), and could be the threat amount of the SAA model (27) (0 ).Appl. Sci.
), and could be the risk degree of the SAA model (27) (0 ).Appl. Sci. 2021, 11,10 ofBased on the system presented in [29,40], the SAA challenge (27) is implemented S iterations. In each iteration, this model might be solved M instances in correspondence to M m sample sets so that we can get M GYKI 52466 web first-stage optimal options xs and optimal values Vsm (1 s S, 1 m M ). As the optimal difficulty includes chance constraint, so we want m to verify the feasibility from the first-stage option xs by evaluating the (1 – )-confidence upper bound in the likelihood constraint with N samples ( N N ) as follows:m m U ( x s ) = g ( x s ) + -1 (1 -) m m g( xs )(1 – g( xs )) N(29)N 1 m m m where g( xs ) = Pr( G ( xs , y,) 0) = N n=1 1(0,) ( G ( xs , yn , n )); and -1 could be the inm ) is significantly less than or equal for the risk level then x m verse standard distribution function. If U ( xs s is really a feasible option with the confidence level (1 – ). The conclusion in [29] shows that we can acquire the ideal solution if = /2. Following [29,40], the average from the Lth smallest optimal values VsL obtained in ^ S iterations could be treated because the decrease bound L in the accurate optimal value, where L is calculated as in [29]. Furthermore, the accurate optimal value’s upper bound could be estimated by Equation (30).U = min1 m M 1 s Sm U (Vsm ) = f ( xs ) +1 Nn =Q(yn , n )N(30)^ If the optimality gap U – L /U one hundred is smaller sized than a provided threshold , the ^ algorithm terminates, and the first-stage optimal resolution x which corresponds for the upper bound U will be the optimal answer for the original trouble.Algorithm 1. SAA method combined K-means clustering strategy 1. For s = 1, 2, . . . , S do (a) For m = 1, two, . . . , M do (i) (ii) (iii) (iv) Generate a sample set of size N. Divide N samples into NL clusters by the K-means clustering strategy. Decide NL centroids and their probability. m Solve the SAA model in Equation (27) to obtain the option xs and also the m. optimal value Vs Create a large sample set of size N and evaluate the upper bound in the m m chance constraint U ( xs ) by Equation (29). If U ( xs ) , go to (v); else, skip (v) and visit the subsequent iteration. Estimate the upper bound from the optimal value U (Vsm ).(v) (b) two. 3. four.Figure out the Lth smallest optimal values VsL PF-05105679 References primarily based on the technique presented in [29].Determine the upper bound U of your correct optimal by Equation (30) and also the corresponding ^ solution x. ^ Calculate the reduced bound L as the typical of all VsL . ^ Calculate the optimality gap g = U – L /U one hundred and evaluate it for the threshold . If ^ g , x is the final result; else, adjust NL and go back to step 1.four. Final results and Discussion four.1. Study System Within this section, the proposed optimal model is implemented on a CVPP test method which includes RESs, battery storage systems, and residential customers. Assuming that the CVPP test method is positioned inside the Vietnamese energy grid, this method uses the data collected from Vietnam’s electricity marketplace, including wholesale tariff and standard wind, solar, and load profiles. In fact, the VPP model plus a BC market haven’t been applied inAppl. Sci. 2021, 11, x FOR PEER Review Appl. Sci. 2021, 11,12 of 25 11 ofIn the VPP test method, the RESs are assumed to be wind power plants with all the foreVietnam. Nevertheless, of a wind generator (in p.u.) illustrated is anticipated that this model casted power curveswith the fast increase in RES sources, itin Figure four. Meanwhile, the will soon turn out to be relevant. battery storage systems could be treated as a large-sca.
