A new hybrid stochastic-robust optimization approach for self-scheduling of generation companies

Abstract

Summary This paper presents a new mixed‐integer linear programming model for day‐ahead self‐scheduling of generating companies integrating the underlying ideas of robust optimization (RO) and stochastic programming (SP) to cope with the uncertainties of electricity market prices and availability/unavailability of units. The proposed hybrid approach models the uncertainty of electricity market prices by bounded intervals instead of probability distributions, aiming to derive a more tractable optimization model. Conservatism against uncertain electricity market prices is adjusted by a certain parameter named budget of robustness. Also, a renovated Markov chain approach considering the chance of return (i.e., return rate) for failed units, in addition to forced outage rate of units, in each hour of the scheduling period is introduced in this paper to produce a set of scenarios modeling the availability/unavailability of units. Therefore, the proposed hybrid self‐scheduling approach benefits from both the tractability of RO and modeling accuracy of SP. The proposed approach is implemented on IEEE 118‐bus test system under different circumstances to illustrate its effectiveness compared to deterministic self‐scheduling model as well as the models only employing RO or SP. Copyright © 2015 John Wiley & Sons, Ltd.

A linearized energy hub operation model at the presence of uncertainties: An adaptive robust solution approach

“…The uncertain parameters are first bounded through (6a) to (6c). The budget of uncertainty “ DR ” is used to control the robustness level of the proposed adaptive robust approach through limiting the size of the polyhedral uncertainty set in (6d) . The minimum value for the budget of uncertainty is 0.…”

“…The budget of uncertainty "DR" is used to control the robustness level of the proposed adaptive robust approach through limiting the size of the polyhedral uncertainty set in (6d). 24,25,[32][33][34][35][36][37] The minimum value for the budget of uncertainty is 0. When DR = 0, no uncertain parameter can deviate from its forecasted value, which leads to a deterministic representation with no robustness.…”

“…To obtain more optimal decisions, the uncertainty sources in an EH (eg, wind generations and energy prices) have been modeled through stochastic programing (SP) approaches in Najafi et al and Pazouki et al However, SP faces two main challenges including the lack of tractable methodology and requiring full distributional knowledge of uncertain parameters, which may not be easily available in practice . To overcome these challenges, robust optimization (RO) technique as a tractable approach, eliminating the need for having full distributional knowledge of uncertain parameters, has been recently developed and applied to different applications in power systems, such as day‐ahead market participation and transmission expansion planning . In Parisio et al, a single‐stage RO model is developed for EH optimal operation, considering the uncertainty of converters' efficiency.…”

An Improved Lagrangian Relaxation Algorithm for the Robust Generation Self-Scheduling Problem

“…When the Lagrangian relaxation algorithm is used to solve a generation scheduling problem, constraints that couple different units are typically relaxed to make the relaxed problem separable in units. In this paper, constraints that couple different units include constraints (11) and (20). If constraints (20) are relaxed, the resulting subproblem that contains dual variables 0 and , = 1, .…”

“…From Table 1, we can observe that the robust generation self-scheduling problem was usually solved by commercial solvers. In order to make the problem solvable by the solvers, the model was simplified by piecewise linearly approximating the quadratic fuel cost function [8,10,11], reducing the time-dependent exponential startup cost function as a constant [8,10], omitting the startup cost [9,12], or omitting the unit commitment decision [12]. The solution approach has two disadvantages.…”