Scenario reduction for stochastic unit commitment with wind penetration

Uncertainties in the day-ahead forecasts for load and wind energy availability are considered in a reliability unit commitment problem. A two-stage stochastic program is formulated to minimize total expected cost, where commitments of thermal units are viewed as first-stage decisions and dispatch is relegated to the second stage. Scenario paths of hourly loads are generated according to a weather forecast-based load model. Wind energy scenarios are obtained by identifying analogue historical days. Net load scenarios are then created by crossing scenarios from each set and subtracting wind energy from load. A new heuristic scenario reduction method termed forward selection in recourse clusters (FSRC) is customized to alleviate the computational burden. Results of applying FSRC are compared with those of a classical scenario reduction method, fast forward selection (FFS) by evaluating the expected dispatch costs when the commitment decisions derived from each subset of scenarios are applied to the whole scenario set. In an instance down-sampled from data of an Independent System Operator in the U.S., the expected dispatch costs for both scenario reduction methods are similar, but FSRC improves reliability

Contingency-Constrained Unit Commitment with Post-Contingency Corrective Recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-e reliability criterion. This reliability criterion is a generalization of the well-known $N$-$k$ criterion, and dictates that at least $(1-e_ j)$ fraction of the total system demand must be met following the failures of $k$ or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art

Hydrothermal Unit Commitment with Deterministic Optimization: Generation and Transmission Including Pumped Storage Units

This work presents a novel approach for solving the short-therm scheduling of hydro-thermal power generation, including pumped storage systemsand transmission constraints. The problem addressed is known as Security Constrained Unit Commitment (SCUC). Pumped Storage Units (PSUs) are importantin electric systems during the off-peak and the peak demand periods, providing economic and technical benefits. Linear aproximations are applied to nonlinear equations of this kind of mathematical problems which are: fuel cost functions, generation-discharge curves of PSUs and transmission constraints modeled with Alternating Current power flow model. Thus, MILP models are presented for the problem addessed. To prove the efficiency of the proposed models, two systems with PSUs will be tested: a modified 6-bus and the IEEE 31-bus power system. Results show that the proposed MILP models allow: modeling the SCUC problem more realistically, obtaining feasible solutions within efficient computational times, and reaching production cost savings up to almost 20% compared to power systems that lack capacities to pumping water. Several indicators obtained from results are presented through graphs, as a tool for improving operation and maintenance of power systems. The analysis of these indicators and the graphic interpretation allow to identify and classify critical parts of systems as well as to make recommendations about future system improvements.Fil: Alvarez, Gonzalo Exequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; ArgentinaFil: Marcovecchio, Marian Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; ArgentinaFil: Aguirre, Pio Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; Argentin

Optimal Allocation of Series FACTS Devices in Large Scale Systems

Series FACTS devices, such as the variable series reactor (VSR), have the ability to continuously regulate the transmission line reactance so as to control power flow. This paper presents a new approach to optimally locating such devices in the transmission network considering multiple operating states and contingencies. To investigate optimal investment, a single target year planning with three different load patterns is considered. The transmission contingencies may occur under any of the three load conditions and the coupling constraints between base case and contingencies are included. A reformulation technique transforms the original mixed integer nonlinear programming (MINLP) model into mixed integer linear programing (MILP) model. To further relieve the computational burden and enable the planning model to be directly applied to practical large scale systems, a two phase decomposition algorithm is introduced. Detailed numerical simulation results on IEEE 118-bus system and the Polish 2383-bus system illustrate the efficient performance of the proposed algorithm.Comment: Accepted by IET Generation, Transmission & Distributio

Toward scalable stochastic unit commitment. Part 2: Solver Configuration and Performance Assessment

In this second portion of a two-part analysis of a scalable computa- tional approach to stochastic unit commitment, we focus on solving stochastic mixed-integer programs in tractable run-times. Our solution technique is based on Rockafellar and Wets\u27 progressive hedging algorithm, a scenario-based decomposi- tion strategy for solving stochastic programs. To achieve high-quality solutions in tractable run-times, we describe critical, novel customizations of the progressive hedging algorithm for stochastic unit commitment. Using a variant of the WECC- 240 test case with 85 thermal generation units, we demonstrate the ability of our approach to solve realistic, moderate-scale stochastic unit commitment problems with reasonable numbers of scenarios in no more than 15 minutes of wall clock time on commodity compute platforms. Further, we demonstrate that the result- ing solutions are high-quality, with costs typically within 1-2.5% of optimal. For larger test cases with 170 and 340 thermal generators, we are able to obtain solu- tions of identical quality in no more than 25 minutes of wall clock time. A major component of our contribution is the public release of the optimization model, as- sociated test cases, and algorithm results, in order to establish a rigorous baseline for both solution quality and run times of stochastic unit commitment solvers

Hydrothermal Unit Commitment with Deterministic Optimization : Generation and Transmission Including Pumped Storage Units

This work presents a novel approach for solving the short-therm scheduling of hydro-thermal power generation, including pumped storage systemsand transmission constraints. The problem addressed is known as Security Constrained Unit Commitment (SCUC). Pumped Storage Units (PSUs) are importantin electric systems during the off-peak and the peak demand periods, providing economic and technical benefits. Linear aproximations are applied to nonlinear equations of this kind of mathematical problems which are: fuel cost functions, generation-discharge curves of PSUs and transmission constraints modeled with Alternating Current power flow model. Thus, MILP models are presented for the problem addessed. To prove the efficiency of the proposed models, two systems with PSUs will be tested: a modified 6-bus and the IEEE 31-bus power system. Results show that the proposed MILP models allow: modeling the SCUC problem more realistically, obtaining feasible solutions within efficient computational times, and reaching production cost savings up to almost 20% compared to power systems that lack capacities to pumping water. Several indicators obtained from results are presented through graphs, as a tool for improving operation and maintenance of power systems. The analysis of these indicators and the graphic interpretation allow to identify and classify critical parts of systems as well as to make recommendations about future system improvements.Sociedad Argentina de Informática e Investigación Operativ