Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.

Higher moment coherent risk measures

Abstract: The paper considers modelling of risk-averse preferences in stochastic programming problems using risk measures. We utilize the axiomatic foundation of coherent risk measures and deviation measures in order to develop simple representations that express risk measures via specially constructed stochastic programming problems. Using the developed representations, we introduce a new family of higher-moment coherent risk measures (HMCR), which includes, as a special case, the Conditional Value-at-Risk measure. It is demonstrated that the HMCR measures are compatible with the second order stochastic dominance and utility theory, can be efficiently implemented in stochastic optimization models, and perform well in portfolio optimization case studies.

Risk-Averse Optimal Bidding Strategy for Demand-Side Resource Aggregators in Day-Ahead Electricity Markets Under Uncertainty

Abstract: This paper first presents a generic model to characterize a variety of flexible demand-side resources (e.g., plug-in electric vehicles and distributed generation). Key sources of uncertainty affecting the modeling results are identified and are characterized via multiple stochastic scenarios. We then propose a risk-averse optimal bidding formulation for the resource aggregator at the demand side based on the conditional value-at-risk (VaR) theory. Specifically, this strategy seeks to minimize the expected regret value over a subset of worst-case scenarios whose collective probability is no more than a threshold value. Our approach ensures the robustness of the day-ahead (DA) bidding strategy while considering the uncertainties associated with the renewable generation, real-time price, and electricity demand. We carry out numerical simulations against three benchmark bidding strategies, including a VaR-based approach and a traditional scenario based stochastic programming approach. We find that the proposed strategy outperforms the benchmark strategies in terms of hedging high regret risks, and results in computational efficiency and DA bidding costs that are comparable to the benchmarks.

Long- and Medium-term Operations Planning and Stochastic Modelling in Hydro-dominated Power Systems Based on Stochastic Dual Dynamic Programming

Abstract: This chapter reviews how stochastic dual dynamic programming (SDDP) has been applied to hydropower scheduling in the Nordic countries. The SDDP method, developed in Brazil, makes it possible to optimize multi-reservoir hydro systems with a detailed representation. Two applications are described: (1) A model intended for the system of a single power company, with the power price as an exogenous stochastic variable. In this case the standard SDDP algorithm has been extended; it is combined with ordinary stochastic dynamic programming. (2) A global model for a large system (possibly many countries) where the power price is an internal (endogenous) variable. The main focus is on (1). The modelling of the stochastic variables is discussed. Setting up proper stochastic models for inflow and price is quite a challenge, especially in the case of (2) above. This is an area where further work would be useful. Long computing time may in some cases be a consideration. In particular, the local model has been used by utilities with good results.

Value of seasonal flow forecasts in Bayesian stochastic programming

Abstract: This paper presents a Bayesian Stochastic Dynamic Programming (BSDP) model to investigate the value of seasonal flow forecasts in hydropower generation. The proposed BSDP framework generates monthly operating policies for the Skagit Hydropower System (SHS), which supplies energy to the Seattle metropolitan area. The objective function maximizes the total benefits resulting from energy produced by the SHS and its interchange with the Bonneville Power Administration. The BSDP-derived operating policies for the SHS are simulated using historical monthly inflows, as well as seasonal flow forecasts during 60 years from January 1929 through December 1988. Performance of the BSDP model is compared with alternative stochastic dynamic programming models. To illustrate the potential advantage of using the seasonal flow forecasts and other hydrologic information, the sensitivity of SHS operation is evaluated by varying (1) the reservoir capacity; (2) the energy demand; and (3) the energy price. The simulation results demonstrate that including the seasonal forecasts is beneficial to SHS operation.