Long-term Hydrothermal Scheduling Research Articles

Approximating hydropower systems by feasibility spaces in stochastic dual dynamic programming

This work investigates and improves methodology for approximating hydropower systems by feasibility spaces, which can be embedded in the stochastic dual dynamic programming algorithm and applied in the context long-term hydrothermal scheduling. The feasibility spaces are derived from optimization of the detailed hydropower system and are expressed in few dimensions to facilitate efficient computations. Test results from a case study for the Norwegian power system demonstrate how feasibility spaces serve to realistically constrain the hydropower system.

Non-anticipative risk-averse analysis with effective scenarios applied to long-term hydrothermal scheduling

Non-anticipative risk-averse analysis with effective scenarios applied to long-term hydrothermal scheduling

Dealing with Negative Inflows in the Long-Term Hydrothermal Scheduling Problem

The long-term hydrothermal scheduling (LTHS) problem seeks to obtain an operational policy that optimizes water resource management. The most employed strategy to obtain such a policy is stochastic dual dynamic programming (SDDP). The primary source of uncertainty in predominant hydropower systems is the reservoirs inflow, usually a linear time series model (TSM) based on the order-p periodic autoregressive [PAR(p)] model. Although the linear PAR(p) can represent the seasonality and autocorrelation of the inflow datasets, negative inflows may appear during SDDP iterations, leading to water balance infeasibilities in the LTHS problem. Different from other works, the focus of this paper is not avoiding negative inflows but instead dealing with the negative values that cause infeasibilities. Hence, three strategies are discussed: (i) inclusion of a slack variable penalized in the objective function, (ii) negative inflow truncation to zero, and (iii) optimal inflow truncation, among which the latter is a novel approach. The strategies are compared individually and combined. Methodological conditions and evidence of the algorithm convergence are presented. Out-of-sample simulations show that the choice of negative inflow strategy significantly impacts the performance of the resultant operational policy. The combination of strategy (i) and (iii) reduces the expected operation cost by 15%.

Node Aggregation and Parallelization in Stochastic Dual Dynamic Programming Applied to the Long-Term Hydrothermal Scheduling Problem

Node Aggregation and Parallelization in Stochastic Dual Dynamic Programming Applied to the Long-Term Hydrothermal Scheduling Problem

Comparison of dynamic programming policies for long-term hydrothermal scheduling of single-reservoir systems in steady-state regime

Markov stochastic dynamic programming (MSDP) has been extensively used for long-term hydrothermal systems (LTHS) of single-reservoir systems and has inspired many approaches to multiple-reservoir systems, despite the lack of comprehensive studies that test their performance. This study is concerned with the evaluation of classic dynamic programming policies in LTHS of single-reservoir systems considering the operation in steady-state regime. The Markov stochastic dynamic programming was compared with deterministic dynamic programming (DDP) considering average inflows, and unconditional stochastic dynamic programming (USDP) considering uncorrelated inflows. Performance measures were obtained through simulation over long horizons using historical and synthetically generated inflows. Sensitivity analysis related to hydro plant characteristics, the hydro generation share in the system, and the inflow considered in DDP was performed. Results show that MSDP provides small performance gains whatever the hydro plant considered, that become smaller with the reduction in the share of hydro generation in the system, and the proper consideration of inflows in DDP.

Assessing the cost of the Hazard-Decision simplification in multistage stochastic hydrothermal scheduling

Hydropower is one of the world’s primary renewable energy sources whose usage has profound economic, environmental, and social impacts. We focus on the dispatch of generating units and the storage policy of hydro resources. In this context, an accurate assessment of the water opportunity-cost is crucial for driving the sustainable use of this scarce resource. Nevertheless, traditional computational tools use stochastic dual dynamic programming under the Hazard-Decision (HD) modeling simplification, where dispatch decisions are determined assuming perfect information about the current inflows. In practice, however, some dispatch decisions are made before water inflows are observed, i.e., under a Decision-Hazard (DH) scheme. This inconsistency generates an optimistic assessment of the opportunity cost of the water, inducing a sub-optimal use of energy resources. Thus, our objectives are: (i) to raise awareness of the HD issue bridging research and implementation with a clear recommendation to system operators and regulators; (ii) to incorporate the DH scheme into the long-term hydrothermal scheduling problem; (iii) to assess the economic impacts and other market distortions due to the actual energy usage policy based on the HD simplification. For a representative case-study with realistic data from the Brazilian power system, results show that the HD simplification introduces a regret cost of 12%. Furthermore, we show that incorporating the DH scheme into the hydrothermal planning model, the energy supply cost can be reduced up to 5.3%. We also show that spot-price distortions and expensive thermal generation could be mitigated in the DH scheme.

Improving the performance of the stochastic dual dynamic programming algorithm using Chebyshev centers

In hydro predominant systems, the long-term hydrothermal scheduling problem (LTHS) is formulated as a multistage stochastic programming model. A classical optimization technique to obtain an operational policy is the stochastic dual dynamic programming (SDDP), which employs a forward step, for generating trial state variables, and a backward step to construct Benders-like cuts. To assess the quality of the obtained policy (the cuts obtained over the iterations), a confidence interval is computed on the optimality gap. As the SDDP is a cutting-plane based method, it exhibits slow convergence in large-scale problems. To improve computational efficiency, we explore different regions in which the cuts are usually constructed by the classical algorithm. For that, the cuts in the forward step are translated using ideas related to the definition of Chebyshev centers of certain polyhedrons. Essentially, the cuts are lifted by a parameter that vanishes along with iterations without harming the convergence analysis. The proposed technique is assessed on an instance of the Brazilian LTHS problem with individualized monthly decisions per plant, indicating a higher policy quality in comparison with the classical approach, since it computes lower optimality gaps throughout the iterative process.

Detailed long‐term hydro‐thermal scheduling for expansion planning in the Nordic power system

The authors describe a method for long-term hydro-thermal scheduling allowing treatment of detailed large-scale hydro systems. Decisions for each week are determined by solving a two-stage stochastic linear programming problem considering uncertainty in weather and exogenous market prices. The overall scheduling problem is solved by embedding such two-stage problems in a rolling horizon simulator. The method is verified on data for the Nordic power system, studying the incremental changes in expected socio-economic surplus for expansions in both the transmission and generation systems. Comparisons are made with a widely used existing long-term hydro-thermal scheduling model. The results indicate that the model is well suited to valuate the flexibility of hydropower in systems with a high share of intermittent renewable generation.

Assessment of risk-averse policies for the long-term hydrothermal scheduling problem

The goal of the long-term hydrothermal scheduling (LTHS) problem is to determine an optimal policy that minimises the expected operational cost over a multi-annual planning horizon. In this problem, inflows are naturally random; thus, the development of policies requires the use of specialised techniques such as stochastic optimization algorithms. Although the optimal policy defined by means of the expected cost is economically efficient, the associated decisions can incur a high risk of energy deficit. To overcome such disadvantages, one alternative is to include a risk-measure approach in the LTHS modeling. In this study, we compared two different risk-measure strategies applied to the LTHS problem: (i) a convex combination between the conditional value at risk (CVaR) and the expected operational cost, (ii) a reservoir risk-curve. To accomplish the comparison, we consider the Brazilian power system with a 5-year planning horizon discretized in monthly stages. The policies supplied by the risk-averse strategies are simulated in a set of synthetic inflow scenarios. Thus, the results are obtained in terms of the expected long-term hydrothermal decisions, such as the total operational cost and the reservoir storage. In summary, the CVaR-based policies provided better operational results than the risk-curve one.

Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling

We consider a multistage stochastic linear program in which we aim to assess the quality of an operational policy computed by means of a stochastic dual dynamic programming algorithm. We perform policy assessment by considering two strategies to compute a confidence interval on the optimality gap: (i) using multiple scenario trees and (ii) using a single scenario tree. The first approach has already been considered in several applications, while the second approach has been discussed previously only in a two-stage framework. The second approach is useful in practical applications in order to more quickly assess the quality of a policy. We present these ideas in the context of a multistage stochastic program for Brazilian long-term hydrothermal scheduling, and use numerical instances to compare the confidence intervals on the optimality gap computed via both strategies. We further consider the relative merits of using naive Monte Carlo sampling, randomized quasi Monte Carlo sampling, and Latin hypercube sampling within our framework for assessing the quality of a policy.

Stochastic Long-term Hydrothermal Scheduling with Parameter Uncertainty in Autoregressive Streamflow Models

The optimal scheduling of hydrothermal systems requires the representation of uncertainties in future streamflows to devise a cost-effective operations policy. Stochastic optimization has been widely used as a powerful tool to solve this problem but results will necessarily depend on the stochastic model used to generate future scenarios for streamflows. Periodic autoregressive (PAR) models have been widely used in this task. However, its parameters are typically unknown and must be estimated from historical data, incorporating a natural estimation error. Furthermore, the model is just a linear approximation of the real stochastic process. The consequence is that the operator will be uncertain about the correct linear model that should be used at each period. The objective of this work is to assess the impacts of incorporating the uncertainty of the parameters of the PAR models into a stochastic hydrothermal scheduling model. The proposed methodology is tested with case studies based on data from the Brazilian hydroelectric system. It is shown that when the uncertainty of the parameters is ignored, the policies given by the stochastic optimization tend to be too optimistic.

Improved Immune Algorithm for Hydrothermal Joint Economic Scheduling

China is in a period of rapid economic development, Hydropower construction scale is increasingly expanding, Hydropower accounts for a considerable proportion of the grid, therefore it becomes more important to conduct the hydrothermal joint economic scheduling in gird. Hydrothermal joint scheduling optimization can make water fire and electric play to their strengths and so that to make a great contribution on conserving energy and protecting the environment. Medium and long-term hydrothermal scheduling seems to be more important because its long scheduling period, and can guide the short-term hydrothermal operation. However, under the medium and long-term hydrothermal scheduling, time span and the changing range of reservoir capacity is big, respect to short-term joint scheduling it is a more complex large-scale optimization problem. Therefore, it is very important to establish a reasonable medium and long-term hydrothermal joint scheduling model within the accuracy range and study the corresponding algorithm.

An Introductory Tutorial on Stochastic Programming Using a Long-term Hydrothermal Scheduling Problem

Stochastic programming deals with a class of optimization models and algorithms in which some of the data may be subject to significant uncertainty. Such models are appropriate when data evolve over time and decisions need to be made before observing the entire data stream. Mathematically, this uncertainty is modeled by means of including random variables in the optimization model; however, such strategy demands a different methodological approach in relation to those usually found in deterministic optimization problems. This tutorial focuses on the main methodological aspects of stochastic programming. The long-term hydrothermal scheduling problem is used to present the ideas didactically. Two reasons justify the choice: (i) this problem is inherently stochastic because the generation decisions on hydrothermal systems are directly influenced by the reservoirs’ water availability, which is associated with future inflows uncertainty; (ii) the problem has great practical relevancy as a decision computational model to use the energy resources in an electrical energy system efficiently. Thus, in general terms, this tutorial aims to motivate the use of this important and fascinating methodological tool that is stochastic optimization.

A computational study of a stochastic optimization model for long term hydrothermal scheduling

The long-term hydrothermal scheduling is one of the most important problems that must be solved in power systems area. This problem aims to obtain an optimal policy, under water resources uncertainty, for the hydro and thermal plants over a multi-annual planning horizon. The purpose of this paper is twofold. Firstly, we present a computational model which is in development for solving the long-term hydrothermal scheduling of the Brazilian hydrothermal power system. Secondly, it is described some modeling issues which may cause problems to achieve an optimal policy and are currently included in the official long-term optimization model of the Brazilian regulatory framework. This paper presents some solutions, for those problems, that were implemented on our model. We evaluate the solutions related to the original modeling and the modified one, in order to show evidences of the problems and that the solutions proposed are a good start point. To accomplish this evaluation, we consider in the model the whole Brazilian power system, with a reduced planning horizon.

Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal scheduling

The long-term hydrothermal scheduling is one of the most important problems to be solved in the power systems area. This problem aims to obtain an optimal policy, under water (energy) resources uncertainty, for hydro and thermal plants over a multi-annual planning horizon. It is natural to model the problem as a multi-stage stochastic program, a class of models for which algorithms have been developed. The original stochastic process is represented by a finite scenario tree and, because of the large number of stages, a sampling-based method such as the Stochastic Dual Dynamic Programming (SDDP) algorithm is required. The purpose of this paper is two-fold. Firstly, we study the application of two alternative sampling strategies to the standard Monte Carlo—namely, Latin hypercube sampling and randomized quasi-Monte Carlo—for the generation of scenario trees, as well as for the sampling of scenarios that is part of the SDDP algorithm. Secondly, we discuss the formulation of stopping criteria for the optimization algorithm in terms of statistical hypothesis tests, which allows us to propose an alternative criterion that is more robust than that originally proposed for the SDDP. We test these ideas on a problem associated with the whole Brazilian power system, with a three-year planning horizon.

Comparison between Closed-Loop and Partial Open-Loop Feedback Control Policies in Long-Term Hydrothermal Scheduling

Comparison between Closed-Loop and Partial Open-Loop Feedback Control Policies in Long-Term Hydrothermal Scheduling

Optimal operation of large hydrothermal systems applying parallelization techniques

Different alternatives to instrument parallelization techniques of long-term hydrothermal scheduling algorithms are given. First, a model for long-term operation planning is outlined, where uncertainties are handled with probabilistic and simulation techniques, and where hydrothermal optimization is carried out using dynamic programming (DP). Then, the application of parallelization to stochastic calculation is given, followed by four ways to solve DP in parallel. Finally, a cross-comparison is made regarding performance and code complexity using a test case, focusing on run-time characteristics of parallel DP algorithms.

A new long-term hydro production scheduling method for maximizing the profit of hydroelectric systems

This paper presents a new long-term hydrothermal production scheduling method. The proposed method maximizes the profit of hydroelectric plants, based on the monthly energy requirement of the system, instead of minimizing the production cost of thermal units. It is shown that different forms of composite thermal marginal costs will lead to the same hydro production schedule. Thus a linear marginal cost, the simplest form, is sufficient for long-term hydrothermal scheduling. A linear hydro marginal profit is also sufficient for this purpose. An immediate conclusion is that an actual composite thermal cost function, which is complicated by thermal unit availability, may not be needed for the long-term optimal hydrothermal scheduling. Due to this simplification, traditional long and mid-term hydrothermal scheduling, a complicated problem, becomes easier to solve. The method can be used by the owners of independent hydro plants in a region for long-term hydroelectric scheduling under both deregulation and competition. A case study shows that the model allocates successfully and efficiently the hydroelectric resources to peak demand periods with negligible computation time.

A dynamic programming two-stage algorithm for long-term hydrothermal scheduling of multireservoir systems

A new dynamic programming based algorithm is used for the long-term hydrothermal scheduling of multireservoir systems. The proposed method minimizes the sum of operation costs in two consecutive periods, formulating the hydrothermal scheduling problem as a function of reservoirs' water content in one period. No discretization of state and control variables is required. The proposed algorithm has smaller storage and computing time requirements than the dynamic programming-successive approximations (SA) method. The operation of an example multireservoir system is simulated indicating that the proposed method leads to lower operation costs than those of the SA method.

Non-uniform composite representation hydroelectric systems for long-term hydrothermal scheduling

This paper presents a nonuniform composite representation of hydroelectric power systems for use in long-term hydrothermal generation scheduling. This representation was developed from reservoir operational rules based on optimal reservoir trajectories obtained with a deterministic hydrothermal scheduling algorithm. A test system consisting of 7 large hydroelectric power plants of the Southeast Brazilian power system with 12572 MW of installed power capacity was selected for a case study. Operational cost comparisons with the classical uniform composite representation reveal significant savings.