cascade reservoir inflow to remove the high-frequency fluctuations that can be generated by measurement and estimation errors. The proposed procedures have been compared with the traditionally used ones in terms of Inflow Variability (the difference between inflow at two consecutive time steps) and Storage Error (the difference between the estimated reservoir storage and the observed one). Results show that both the OIEWB and FIEWB methods generate smoother inflows compared to the SWB, reducing the average Inflow Variability standard deviation, of 86.6% and 79.3%, respectively. However, the FIEWB does not guarantee the positivity of the inflows and can lead to large Storage Errors. The OIEWB method has been found to be more flexible and automatically adaptable to reservoirs with a wide range of physical characteristics. Nevertheless, a relationship between the OIEWB and the FIEWB has emerged. This relationship can be used to design new low-pass filters that can emulate the behavior of the OIEWB, combining the flexibility of the latter with the simplicity of the FIEWB. By contributing to provide more accurate and reliable inflow predictions, the proposed methodologies reveal their utility in optimizing cascade reservoir operation, thereby facilitating better decision-making.

Rate-distortion-smoothness optimized rate allocation schemes for Spectral Fine Granular Scalable video coding technique

This paper studies the online dispatch of distribution networks (DNs), which is formulated as a multi-stage dynamic programming (MSDP) to ensure the non-anticipativity of dispatch decisions. Existing approaches usually relegate expensive online optimization to offline learning (typically value function learning) using the given uncertainty distribution or training samples. However, practical DNs may encounter various scenarios where the distributions of uncertainty differ significantly. The optimality of these approaches may degrade substantially in out-of-distribution scenarios unless frequent re-training is conducted. To address this obstacle, this paper proposes a scenario-generalized MSDP (S-MSDP) scheme for online dispatch of DNs. Its main advantage is the ability to directly adapt to new scenarios with high optimality, without re-training or fine-tuning. S-MSDP extends MSDP by learning a universal value function that maps scenario contexts to the corresponding value functions, so that the optimal dispatch policies under different scenarios can be directly inferred by using the learned universal value function. To facilitate the computation and storage burdens brought by large scenario space, a sparse and low-rank tensor approximation is introduced for universal value function learning. Numerical studies verify the optimality, generalization, and scalability of S-MSDP.

The coordinated operation for hydropower generation in cascade reservoirs is critical to resolve the conflicts in hydropower needs between upstream and downstream reservoirs. Due to the individual rationality and collective rationality highlighted by game theory, we propose an integrated game-theoretical model to simulate the coordination behaviors among cascade reservoirs for hydropower generation. In the case study of a cascade-reservoir system in the Yangtze River of China, three operation models are compared and analyzed: the non-cooperative model, centralized model, and integrated game-theoretical model. The factors influencing the coordination efficiency of the integrated game-theoretical model are also explored in this study. The results indicate that the system’s hydropower generation obtained by the integrated game-theoretical model is closer to the ideal solution obtained by the centralized model compared to that obtained by the non-cooperative model. Moreover, individual hydropower generation in non-cooperation (rational individual gains) is guaranteed by the integrated game-theoretical model, which is neglected by the centralized model. Furthermore, the coordination efficiency of the integrated game-theoretical model is influenced by the water availability variation and regulation capacities of cascade reservoirs.

Oscillation method is one of the most instructive methods to evaluate lower permeability and storage capacity coincidently. Constant sinusoidal pore pressure changes at upstream side of the specimen give rise to a response of sinusoidal pressure changes at downstream reservoir with amplitude attenuation and phase retardation. By measuring the attenuation and the retardation, the permeability and the storage capacity can be calculated. If the specimen has lower permeability, the pressure of downstream reservoir responds smaller amplitude and larger retardation against pressure wave at upstream reservoir. The usual graphical analysis estimates how the range of the attenuation and the retardation measured can produce most accurate values of permeability and storage capacity respectively. The most accurate value of the permeability can be required at 0.08 of attenuation and -87° of retardation, and that of the storage capacity is at 0.12 of attenuation and -117° of retardation. However, the graphical analysis is inefficient because of requires lot of data set of permeability and storage capacity. Then, we developed a calculation program to increase the calculation efficiency by using the iterated Newton method.As examples, we investigate the permeability and the storage capacity changes while a fault in sandstone entrained low-permeable siltstone along sandstone surface during the sliding. To obtain the amplitude and the phase of both pressure waves of upstream and downstream reservoirs, Fourier transform was adopted. This Fourier analysis occurs periodic errors with twice frequency of the oscillation test on the data of the amplitude attenuation and the phase retardation. These periodic errors on the attenuation and the retardation induced more 2 orders of magnitude variations on the result of storage capacity when the attenuation and the retardation are lower. With these reductions, the variation of storage capacity becomes less than one order of magnitude. On the other hand, the permeability resulted from the oscillation method is independent on the pressure conditions and the accuracy is higher than that of the storage capacity.

Carbon emission from reservoirs is considered to tarnish the green credentials of hydropower and has been extensively studied in single reservoirs. However, it remains unclear how carbon emission differs in cascade reservoirs and the mechanism behind the differences. In this study, carbon dioxide (CO2) and methane (CH4) emissions from cascade hydropower reservoirs were measured in the Lancang River, the Chinese section of the Mekong River. Our results demonstrate that carbon emissions from the river were increased by dam construction but exhibited spatial heterogeneity among cascade reservoirs. The first, most upstream, reservoir acted as the hotspot of CH4 and CO2 emissions, which were 13.1 and 1.7 times higher than those in downstream reservoirs, respectively. Similarly, the CH4/CO2 ratio of 0.023 in the first reservoir was higher than the others and made a greater contribution to the global warming effects of the cascade reservoirs. The sediment organic carbon in downstream reservoirs was negatively correlated with reservoir age (r2 = 0.993) and decreased at a rate of 0.389 mg g-1 yr-1, suggesting a potential decrease of carbon emission in the future. This study adds to our understanding of carbon emissions from cascade reservoirs and helps to screen effective strategies for future mitigation of the global warming effects from cascade hydropower systems.

Accurate and reliable forecasting of reservoir inflow is necessary for efficient and effective water resources planning and management. The aim of this study is to develop an ensemble modeling approach based on wavelet analysis, bootstrap resampling and neural networks (BWANN) for reservoir inflow forecasting. In this study, performance of BWANN model is also compared with wavelet based ANN (WANN), wavelet based MLR (WMLR), bootstrap and wavelet analysis based multiple linear regression models (BWMLR), standard ANN, and standard multiple linear regression (MLR) models for inflow forecasting. Robust ANN and WANN models are ensured considering state of the art methodologies in the field. For development of WANN models, initially original time series data is decomposed using wavelet transformation, and wavelet sub-time series are considered to develop WANN models instead of standard data used for development of ANN model. To ensure a robust WANN model different types of wavelet functions are utilized. Further, a comparative analysis is carried out among different approaches of WANN model development using wavelet sub time series. Seven years of reservoir inflow data along with outflow data from two upstream reservoirs in the Damodar catchment along with rainfall data of 5 upstream rain gauge stations are considered in this study. Out of 7 years daily data, 5 years data are used for training the model, 1 year data are used for cross-validation and remaining 1 year data are used to evaluate the performance of the developed models. Different performance indices indicated better performance of WANN model in comparison with WMLR, ANN and MLR models for inflow forecasting. This study demonstrated the effectiveness of proper selection of wavelet functions and appropriate methodology for wavelet based model development. Moreover, performance of BWANN models is found better than BWMLR model for uncertainty assessment, and is found that instead of point predictions, range of forecast will be more reliable, accurate and can be very helpful for operational inflow forecasting.

In this paper, a method for long-term optimal operation of hydropower station is proposed to control the frequency of reservoir level fluctuation. We introduce the integer variable which describes the rise and fall of the reservoir level, the number of changes, and the state transition equation for the change of the reservoir level fluctuation into the dynamic programming method. This method can obtain the global optimal solution under the control of different numbers of reservoir level rise and fall, thus improving the controllability and practicability of optimal operating results. We consider the maximum number of water level fluctuations as a constraint condition while the reservoir level, the state of fluctuation, and the number of state changes that have occurred as the three state variables to construct a dynamic programming model. Three state transition equations are the water balance, the state of the reservoir level rise and fall, and the number of fluctuations. Besides, the penalty function is used to handle minimum output and surplus water. We solve this model by using a dynamic programming reverse recursion equation. The application of this method in the Manwan Hydropower Station shows that it can effectively solve the frequent water level fluctuation problem that is generally inconsistent with the actual situation in the long-term optimal dispatch scheme of hydropower stations and improve the practicability of the optimal dispatch results.

In order to study the problem of selecting suppliers and ordering different categories of raw materials, a decision-making method combined with evaluation models and dynamic planning is proposed based on relevant data from suppliers and forwarders between 2016 and 2020. Firstly, an evaluation model applying gray correlation analysis and entropy weight method is developed to narrow down the range of suppliers waiting to be selected, and then a multi-stage dynamic planning model is established to make a decision on the order policy. After that, it is analyzed empirically. And the final results demonstrates that the selected suppliers supply raw materials stably, the order policy is feasible for long-term implementation and the total cost of it is low.

The construction of cascade reservoirs on the Lancang River (the upper Mekong) has an important influence on the distribution and accumulation of heavy metals. Heavy metal contents in porewater provide vital information about their bioavailability, studies on this aspect are rare until now. In this study, sediment cores were collected from four adjacent cascade reservoirs in the upper Mekong River to study the distribution, potential sources, diffusive fluxes and toxicity of heavy metals in porewater. The findings indicated that the average contents of Mn, Fe, As, Ni, Cu, Zn, Cd, and Pb in the sediment porewater were 6442, 644, 11.50, 2.62, 1.23, 3.95, 0.031, and 0.24µg/L, respectively; these contents varied as the sediment depth increased. Correlation analysis and principal component analysis showed that Cu, Zn, Cd and Pb were mainly associated with anthropogenic sources, As, Mn and Fe were primarily affected by natural inputs, and Ni was affected by a combination of natural and anthropogenic effects. The diffusive fluxes of Mn, Fe, As, Ni, Cu, Zn, Cd, and Pb in the cascade reservoirs of the Lancang River were 919 - 35,022, 2.12 - 2881, 0.17 - 750, 0.71 - 7.70, 2.30 - 31.18, (-3.35) - 6.40, 0.06 - 0.54, and (-0.52) - 4.08µg/(m2 day), respectively. The results of toxic units suggested that the contamination and toxicity of heavy metals in porewater were not serious. Overall, in the cascade reservoirs, the content and toxicity of heavy metals in porewater of the upstream reservoirs were higher than that of the downstream reservoirs. The operation of the cascade reservoirs enabled greater accumulation of contaminants in sediments of the upstream reservoirs. This research gives strong support for the prevention of heavy metal contamination and the sustainability of water resources under the running condition of cascade reservoirs on such a large international river (the Lancang-Mekong River).

Unveiling the potential phosphorus retention effect in small-scale cascade reservoir systems: evidence from the Weiyuan River.

A proposed stochastic dynamic programming (SDP) method with uncertainties in stream flow and water demand is developed to calculate optimal reservoir operation rules. The SDP method extends the classic SDP method that considers only one uncertainty in its operation rules. Time series of reservoir inflow and agricultural water demand for the Aydoghmoush Reservoir in eastern Azarbayejan, Iran, were obtained from meteorological data, available climate parameters, hydrologic data, and crop water demand. The application of the developed SDP with two uncertainties was evaluated with operation rules corresponding to four different scenarios, and optimal reservoir releases were determined for a drought year. Reservoir operation results were evaluated with different performance indices. This study's results demonstrate the advantage of considering uncertainties in reservoir inflow and water demand with the SDP method. The developed SDP method has general applicability under a range of climatic conditions, and the calculated operation rules cover the expected ranges of streamflow and water demand during the operating years.

Unveiling the effects of dissolved organic matter on heavy metal(loid)s distribution in the Wujiang cascade reservoirs, China.