TY - GEN
T1 - SDP Based Unit Commitment Via Moment Relaxation
AU - Li, Yikui
AU - Wu, Lei
AU - Li, Jie
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - Unit commitment (UC) problems are the most fundamental problems that system operators solve every day in both day-ahead and real-time markets to guarantee secure and economic operation. UC problems are usually formulated as a mixed-integer linear programming (MILP) or a mixed-integer quadratic programming (MIQP) model with binary variables representing ON/OFF statuses of generators, and is solved via Branch and bound (B&B) type algorithms. With the prosperity of applying semidefinite programing (SDP) in the power system field, researchers attempt to solve UC under the SDP framework by relaxing integrality requirements, seeking an optimal solution or a better lower bound than the traditional linear programming (LP) relaxation. This paper uses 2-order moment relaxation technique to reformulate UC problems as an SDP model, which can be solved by an interior point method. Considering significant computational burden by 2-order moment relaxation, a variable reduction strategy and two refined moment relaxation based UC models are further applied. The relationship among the proposed models in terms of their tightness is studied. In addition, a sufficient condition under which a solution is exact is stated. Numerical studies illustrate effect of the proposed models and potential applicability of the proposed models is also discussed.
AB - Unit commitment (UC) problems are the most fundamental problems that system operators solve every day in both day-ahead and real-time markets to guarantee secure and economic operation. UC problems are usually formulated as a mixed-integer linear programming (MILP) or a mixed-integer quadratic programming (MIQP) model with binary variables representing ON/OFF statuses of generators, and is solved via Branch and bound (B&B) type algorithms. With the prosperity of applying semidefinite programing (SDP) in the power system field, researchers attempt to solve UC under the SDP framework by relaxing integrality requirements, seeking an optimal solution or a better lower bound than the traditional linear programming (LP) relaxation. This paper uses 2-order moment relaxation technique to reformulate UC problems as an SDP model, which can be solved by an interior point method. Considering significant computational burden by 2-order moment relaxation, a variable reduction strategy and two refined moment relaxation based UC models are further applied. The relationship among the proposed models in terms of their tightness is studied. In addition, a sufficient condition under which a solution is exact is stated. Numerical studies illustrate effect of the proposed models and potential applicability of the proposed models is also discussed.
KW - Mixed-integer linear programming
KW - Moment relaxation
KW - Semidefinite programming
KW - Unit commitment
UR - http://www.scopus.com/inward/record.url?scp=85061769759&partnerID=8YFLogxK
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U2 - 10.1109/NAPS.2018.8600555
DO - 10.1109/NAPS.2018.8600555
M3 - Conference contribution
AN - SCOPUS:85061769759
T3 - 2018 North American Power Symposium, NAPS 2018
BT - 2018 North American Power Symposium, NAPS 2018
T2 - 2018 North American Power Symposium, NAPS 2018
Y2 - 9 September 2018 through 11 September 2018
ER -