Extracting Optimal Policies of Hydropower Multi-Reservoir Systems Utilizing Enhanced Differential Evolution Algorithm

Deriving the optimal policies of hydropower multi-reservoir systems is a nonlinear and high-dimensional problem which makes it difficult to achieve the global or near global optimal solution. In order to optimally solve the problem effectively, development of optimization methods with the purpose of optimizing reservoir operation is indispensable as well as inevitable. This paper introduces an enhanced differential evolution (EDE) algorithm to enhance the exploration and exploitation abilities of the original differential evolution (DE) algorithm. The EDE algorithm is first applied to minimize two benchmark functions (Ackley and Shifted Schwefel). In addition, a real world two-reservoir hydropower optimization problem and a large scale benchmark problem, namely ten-reservoir problem, were considered to indicate the effectiveness of the EDE. The performance of the EDE was compared with the original DE to solve the three optimization problems. The results demonstrate that the EDE would have a powerful global ability and faster convergence than the original DE to solve the two benchmark functions. In the 10-reservoir optimization problem, the EDE proved to be much more functional to reach optimal or near optimal solution and to be effective in terms of convergence rate, standard deviation, the best, average and worst values of objective function than the original DE. Also, In the case of two-reservoir system, the best values of the objective function obtained 93.86 and 101.09 for EDE and DE respectively. Based on the results, it can be stated that the most important reason to improve the performance of the EDE algorithm is the promotion of local and global search abilities of the DE algorithm using the number of novel operators. Also, the results of these three problems corroborated the superior performance, the high efficiency and robustness of the EDE to optimize complex and large scale multi-reservoir operation problems.     

Sustainable Basin-Scale Water Allocation with Hydrologic State-Dependent Multi-Reservoir Operation Rules

This study extends the PSO-MODSIM model, integrating particle swarm optimization (PSO) algorithm and MODISM river basin decision support system (DSS) to determine optimal basin-scale water allocation, in two aspects. The first is deriving hydrologic state-dependent (conditional) operating rules to better account for drought and high-flow periods, and the second is direct, explicit consideration of sustainability criteria in the model’s formulation to have a better efficiency in basin-scale water allocation. Under conditional operating rules, the operational parameters of reservoir target storage levels and their priority rankings were conditioned on the hydrologic state of the system in a priority-based water allocation scheme. The role of conditional operating rules and policies were evaluated by comparing water shortages associated with objective function values under unconditional and conditional operating rules. Optimal basin-scale water allocation was then evaluated by incorporating reliability, vulnerability, reversibility and equity sustainability indices into the PSO objective function. The extended model was applied for water allocation in the Atrak River Basin, Iran. Results indicated improved distribution of water shortages by about 7.5% using conditional operating rules distinguishing dry, normal and wet hydrologic states. Alternative solutions with nearly identical objective function values were found with sustainability indices included in the model.     

Medium-Term Hydro Generation Scheduling (MTHGS) with Chance Constrained Model (CCM) and Dynamic Control Model (DCM)

Medium-Term Hydro Generation Scheduling (MTHGS) plays an important role in the operation of hydropower systems. In the first place, this paper presents a Chance Constrained Model for solving the optimal MTHGS problem. The model recognizes the impact of inflow uncertainty and the constraints involving hydrologic parameters subjected to uncertainty are described as probabilistic statements. It aims at providing a more practical technique compared to the traditional deterministic approaches used for MTHGS. The stochastic inflow is expressed as a simple discrete-time Markov chain and Stochastic Dynamic Programming is adopted to solve the model. Then in order to use the information of long-term inflow forecast to improve dispatching decisions, a Dynamic Control Model is developed. Short-term forecast results of the current period and long-term forecast results of the remaining period are treated as inputs of the model. Finally, the two methods are applied to MTHGS of Xiluodu hydro plant in China. The results are compared to those obtained from Deterministic Dynamic Programming with hindsight and advantages and disadvantages of the two methods are analyzed.     

Informational Entropy: a Failure Tolerance and Reliability Surrogate for Water Distribution Networks

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies.     

Assessment of Sustainability in Water Supply-Demand Considering Uncertainties

Water is a vital resource for life on earth; hence its maintenance is very important. Different regions especially in arid and semi-arid areas are facing population growth and subsequent increase in the domestic, industrial and agricultural activities. Planning of water systems in order to be ready for future development conditions needs further studies on the estimation of the sustainable levels of demands based on the sustainable levels of supplies. In this study a threefold approach for estimating sustainability level of supply and demand in Ahachay river basin in northwestern part of Iran as a case study is taken. In the first method, the internal flows and the origins and final uses of the total resources for each subsystem are estimated and planning for sustainability use index is determined by calculating the available water. Second method introduced a simulation model which is utilized to estimate reliability, resiliency, vulnerability and maximum deficit for a river basin to determine a group sustainability index. In the third method, for evaluating the movement toward sustainability, an index is developed. This index includes parameters that are the difference between supply and demand, percentage of the satisfied demand, productivity of water resources and an indicator for evaluating the reduction of aquifer storage. Finally these methods are compared and a hybrid index combining the indices is developed. An uncertainty analysis is also performed to investigate the random nature of variables in estimating water balance and quantifying the water sustainability. This hybrid index can be used for evaluating the planning scenarios and for maintaining and improving the sustainable state of supply-demand for the region.     

Multiple Random Forests Modelling for Urban Water Consumption Forecasting

The precise forecasting of water consumption is the basis in water resources planning and management. However, predicting water consumption fluctuations is complicated, given their non-stationary and non-linear characteristics. In this paper, a multiple random forests model, integrated wavelet transform and random forests regression (W-RFR), is proposed for the prediction of daily urban water consumption in southwest of China. Raw time series were first decomposed into low- and high-frequency parts with discrete wavelet transformation (DWT). The random forests regression (RFR) method was then used for prediction using each subseries. In the process, the input and output constructions of the RFR model were proposed for each subseries on the basis of the delay times and the embedding dimension of the attractor reconstruction computed by the C-C method, respectively. The forecasting values of each subseries were summarized as the final results. Four performance criteria, i.e., correlation coefficient (R), mean absolute percentage error (MAPE), normalized root mean square error (NRMSE) and threshold static (TS), were used to evaluate the forecasting capacity of the W-RFR. The results indicated that the W-RFR can capture the basic dynamics of the daily urban water consumption. The forecasted performance of the proposed approach was also compared with those of models, i.e., the RFR and forward feed neural network (FFNN) models. The results indicated that among the models, the precision of the predictions of the proposed model was greater, which is attributed to good feature extractions from the multi-scale perspective and favorable feature learning performance using the decision trees.     

Comprehensive Benefit Evaluation System for Low-Impact Development of Urban Stormwater Management Measures

In recent years, plenty of simulation research about the low impact development(LID) control effect has emerged, but studies on scheme comparison and evaluation are lacking. In this study, a comprehensive benefit evaluation system for LID, including environmental, economic, and social benefits, was established on the basis of Analytic Hierarchy Process(AHP) and urban storm water model. Above all, benefit identification, quantitative evaluation and scheme comparison of single LID measures were obtained according to site investigation, simulated calculation and theoretical analysis. Whereafter, LID combination plans were designed based on single LID measures with high comprehensive benefit values, and their comprehensive benefits were evaluated to obtain the optimal plan. Then, based on well-founded system combined with Storm Water Management Model (SWMM), the design and optimization of LID were conducted, with a case in Xi’an, China. It turned out that the preferential order of the LID single measures according to the comprehensive benefit was: bio-retention > rain barrels > low-elevation greenbelt > green roofs > permeable pavement. Five LID combination plans were designed based on bio-retention, rain barrels, low-elevation greenbelt, and green roofs. Evaluation results showed that plan I (bio-retention and green roofs) was the optimal LID combination plan.     

Performance Assessment of a Coupled Particle Swarm Optimization and Network Flow Programming Model for Optimum Water Allocation

Water resources allocation problems are mainly categorized in two classes of simulation and optimization. In most cases, optimization problems due to the number of variables, constraints and nonlinear feasible search space are known as a challenging subject in the literature. In this research, by coupling particle swarm optimization (PSO) algorithm and a network flow programming (NFP) based river basin simulation model, a PSO-NFP hybrid structure is constructed for optimum water allocation planning. In the PSO-NFP model, the NFP core roles as the fast inner simulation engine for finding optimum values for a large number of water discharges in the network links (rivers and canals) and nodes (reservoirs and demands) while the heuristic PSO algorithm forms the outer optimization cover to search for the optimum values of reservoirs capacities and their storage priorities. In order to assess the performance of the PSO-NFP model, three hypothetical test problems are defined, and their equivalent nonlinear mathematical programs are developed in LINGO and the results are compared. Finally, the PSO-NFP model is applied in solving a real river basin water allocation problem. Results indicate that the applied method of coupling PSO and NFP has an efficient ability for handling river basin-scale water resources optimization problems.     

Flood Forecasting and Decision Making in the new Millennium. Where are We?

This paper reviews the development of real time flood forecasting systems from the early 1970 approaches to the recent probabilistic ones. A preliminary discussion on the motivations for developing real time flood forecasting systems is introduced to explain their evolution in the last four to five decades. It will be shown how recent probabilistic flood forecasts are more robust and effective than the traditional deterministic ones. In particular, when combined with Bayesian decision approaches, probabilistic forecasts are the most appropriate tools for rational decision making in flood warning and flood management.Moreover, they allow taking into account the information from several models to be taken into account by combining into a unique predictive density the deterministic predictions of several hydrological or hydraulic models of a different nature, while in the multi-temporal forecasting extensions, they provide to answers questions such as: Which is the probability of overtopping a dyke in the next 24 h? When will this event be more likely to occur during the next 24 h?The work concludes with a discussion on the still unresolved problems, namely how decisions makers can fully take advantage of the probabilistic forecasts and how these forecasts must be communicated to them in order to meet this objective.