Ping-an Zhong

Scenario tree reduction in stochastic programming with recourse for hydropower operations

A stochastic programming with recourse model requires the consequences of recourse actions be modeled for all possible realizations of the stochastic variables. Continuous stochastic variables are approximated by scenario trees. This paper evaluates the impact of scenario tree reduction on model performance for hydropower operations and suggests procedures to determine the optimal level of scenario tree reduction. We first establish a stochastic programming model for the optimal operation of a cascaded system of reservoirs for hydropower production. We then use the neural gas method to generate scenario trees and employ a Monte Carlo method to systematically reduce the scenario trees. We conduct in-sample and out-of-sample tests to evaluate the impact of scenario tree reduction on the objective function of the hydropower optimization model. We then apply a statistical hypothesis test to determine the significance of the impact due to scenario tree reduction. We develop a stochastic programming with recourse model and apply it to real-time operation for hydropower production to determine the loss in solution accuracy due to scenario tree reduction. We apply the proposed methodology to the Qingjiang cascade system of reservoirs in China. The results show: (1) The neural gas method preserves the mean value of the original streamflow series but introduces bias to variance, cross variance and lag-one co-variance due to information loss when the original tree is systematically reduced; (2) Reducing the scenario number by as much as 40% results in insignificant change in the objective function and solution quality, but significantly reduces computational demand. This article is protected by copyright. All rights reserved.

Risk Analysis for Real-Time Flood Control Operation of a Reservoir

AbstractThere are many uncertainties in real-time flood control operation of a reservoir, which create risks in flood control decision making. In this paper, three uncertainty factors—reservoir inflow-forecasting errors, outflow errors, and observation errors of reservoir storage capacity curve—are taken into account and quantified methods are proposed. With consideration of the three uncertainties and correlation between inflow-forecasting errors, reservoir water-level errors are derived using the stochastic differential equation of reservoir flood routing. Then the definition and calculation methods for flood risk at each moment and the integrated risk of the entire flood process are proposed. The Dahuofang reservoir in China is selected as the case study. The results shows that the risk resulting from the uncertainties is decreased by the reservoir flood regulation function and that the proposed method can provide a useful way to estimate the risks in real-time reservoir flood control.

Stochastic Programming with a Joint Chance Constraint Model for Reservoir Refill Operation Considering Flood Risk

AbstractReservoir refill operation modeling attempts to maximize a set of benefits while minimizing risks. The benefits and risks can be in opposition to each other, such as having enough water for hydropower generation while leaving enough room for flood protection. In addition to multiple objects, the uncertainty of streamflow can make decision making difficult. This paper develops a stochastic optimization model for reservoir refill operation with the objective of maximizing the expected synthesized energy production for a cascade system of hydropower stations while considering flood risk. Streamflow uncertainty is addressed by discretized streamflow scenarios and flood risk is controlled by a joint chance constraint restricting the occurrence probability. With the variability of flood risk level, two advancing refill scenarios for exploring operation benefit are presented. Scenario I loosens the current stagewise storage bounds conditions and allows advancing reservoir refills but keeps the flood risk...

Risk analysis for the downstream control section in the real-time flood control operation of a reservoir

Many uncertainty factors are associated with the joint operation of a reservoir and its downstream river, which create risks in flood control decisions. Therefore, this paper proposes an analytical method for the estimation of the uncertainties and their risks in real-time flood control decisions. Three uncertainty factors, including reservoir discharge errors, forecasting errors of lateral inflows and river food routing errors are proposed and modeled as stochastic processes, and their internal transforming formulas are derived based on the theory of routing before combination. The definition and calculation formulas for the risks of each moment and the integrated risk of the entire flood process at the downstream flood control section are proposed by an analytical approach based on the combination theory of stochastic processes. The Dahuofang reservoir in northern China is selected as the study case. The results indicate that the risk of the flood peak is higher than that of other moments under the same controlled flood discharge and that the risk that arises from the uncertainties of the reservoir discharge and lateral inflow is decreased by the river storage function. Compared with the Monte Carlo method, the proposed method is effective and efficient for performing risk analysis of the downstream control section in the real-time flood control operation of a reservoir. The risk analysis results could provide important information regarding flood risks for the operators to implement flood control arrangements.

SMAA-based stochastic multi-criteria decision making for reservoir flood control operation

In reservoir flood control operation, candidate alternatives are generally evaluated, ranked and selected through multi-criteria decision making (MCDM) techniques, yet stochastic uncertainties both in the criteria performance values (PVs) and criteria weights (CWs) exist in the MCDM process. This paper extends the traditional MCDM methods to stochastic environments for reservoir flood control operation. The criteria PVs and CWs are treated as stochastic variables with certain probability distributions. The stochastic multicriteria acceptability analysis (SMAA) theory is introduced and the differences between conventional MCDM models and the SMAA-2 model are discussed. Methods for quantifying stochastic uncertainties in the criteria PVs are discussed and four kinds of CWs are proposed. Moreover, we define the concept of the risk of decision making errors and propose the corresponding quantitative calculation method. A three-stage MCDM procedure is recommended to guide decision makers to solve MCDM problems under stochastic environments. We apply the proposed methodology to a case study through Monte Carlo simulation to demonstrate its effectiveness and advantage. The results show that the proposed methodology can provide significant risk information for decision makers and improve the reliability of decisions for reservoir flood control operation.

A multiobjective short‐term optimal operation model for a cascade system of reservoirs considering the impact on long‐term energy production

This paper examines the impact of short-term operation on long-term energy production. We propose a multiobjective optimization model for the short-term, daily operation of a system of cascade reservoirs. The two objectives considered in the daily model are: (1) minimizing the total amount of water released and (2) maximizing the stored energy in the system. Optimizing short-term operation without considering its impact on long-term energy production does not guarantee maximum energy production in the system. Therefore, a major goal of this paper is to identify desirable short-term operation strategies that, at the same time, optimize long-term energy production. First, we solve the daily model for 1 month (30 days) using a nondominated genetic algorithm (NSGAII). We then use the nondominated solutions obtained by NSGAII to assess the impact on long-term energy production using a monthly model. We use historical monthly inflows to characterize the inflow variability. We apply the proposed methodology to the Qingjiang cascade system of reservoirs in China. The results show: (1) in average hydrology scenarios, the solution maximizing stored energy produces the most overall long-term energy production; (2) in moderately wet hydrology scenarios, the solution minimizing water released outperforms the maximizing stored energy solution; and (3) when extremely wet hydrology scenarios are expected, a compromise solution is the best strategy.

Multi-criteria group decision making under uncertainty: Application in reservoir flood control operation

This paper proposes an innovative framework for solving stochastic multi-criteria decision making (MCDM) problems when uncertainties exist in criteria performance values (PVs) and criteria weights (CWs) simultaneously. Methods for quantifying uncertainties in criteria PVs and CWs are presented. We establish the SMAA-TOPSIS model by combining stochastic multicriteria acceptability analysis (SMAA) and technique for order preference by similarity to ideal solution (TOPSIS). The risk of decision making errors is proposed to assess the impact of uncertainties on MCDM. We develop the LHS-based Monte Carlo simulation algorithm and corresponding computer program for solving the SMAA-TOPSIS model. We also suggest a three-stage MCDM procedure for stochastic MCDM problems. We apply the proposed methodology to a flood control operation case study to demonstrate its applicability. Our results indicate that the proposed methods can provide valuable risk information and enable risk-informed decisions to be made with higher reliabilities. A novel SMAA-TOPSIS model for stochastic MCDM problems is proposed.The algorithm and program are designed for solving the SMAA-TOPSIS model.Methods for quantifying multiple uncertainties in MCDM are proposed.The risk of decision making errors is proposed to assess the effect of uncertainty.Helps decision makers make risk-informed decisions with higher reliabilities.

A decomposition‐integration risk analysis method for real‐time operation of a complex flood control system

Risk analysis plays an important role in decision making for real-time flood control operation of complex flood control systems. A typical flood control system consists of reservoirs, river channels, and downstream control points. The system generally is characterized by nonlinearity and large scale. Additionally, the input variables are mostly stochastic. Because of the dimensionality problem, generally, it would not be possible to carry out risk analysis without decomposition. In this paper, we propose a decomposition-integration approach whereby the original complex flood control system is decomposed into a number of independent subsystems. We conduct risk analysis for each subsystem and then integrate the results by means of combination theory of stochastic processes. We evaluate the propagation of uncertainties through the complex flood control system and calculate the risk of reservoir overtopping, as well as the risk of flooding at selected downstream control points. We apply the proposed methodology to a flood control system in the middle reaches of the Huaihe River basin in China. The results show that the proposed method is practical and provides a way to estimate the risks in real-time flood control operation of a complex flood control system. This article is protected by copyright. All rights reserved.

Real-Time Optimal Flood Control Decision Making and Risk Propagation Under Multiple Uncertainties

Multiple uncertainties exist in the optimal flood control decision-making process, presenting risks involving flood control decisions. This paper defines the main steps in optimal flood control decision making that constitute the Forecast-Optimization-Decision Making (FODM) chain. We propose a framework for supporting optimal flood control decision making under multiple uncertainties and evaluate risk propagation along the FODM chain from a holistic perspective. To deal with uncertainties, we employ stochastic models at each link of the FODM chain. We generate synthetic ensemble flood forecasts via the martingale model of forecast evolution. We then establish a multiobjective stochastic programming with recourse model for optimal flood control operation. The Pareto front under uncertainty is derived via the constraint method coupled with a two-step process. We propose a novel SMAA-TOPSIS model for stochastic multicriteria decision making. Then we propose the risk assessment model, the risk of decision-making errors and rank uncertainty degree to quantify the risk propagation process along the FODM chain. We conduct numerical experiments to investigate the effects of flood forecast uncertainty on optimal flood control decision making and risk propagation. We apply the proposed methodology to a flood control system in the Daduhe River basin in China. The results indicate that the proposed method can provide valuable risk information in each link of the FODM chain and enable risk-informed decisions with higher reliability.

A Multiobjective Stochastic Programming Model for Hydropower Hedging Operations under Inexact Information

This study develops a multiobjective stochastic programming model for informing hedging decisions for hydropower operations under an electricity market environment considering the benefit from selling energy production and the cost of penalizing energy shortfall. Aiming to determine the optimal strategy that hedges the risk of energy shortfall while keeping a high level of direct revenue from energy production under uncertain streamflows and inexact penalizing price conditions, competing objectives of minimizing energy shortfall percentage and maximizing direct revenue from energy production are analyzed. The conflict is resolved by determining the optimal level of energy shortfall percentage such that the net benefit of the hydropower system is maximized. The first-order optimality condition of maximized system net revenue is derived, which states that the marginal benefit of hedging equals the marginal cost of hedging at optimality. The tradeoff ratio between the competing objectives serves as the marginal cost of hedging and the penalizing price of energy shortfall represents the marginal benefit of hedging. Using the optimality condition, sensitivity tests are conducted for investigating the influence of different ranges of penalizing prices and reservoir initial storages on hedging decisions. The proposed method is evaluated on the operations of the Three Gorges cascade hydropower system during the drawdown season. Results show that: (1) minimizing the energy shortfall percentage adversely affects the maximization in system direct revenue from energy production, and the conflicting results are related to the depletion strategies of reservoir storage; (2) to reduce the energy shortfall percentage to the lowest level could result in significant reduction in total energy production and the direct revenue, especially when reservoir initial storages are low; and (3) the optimal level of energy shortfall percentage would decrease as penalizing price increases, when the influence of penalizing cost from energy shortfall gradually dominates the influence of energy production on the net revenue. The model framework and the implications could be applied to rationalize hedging decisions for hydropower operations under inexact information upon streamflow and penalizing prices.