An Enhanced McCormick Envelopes to Represent Kron's Loss Formula

Abstract

Parameters𝑃 𝑘 Generation level of unit k 𝑐 𝑘 , 𝑏 𝑘 , 𝑎 𝑘 , 𝑒 𝑘 , 𝑓 𝑘 Coefficients of cost function. characteristics 𝑝 ̃ℎ,𝑘 Generation level of unit k in segment h for piecewise linear approximation of cost. function 𝐵 00 , 𝐵 𝑘0 , 𝐵 𝑘𝑗 Loss coefficients in Kron's formula 𝑃 𝑙𝑜𝑠𝑠𝑒𝑠 Transmission losses 𝑣 𝑘,𝑗 Auxiliary continuous variables in the McCormick relaxation Functions 𝑣 𝑘,𝑗 𝑛 Auxiliary continuous variables in the partitioned McCormick relaxation 𝑂(𝑃) The total cost of generating units 𝑧 𝑅 𝑘,𝑛 Binary variables in the McCormick relaxation 𝑂 ̃(𝑃) The approximated total cost of generating units 𝑧 ℎ,𝑘 Binary variables in the partitioned McCormick relaxation 𝑃𝐶 𝑘 Generation cost of unit k