An Implementation of the Stochastic OPF Problem

RETRACTED: Active robust optimization for wind integrated power system economic dispatch considering hourly demand response

“…Let z t ¼ ðP d1 t ; P w t Þ, ct2T be the vector of the environmental parameters, including the first category of loads and undispatchable WP generation which has been totally accessed to the grid. The system uncertainty includes both the available WP described by (14) and the second category of the loads described by (16). For a 24-h dispatch horizon, let l ¼ (l 1 , /, l 24 ) be the vector of nodal prices l t ¼ ðl t1 ; /; l tN d Þ T for each bus at time t, which is determined by x, y and z through multi-period OPF calculation expressed as l t ¼ l t ðx t ; y t ; z t Þ T , ct2T .…”

“…For calculation convenience, the power factor of each load computed from the load data is kept constant. The uncertainty in load is simulated by (16). The maximum load is set to 120% of the total load at each bus.…”

“…In simulation, the traditional static uncertainty set (16) for load is incorporated. The load at each time period is independently generated as a normal random variable with a std equaling 5% of its mean.…”

“…The SO-based approach introduced as early as Dantzig [7] relies on pre-sampling discrete scenarios of the uncertainty realizations [8,9] via presumed probability distribution functions (PDFs) of uncertainty parameters and tries to compute a solution which optimizes the expected value of the objective function. Representative researches include stochastic security-constrained unit commitment (SCUC) [8], [10,11], stochastic ED [12,13], DR dispatch [14,15], stochastic optimal power flow (OPF) [16,17], and stochastic electric vehicle (EV) charging [18,19]. But the SO-based approach still has practical limitations in its application to large scale power systems.…”

Adjustable risk-based direct current optimal power flow

“…Risk-based optimal power flow (RBOPF) [3][4][5][6][7][8][9][10][11][12] is an emerging new approach proposed in previous work. Existing literature on this subject shows that system operating risk can be mitigated in expectation by jointly optimizing the pre-contingency dispatch and the post-contingency recourse in a twostage stochastic programming framework [3,[9][10][11][12]. Compared with the SCOPF, such stochastic RBOPF (S-RBOPF) problems account for the probabilistic nature of system conditions and can quantify and manage system operating risk.…”