A two-stage two-layer optimization approach for economic operation of a microgrid under a planned outage

Pre-Perturbation Operational Strategy Scheduling in Microgrids by Two-Stage Adjustable Robust Optimization

“…Eqs. (29)(30)(31)(32)(33)(34)(35) pertain to the day-ahead electricity market including on/off constraints of the DGs (29-30) (29) 𝑥 𝑔(𝑡−1) − 𝑥 𝑔𝑡 + 𝑢 𝑔𝑡 ≥ 0, ∀ 𝑔 ∈ Ω 𝐷𝐺 , 𝑡 ∈ Ω 𝑇 ;…”

“…(30) 𝑥 𝑔𝑡 − 𝑥 𝑔(𝑡−1) + 𝑣 𝑔𝑡 ≥ 0, ∀ 𝑔 ∈ Ω 𝐷𝐺 , 𝑡 ∈ Ω 𝑇 ; constraints on the minimum time of increasing and decreasing the DGs' power (31)(32), decomposition of the day-ahead energy scheduling of the MG to positive and negative parts (33) actual power exchanged between the grid and MG (56-57), 6) Constraint 𝐾 𝑧 ≤ 𝐼, where 𝐾 denotes the matrix of coefficients of second-stage decision variables, 𝐼 is the uncertain parameter and includes the following equation, 7) Constraint 𝑄 𝑧 = 𝑑, where 𝑄 denotes the matrix of coefficients of second-stage decision variables, d uncertain parameter and includes the following equations.…”

“…Alternatively, in the multi-stage approaches, these sets can be considered as auxiliary decision variables in the second stage, which result in a smaller number of iterations and faster convergence. However, in the majority of relevant works, the values of these parameters are not indicated [31][32][33]. As a result, there is no guarantee that the parameter values are in defined sets and thus the obtained optimal solution is not reliable/valid.…”