Risk Measure Based Robust Bidding Strategy for Arbitrage Using a Wind Farm and Energy Storage

Load Scheduling and Power Trading in Systems With High Penetration of Renewable Energy Resources

“…If constraint (20) is inactive, i.e., S n t ≥ D t , d n t can be either 0 or 1. To satisfy constraint (19) and to enforce condition 2) for evaluating the MCP, one of the variables d n t , n ∈ G t , or d 0 t has to be set to 1 if its corresponding constraint (20) is inactive and the associated set S n t has the smallest number of members. To this end, an auxiliary term…”

“…For the added term, the coefficients of the binary variables d n t , n ∈ G t , are equal to the size of the groups S n t . Thus, to minimize the objective function, among the variables d n t , n ∈ G t , for which the corresponding constraint (20) is inactive, the one with the smallest weight is set to 1. However, if the corresponding constraint (20) is active for all variables d n t , n ∈ G t , variable d 0 t will be set to 1.…”

“…Thus, to minimize the objective function, among the variables d n t , n ∈ G t , for which the corresponding constraint (20) is inactive, the one with the smallest weight is set to 1. However, if the corresponding constraint (20) is active for all variables d n t , n ∈ G t , variable d 0 t will be set to 1. Finally, to evaluate the payoff of user u, we define the auxiliary variable f t which indicates whether the offer O u t will place user u in the set of providing users ( f t = 1) or not ( f t = 0).…”

“…t , d n t , z n t , d u t ∈ {0, 1}, ∀ n ∈ G −u t (21b) constraints (17),(19), and(20) (21c)n∈G t d n t π n t + d 0 t λ h t π u t ≥ f t (21d) λ l t ≤ π u t ≤ λ h t (21e) 0 ≤ g u t ≤ G u t (21f) where I t = (d t , z t , f t ), C t = (g u t , π u t ), d t (d 0 t , d n t | n ∈ G t ), z t (z n t | n ∈ G −u t ), and F(I t , C t ) = C u t g u t −…”

Coordination of Hydro Units With Wind Power Generation Using Interval Optimization

“…Worst-case profits were then measured by using conditional value-at-risk (CVaR) and optimized in the problem. Similarly, Dicorato et al [12] proposed a coordination strategy with the CVaR constraint, while Thatte et al [13] employed CVaR to determine uncertainty sets and proposed a robust bidding strategy. Stochastic optimization requires the exact probability distributions of random variables, which are difficult to obtain but without which, expected profits, risk, and chance constraints cannot be computed.…”