Chance-Constrained Two-Stage Unit Commitment Under Uncertain Load and Wind Power Output Using Bilinear Benders Decomposition

Abstract

Abstract-In this paper, we study unit commitment (UC) problems considering the uncertainty of load and wind power generation. UC problem is formulated as a chance-constrained two-stage stochastic programming problem where the chance constraint is used to restrict the probability of load imbalance. In addition to the conventional mixed integer linear programming formulation using Big-M, we present the bilinear mixed integer formulation of chance constraint, and then derive its linear counterpart using McCormick linearization method. Then, we develop a bilinear variant of Benders decomposition method, which is an easy-to-implement algorithm, to solve the resulting large-scale linear counterpart. Our results on typical IEEE systems demonstrate that (i) the bilinear mixed integer programming formulation is stronger than the conventional one; (ii) the proposed Benders decomposition algorithm is generally an order of magnitude faster than using a professional solver to directly compute both linear and bilinear chance-constrained UC models.

Scheduling Model for Renewable Energy Sources Integration in an Insular Power System

“…For the integration of the aforementioned renewable production into the proposed program code, the renewable generators are assumed to be conventional generators, i.e., with operational constraints where the restrictions in Equations (21) and (22) are applied only to the renewable electricity production. Moreover, in this study, power losses and power flow restrictions are not considered, due to the absence of reliable data from the system operator [42].…”

“…For instance, [22] presented an UC problem that considered the uncertainty of load and wind power generation using a chance-constrained two-stage stochastic programming model to reduce the probability of load imbalance, Big-M and Benders' decomposition method with a bilinear mixed integer formulation of chance constraints.…”

Impacts of Power Grid Frequency Deviation on Time Error of Synchronous Electric Clock and Worldwide Power System Practices on Time Error Correction

“…In each month, the median time error over this month is set as the time reference. As shown in Figure 7, although the annual wind power generation has tripled from 2008 (16,225 GWh) to 2016 (57,551 GWh) in Texas [26], which may have negative impacts on power system frequency stability because of wind power fluctuation [27], there seems to be no obvious changes for these time error statistics. This might be because the ERCOT continues to provide TEC services to black out the accumulated time error when it arises.…”

Feasibility of a 100 MW Installed Capacity Wind Farm for Different Climatic Conditions

“…At first, the idea of probabilistic forecasting [11,12] has been proposed to quantify the uncertainty of wind power generation. Then, this uncertainty information is also integrated to power system operation and electricity market through stochastic programming [13,14].…”