Robustness Adjustment of Two-Stage Robust Security-Constrained Unit Commitment

Transcription

1 Robustness Adjustment of Two-Stage Robust Secury-Constrained Un Commment Ping Liu MISSISSIPPI STATE UNIVERSITY U.S.A October 23, 204

2 Challenges in smart grid Integration of renewable energy and prediction of customer demand bring up uncertainty: power (W) /2/2 /3/2 /4/2 /5/2 /6/2 /7/2 /8/2 /9/2 /20/ hour Data from Simrall solar power project, MSU Daily range electric load profile ( Reasons for uncertainty include: Seasonaly-effects of the days of the week and special days, such as holidays Price-the lower the energy price, the higher the energy consumption Size of household-more people at home, means more energy consumption Energy use patterns-the level of people s activies Weather-the hotter is, the more energy is used The uncertainty from intermtent and unpredictable solar power generation, as well as imprecise customer load, causes challenges for reliable energy supply. October 23, 204 2

3 Stochastic optimal operation Properties of stochastic programming (SP) Explicly incorporates a probabily distribution of the uncertainty; Relies on pre-sampling discrete scenarios of the uncertainty realizations; Provides probabilistic guarantees to the system reliabily wh stochastic solutions; Provides the optimal strategy (policy) for the realization of uncertainty. Disadvantages of SP Difficult to identify an accurate probabily distribution of the uncertainty in SP; Only provide probabilistic guarantees to the system reliabily wh stochastic solutions ; Becomes extremely large wh the increase of the number of stages. October 23, 204 7

4 Robust optimal operation Properties of robust optimization Only requires moderate information of the underlying uncertainty, such as the mean and the range of the uncertain data; Provides absolute guarantee wh an optimal solution that immunizes against all realizations of the uncertain data whin a deterministic uncertainty set. October 23,

5 Adaptive robust optimization Min cy + Max Min dx y u x First stage variables First-Stage Constraints Ay b Second-Stage Constraints Dy + Ex + Ru f x x x Second Stage Variables y Z + x R + October 23, 204 P. LIU--PHD DISSERTATION DEFENSE 5

6 Start up and shut down cost System power balance Generation capacy lims Robust formulation NG NT NG NT ND NT Min a I + SUD + Max Min b P + r PC i i j D, I D P, PC i= t= i= t= j= t= SUD SUD P su i sd ( I I ) i, t i ( I i, t I NG ND P = D i j PC = = D, min i I P P i I ) Load shedding lims Power flow lims Un ramping up and down lims Un minimum ON/OFF time lims 0 PC, D D min PL SF( K ppg KD( D PCD)) PL P P UR I I S P i, t i[ ( i, t )] + i ( I Ii, t ) + Pi ( I ) P P DR [ ( I I )] + DP ( I I ) + P ( I ), i, i, i, k+ Ton, i T n= k in on, i ik i, k n= k in ik i, k I T ( I I ), j, k [ I ( I I )] 0, j, k k+ Toff, i T n= k in off, i ik, ik, n= k in ik, ik, ( I ) T ( I I ), j, k [ I ( I I )] 0, j, k October 23, 204 6

7 Uncertainty modeling D min D D min = + D ( D D )/2 ˆ min = ( )/2 D D D D = D + Dˆ η z ˆ + D = D + D η ( β β ) z + = β β β + β + + β, β {0,} October 23, 204 7

8 Robustness adjustment η = { η : η Γ, η } Z = { z : z Γ, z } t j t Z = { z : z Γ, z } j t j These three control patterns can be applied separately or collaborately wh each other to improve the flexibily of the proposed model. October 23, 204 8

9 Benders decomposion The Master Problem dealing wh the binary variables relating to un commment decisions NG NT Min F = a I + SUD + α i= t= i l Subject to the start up and shut down cost, and minimum ON/OFF lims. The first-stage decisions will be forwarded into the second-stage problem The first-stage problem will interact wh the second-stage problem through the optimal cut October 23, 204 9

10 Benders decomposion The Slave Problem sub-problem of adjustable robust SCUC should meet the power dispatch and load shedding requirements related to the integer un commment decisions at the first stage By introducing the dual theory in the slave problem The optimal cut is generated as D P, PC NG NT ND NT Max Min b P + r PC i j D, i= t= j= t= NG NT min R ( Iˆˆˆ ) = Max NG NT Pi I π, + Pi I π2, i= t= ( π3, ) + ( π4, ) D, π i= t= NT ND NL NT NL min + D { π5, t π8, + SFk KD, j ( π6, kt + π7, kt )} + π6, kt PL + π7, kt PL t= j= k= t= k= NG NT NG NT NT ND ˆˆˆˆˆˆ min Pi I, + Pi I 2, ( 3, ) + ( 4, ) + { D 5, t D 8, } i= t= i= t= t= j= α π π π π π π NT NL ND NT NL ND ˆˆ min + π6, kt { PL SFk KD, j D } + π7, kt { PL + SFk KD, j D } t= k= j= t= k= j= October 23, 204 0

11 Impact of Uncertainty Range Computation results wh various uncertainty range Case Uncertainty range Iteration (#) Cost ($) Time elapsed (s) [,] e e+04 2 [0.9,.] e e+03 3 [0.85,.5] 926.3e e+03 4 [0.75,.25] e e+03 5 [0.5,.5] 3422 load shedding applied.7585e+004 October 23, 204

12 Impact of Bus Robustness relative gap(%) gamma(t)=3 gamma(t)= gamma(t)=2 gamma(t)= eration Impact of bus robustness on computation process October 23, 204 2

13 Impact of Hourly Robustness worst-load hours Iteration (#) Cost ($) Time elapsed (s) e e , 7-9, e e+03 2,6, e e+03 6, e e e worst-load hours Iteration (#) Cost ($) Time elapsed (s) e e+03 8, e e+03 2,6,2-4, e e ,8,3-5, e e e worst-load hours Iteration (#) Cost ($) Time elapsed (s) e e+03 8,6, e e , e e e e e October 23, 204 3