Implicit Stochastic Optimization Research Articles

Dynamic reservoir rule curves – Their creation and utilization

This paper presents a methodology for the creation of dynamic reservoir rule curves on the basis of the results of implicit stochastic optimization coupled with optimized demand hedging embedded as constraints to optimization. The novelty of the method is a dynamic rule curve that always starts from the current storage level and projects a range of anticipated target levels in the immediate future based on the statistical analyses of the results of implicit stochastic optimization. The method is particularly useful in dry years when storage is not completely filled at the end of wet seasons. Such situations cannot be addressed with standard traditional rule curves, thus causing reservoir operators to base their decisions on mere judgment. The proposed method can be helpful in such situations. The method has been demonstrated on the Tawa reservoir in the Narmada River Basin in India.

Joint operation rules considering the uncertainty of energy available for multiple cascaded hydropower system

AbstractMulti‐reservoir operation rules have been widely used in practice operation. The operation rules are often derived from historical or simulated run‐off information through implicit stochastic optimization or parameterization‐simulation‐optimization. The output decisions of operation rules are usually obtained without considering inflow forecasting or using perfect runoff forecast information, which is hardly implemented in practical applications. This paper proposes robust joint operation rules for multiple cascaded reservoirs considering the uncertainty of energy available. The rule parameters are optimized using multi‐step genetic algorithm for minimum‐power maximization. A case study for a three‐cascaded‐reservoirs system shows that, compared with deterministic joint operation rules, the accuracy of energy available estimation of joint operation rules is increased by 2.3%, considering inflow uncertainty. The simulated minimum‐power decision of joint operation rules considering the uncertainty of energy available is 40.4% higher than that of determinate joint operation rules. Results indicate that there is a possibility of obtaining greater and more effective power decisions through the joint operation rules considering the uncertainty of available energy.

Identifying effective operating rules for large hydro–solar–wind hybrid systems based on an implicit stochastic optimization framework

Optimization of operational strategies of a hydro–solar–wind hybrid renewable energy system (HRES) could increase resource use efficiency without additional investment. However, because of the myopic nature of the short-term forecast information, the short-term optimal operation strategy of the large HRES cannot guarantee a satisfactory long-term system performance. Therefore, it is necessary to explore reasonable long-term operation strategies for the hydro–solar–wind HRES, especially the establishment of operating rules. In this study, we proposed a method to identify effective long-term operating rules for the large hydro–solar–wind HRES based on an implicit stochastic optimization framework. A large hydro–solar–wind HRES located in the upper Yellow River, China was selected as a case study. It was found that: (1) Operating rules taking reservoir storage or water level as the output variable and available energy as the input variable were most effective to guide the complementary operation of the hydro–solar–wind HRES; (2) Compared with a standard operating policy, the identified best operating rules could increase energy production and guaranteed rate of the HRES by 5.2% and 4%, respectively; and (3) Complementary management of hydro, solar and wind could increase the energy production of the hydropower system, when power transmission capacity was large enough.

Integrating teleconnection factors into long-term complementary operating rules for hybrid power systems: A case study of Longyangxia hydro-photovoltaic plant in China

It is a popular practice that adopting forecast information to improve the efficiency of hybrid power systems, however, resulting in error accumulation along the predictors, forecast models, and operation models. To cope with this issue, complementary operating rules integrated with teleconnection factors were developed for hydro-photovoltaic (PV) hybrid power plants. First, individual and common teleconnection factors, which dominate variations of streamflow and PV output, were identified using Pearson correlation coefficients. Then, three types of operating rules using stochastic optimization integrated with teleconnection factors were proposed. Specifically, teleconnection factors are adopted as state variables in stochastic dynamic programming (SDP), independent variables in implicit stochastic optimization based on linear fitting (LF-ISO) and classification bases in implicit stochastic optimization based on K-Nearest Neighbor (KNN–ISO). China's Longyangxia hydro-PV hybrid power plant was chosen as case study. Results show that (1) Teleconnection factors including Asia Polar Vortex Intensity Index and North Atlantic Oscillation dominate streamflow and PV output; (2) The proposed operating rules realize direct relationship mapping from teleconnection factors to operation decisions, and increase total power generation by 0.070–0.369 billion kWh when compared with same type rules using forecast scenarios; (3) SDP is preferred for Longyangxia hydro-PV hybrid power plant regardless of forecast categories.

Stochastic generation of runoff series for multiple reservoirs based on generative adversarial networks

The implicit stochastic optimization (ISO) model is a methodology that has been extensively employed in the mid-long term optimal operation of a reservoir system. The generation of runoff series is the key technology to make up for the poor representativeness and reliability of historical runoff samples and is the premise to guarantee the accuracy of the ISO model. However, the traditional methods are not suitable for the stochastic generation of runoff series, among reservoirs with spatial–temporal correlation. In this work, the generative adversarial network called DC-WGAN is developed as a runoff generation model. DC-WGAN is based on a data-driven model and can capture the correlation of runoff series in time and space dimensions simultaneously. The proposed method is applied to the downstream Jinsha river cascade and Three Gorges cascade reservoirs in China to generate ten-day runoff series and is compared with the stochastic generation method based on Copula function. The focus of this paper is the model's performance in replicating the spatial–temporal correlation of ten-day runoff series. Results are as follows. (1) DC-WGAN has strong learning and generalization ability, which can learn the correct distribution of original runoff samples and generate runoff series similar to that from the validation set. (2) The runoff series among reservoirs with spatial–temporal correlation can be generated through DC-WGAN without assuming the probability distribution of samples in advance. (3) DC-WGAN is better than Copula function in capturing the spatial–temporal correlation, especially the moderate and weak correlation. The proposed methodology has a high practical value and application prospect for the stochastic generation of runoff series with spatial–temporal correlation.

Stochastic reservoir operation with data-driven modeling and inflow forecasting

This work applied implicit stochastic optimization (ISO) refined by long-term mean inflow forecasting and instance-based learning for the operation of the Sobradinho reservoir, Brazil. For efficiency assessment, the reservoir was also operated by perfect-forecast deterministic optimization, the standard operating policy, stochastic dynamic programming and two parameterization-simulation-optimization models, which were compared in terms of vulnerability, reliability and resilience found in each of the 100 synthetic inflow scenarios they were applied to. Evidence of long-term persistence was found in Sobradinho's records and this was replicated in the scenarios. The ISO model was employed with forecast horizons of 0, 1, 3, 6, 9, 12, 18 and 24 months. The operations demonstrated that the model with forecast horizons of 3 months or more was less vulnerable than all other models, revealing that it may be used efficiently for reservoir operation.

GA-based implicit stochastic optimization and RNN-based simulation for deriving multi-objective reservoir hedging rules.

Management of reservoir systems is a complicated process involving many uncertainties regarding future events and the diversity of purposes these reservoirs serve; therefore, an effective management of these systems could help improve resource utilization and avoid stakeholder disputes. The aim of this paper was to build an optimization-simulation framework based on implicit stochastic optimization (ISO), genetic algorithms (GA), and recurrent neural network (RNN) for addressing the issue of reservoir operation. Inflow scenarios were generated synthetically based on a monthly scale to be used as an input to a multi-objective genetic programming model to construct an optimal operating rules database. Such database was subsequently used simultaneously with the output of the inflow forecasting model to simulate monthly reservoir hedging rules using RNN. Our results demonstrate the effectiveness of the GA-ISO-RNN model for simulating and predicting optimal reservoir release with consistent accuracy. Results from both the training and testing phases clearly proved the usefulness of RNN in predicting optimal reservoir release with relatively higher values of the Nash-Sutcliffe model efficiency coefficient, correlation coefficient, and lower values of root mean squared error and mean absolute deviation. Furthermore, by comparing the historical releases and the output of the proposed model, the results show that the proposed model was less vulnerable than standard operating rules. The proposed methodology was applied to the Bigge reservoir in Germany, as it features an extensive management infrastructure, but this methodology can also be easily adopted in other similar cases.

Evaluation of hydro-wind complementarity in the medium-term planning of electrical power systems by joint simulation of periodic streamflow and wind speed time series: A Brazilian case study

Wind variability and hydro-wind complementarity should be both considered in the planning of electrical power systems. In such cases, the spatio-temporal dependence between streamflow and wind speed regimes needs to be asses to balance the electricity generation. Medium-term hydrothermal scheduling problems (MTHS) are used to define operation policies for electrical power systems under 5–10 years horizon. MTHS uses stochastic optimization techniques fed by synthetic streamflow scenarios. To set better operation policies, such scenarios should well represent statistical features of historical data. With the rapid growth in the installed capacity of wind power, operators are encouraged to consider novel approaches to represent the dependence of hydrometeorological variables. This study integrates wind variability and hydro-wind complementarity in the medium-term planning of electrical power systems employing joint simulation of periodic streamflow and wind speed time series. The generated scenarios are used as input to derive monthly operational policies via Implicit Stochastic Optimization. A hydropower plant and a wind farm, both located in the Northeast region of Brazil were selected as a case study. Results show that considering wind variability and hydro-wind complementarity can significantly reduce energy deficits in power systems and increase the flexibility in the operation of water reservoirs.

Parallelizing Comprehensive Learning Particle Swarm Optimization by Open Computing Language on an Integrated Graphical Processing Unit

Comprehensive learning particle swarm optimization (CLPSO) is a powerful metaheuristic for global optimization. This paper studies parallelizing CLPSO by open computing language (OpenCL) on the integrated Intel HD Graphics 520 (IHDG520) graphical processing unit (GPU) with a low clock rate. We implement a coarse-grained all-GPU model that maps each particle to a separate work item. Two enhancement strategies, namely, generating and transferring random numbers from the central processor to the GPU as well as reducing the number of instructions in the kernel, are proposed to shorten the model’s execution time. This paper further investigates parallelizing deterministic optimization for implicit stochastic optimization of China’s Xiaowan Reservoir. The deterministic optimization is performed on an ensemble of 62 years’ historical inflow records with monthly time steps, is solved by CLPSO, and is parallelized by a coarse-grained multipopulation model extended from the all-GPU model. The multipopulation model involves a large number of work items. Because of the capacity limit for a buffer transferring data from the central processor to the GPU and the size of the global memory region, the random number generation strategy is modified by generating a small number of random numbers that can be flexibly exploited by the large number of work items. Experiments conducted on various benchmark functions and the case study demonstrate that our proposed all-GPU and multipopulation parallelization models are appropriate; and the multipopulation model achieves the consumption of significantly less execution time than the corresponding sequential model.

Probabilistic long-term reservoir operation employing copulas and implicit stochastic optimization

This paper explores and combines implicit stochastic optimization (ISO) with copula functions to simulate long-term operating policies for a hydropower reservoir located in the Northeastern region of Brazil. Overall, ISO is considered as one of the most reliable techniques to derive long-term reservoir operating rules for reservoirs. This method employs a deterministic optimization model to estimate the optimal reservoir allocations under different inflow scenarios and later constructs operating rules for each month by relating the ensemble of the optimal releases, the initial storage volume and future inflow values. Those rules are generally established by fitting approaches including linear regression or nonlinear methods. This work illustrates the applicability to combine copulas with ISO to define reservoir operation policies based on a probabilistic procedure. Firstly, synthetic streamflow scenarios are simulated using a periodic vine copula model. Afterward, optimal release data are estimated by ISO for a set of inflow scenarios. Joint probability distribution functions based on copulas are constructed in order to forecast the expected release, conditioned to the initial reservoir volume and future inflows data. Results indicate that the proposed model represents a flexible approach to construct operating rules and derive long-term reservoir operating policies with low variability, allowing to reproduce different dependence structures of simulated data.

Identifying Efficient Operating Rules for Hydropower Reservoirs Using System Dynamics Approach—A Case Study of Three Gorges Reservoir, China

In the long-term operation of hydropower reservoirs, operating rules have been used widely to decide reservoir operation because they can help operators make an approximately optimal decision with limited runoff information. However, the problems faced by reservoir managers is how to make and select an efficient operating rule properly. This study focuses on identifying efficient and reliable operating rules for the long-term operation of hydropower reservoirs using system dynamics (SD) approach. A stochastic hydrological model of reservoir inflow time series was established and used to generate a large number of inflow scenarios. A deterministic optimization operation model of hydropower reservoirs was constructed and then resolved using dynamic programming (DP) algorithm. Simultaneously, within implicit stochastic optimization (ISO) framework, different operating rules were derived using linear fitting methods. Finally, the most efficient one of the existing operating rules was identified based on SD simulation coupled with the operating rules. The Three Gorges Reservoir (TGR) in central China was used as a case study. The results show that the SD simulation is an efficient way to simulate a complicated reservoir system using feedback and causal loops. Moreover, it can directly and efficiently guide reservoir managers to make and identify efficient operating rules for the long-term operation of hydropower reservoirs.

ANNs and inflow forecast to aid stochastic optimization of reservoir operation

Implicit stochastic reservoir optimization (ISO) typically utilizes nonlinear regression to correlate release as a function of initial storage plus inflow forecasted for the month. This study shows that improved ISO-based policies can be derived by replacing current-month forecast and regression for long-term mean inflow forecast (LTF) and artificial neural networks (ANN), respectively. The ISO-LTF-ANN approach is applied to the Aswan High Dam reservoir, Egypt. First, perfect-forecast deterministic optimization (PFDO) defines operation strategies for 100 scenarios of 100-year inflows. Then, optimal release and storage data are grouped into databases corresponding to different forecast horizons. Next, ANNs are trained for each database to serve as release policies. Later, the policies are used to operate the system under other scenarios. Operations by the standard operation policy (SOP), stochastic dynamic programming (SDP) and PFDO are employed for comparison. ISO-LTFANN performs near PFDO and better than SOP, SDP and a regression-based ISO-LTF approach.

Deriving Operating Rules of Hydropower Reservoirs Using Gaussian Process Regression

Operating rules have been widely used to decide reservoir operations because they can help operators make an approximately optimal decision with limited runoff forecast information. As an effective alternative to explicit stochastic optimization (ESO) for considering hydrologic uncertainty, the implicit stochastic optimization (ISO) has been widely used to derive operating rules for the long-term operation of hydropower reservoirs. Within an ISO framework, operating rules extraction is a typical regression problem. In the past decades, various regression methods have been applied to derive operating rules, including artificial neural network (ANN), support vector regression (SVR) and so on, but these methods almost all are parametric regression method and there are few publications applying Bayesian regression method to derive operating rules. Therefore, Gaussian process regression (GPR), which is the representative Bayesian regression method, is introduced to derive operating rules for the first time in this paper and compared with ANN, SVR and conventional scheduling graph (CSG). China’s Three Gorges Reservoir (TGR) is selected as a case study, and four performance indexes are defined to evaluate different methods. The results show that (1) GPR, ANN and SVR can provide better performance than CSG method and are more practical than deterministic optimization operation; (2) GPR method can provide greater power generation benefits and higher reliability than ANN, SVR and CSG methods, and the average annual power generation increases from 88.481 billion kWh, 88.559 billion kWh and 87.563 billion kWh to 88.586 billion kWh, while the generation guarantee rate increase from 86.88%, 87.07% and 81.99% to 87.45%.

Assessment of Stochastic Operation Optimization for Reservoirs of Contrasting Scales

Deriving optimal release policies for dams and corresponding reservoirs is crucial for the sustainable water resources management of a region as they directly control the distribution of water to several users. Mathematical optimization algorithms can help in finding efficient reservoir operating strategies taking into account complex system constraints and hydrologic uncertainty. The robustness of operation optimization models may be influenced by physical reservoir characteristics such as size and scale and the effectiveness of a model for a particular case study does not always guarantee the same level of success for another application. This research focused on assessing the applicability of an implicit stochastic optimization (ISO) procedure to derive rule curves for two different dams of contrasting reservoir scales in terms of physical and operational characteristics. The results demonstrated the feasibility of the proposed technique for both small- and large-scale systems in view of the lower vulnerability provided by the ISO-derived policies in contrast to operations carried out by the standard reservoir operating policy as well as the proximity of the ISO operations with those by perfect-forecast deterministic optimization. The ISO procedure also provided operating rules similar to, and even less vulnerable than, those derived by stochastic dynamic programming.

Deriving operating rules for a large-scale hydro-photovoltaic power system using implicit stochastic optimization

Abstract Complementary operation is a new effective way to simultaneously manage hydropower and photovoltaic (PV) power. With the integration of a PV power into an existing hydropower reservoir system, the original operating rules need to be re-designed to improve operational performance. This study focuses on exploring long-term operating rules for such an integrated system using implicit stochastic optimization, which can address uncertainties in reservoir inflow and PV power. First, a long-term multi-objective optimization model for this system is established by maximizing the total energy production and assurance rate (i.e., reliability) simultaneously. The model is then solved using a dynamic programming technique. Operating rules are derived from the obtained optimal trajectory using a linear fitting method. Finally, a simulation-based optimization framework is used to refine the parameters of these rules. Our case study based on China's Longyangxia hybrid power system shows that: (1) a significant linear correlation between available energy and reservoir storage at the end of each time period, with fitting correlation coefficients above 0.9 for each month. Therefore, the available energy and reservoir storage at the end of each time period are selected, respectively, as independent variables and decision variables in the operating rules; (2) an improved average annual energy production and assurance rate are obtained for the hybrid system when considering complementary operations; and (3) the derived operating rules are effective in improving system benefits when compared with conventional operation. These findings are helpful to offer guidelines for the effective operation of the hydro/PV hybrid power system.

NN-Based Implicit Stochastic Optimization of Multi-Reservoir Systems Management

Multi-reservoir systems management is complex because of the uncertainty on future events and the variety of purposes, usually conflicting, of the involved actors. An efficient management of these systems can help improving resource allocation, preventing political crisis and reducing the conflicts between the stakeholders. Bellman stochastic dynamic programming (SDP) is the most famous among the many proposed approaches to solve this optimal control problem. Unfortunately, SDP is affected by the curse of dimensionality: computational effort increases exponentially with the complexity of the considered system (i.e., number of reservoirs), and the problem rapidly becomes intractable. This paper proposes an implicit stochastic optimization approach for the solution of the reservoir management problem. The core idea is using extremely flexible functions, such as artificial neural networks (NN), for designing release rules which approximate the optimal policies obtained by an open-loop approach. These trained NNs can then be used to take decisions in real time. The approach thus requires a sufficiently long series of historical or synthetic inflows, and the definition of a compromise solution to be approximated. This work analyzes with particular emphasis the importance of the information which represents the input of the control laws, investigating the effects of different degrees of completeness. The methodology is applied to the Nile River basin considering the main management objectives (minimization of the irrigation water deficit and maximization of the hydropower production), but can be easily adopted also in other cases.

Self-optimization system dynamics simulation of reservoir operating rules

Operating rules have been used widely in the reservoir long-term operation duo to its characteristics of coping with inflow uncertainty and easy implementation. And implicit stochastic optimization (ISO) has been widely applied to derive reservoir operation rules, based on linear regression or nonlinear fitting method. However, the maximum goodness-of-fit criterion of fitting method may be unreliable to determine the effective rules. Therefore, this paper develops a self-optimization system dynamics (SD) simulation of reservoir operation for optimizing the operating rules, by taking advantages of feedback loops in SD simulation. A deterministic optimization operation model is firstly established, and then resolved using dynamic programming (DP). Simultaneously, the initial operating rules (IOR) are derived using the linear fitting method. Finally, the refined optimal operating rules (OOR) are obtained by improving the IOR based on the self-optimization SD simulation. China’s Three Gorges Reservoir is used as a case study. The results show that the SD simulation is competent in simulating a complicated hydropower system with feedback and causal loops. Moreover, it makes a contribution to improve the IOR derived by fitting method within an ISO frame. And the OOR improve effectively the guarantee rate of power generation on the premise of ensuring power generation.

Short Term Optimal Operation of Water Supply Reservoir under Flood Control Stress using Model Predictive Control

Reservoir operations require enhanced operating procedures for water systems under stress attributed to growing water demand and consequences of changing hydro-climatic conditions. This study focuses on the management of the Yuvacik Dam Reservoir for water supply and flood mitigation in the Marmara Region of Turkey. We present an improved operating technique for fulfilling the conflicting water supply and flood mitigation objectives. This is accomplished by incorporating the long term water supply objectives into a Guide Curve (GC) whereas the extreme floods are attenuated by means of short-term optimization based on Model Predictive Control (MPC). The reference case implements operating rules with a constant GC at maximum forebay elevation targeting the fulfillment of the water supply objective. We compare the reference with a new time-dependent GC, derived using an Implicit Stochastic Optimization (ISO) approach. This new curve shows nearly the same performance regarding the water supply objectives, but significantly reduces the flooding risk downstream of the dam. Possible flood events observed at the end of the wet season, when the reservoir is at the maximum level to enable water supply for the dry season, can be eliminated by the application of an additional short-term optimization by MPC. The robustness of the approach is demonstrated via hindcasting experiments.

Improved Implicit Stochastic Optimization technique under drought conditions: the case study of Agri–Sinni water system

ABSTRACTIn this paper, a methodology is proposed to support water decisions by selecting and evaluating reservoir operating rules (OR) based on hydrological scenarios. The methodology includes optimization and simulation tools within an Implicit Stochastic Optimization (ISO) framework. The paper presents some improvements to the traditional ISO that overcome some limitations affecting previous works. Thanks to the collaboration with Regional Water Authorities in Southern Italy, the proposed methodology, called Modified Implicit Stochastic Optimization (MISO), has been tested in the Agri–Sinni water system. In a participatory and integrated risk management approach to drought events, the reservoir OR defined in the MISO approach based on correlations between releases, storages and inflows performed better than the actual OR in the Agri–Sinni water system and the OR from a simulation-alone procedure. In addition, the user can obtain a significant reduction of computational time by applying the MISO technique in a Grid computing approach.

Offline training for improving online performance of a genetic algorithm based optimization model for hourly multi-reservoir operation

A novel framework, which incorporates implicit stochastic optimization (Monte Carlo method), cluster analysis (machine learning algorithm), and Karhunen-Loeve expansion (dimension reduction technique) is proposed. The framework aims to train a Genetic Algorithm-based optimization model with synthetic and/or historical data) in an offline environment in order to develop a transformed model for the online optimization (i.e., real-time optimization). The primary output from the offline training is a stochastic representation of the decision variables that are constituted by a series of orthogonal functions with undetermined random coefficients. This representation preserves covariance structure of the simulated decisions from the offline training as gains some “knowledge” regarding the search space. Due to this gained “knowledge”, better candidate solutions can be generated and hence, the optimal solutions can be obtained faster. The feasibility of the approach is demonstrated with a case study for optimizing hourly operation of a ten-reservoir system during a two-week period.