Unit Commitment Scheduling by Lagrange Relaxation Method Taking into Account Transmission Losses

After the application of the Lagrange relaxation method to the unit commitment scheduling by Muckstadt in 1979, many papers using this method have been reported so far. The greatest advantage of applying the Lagrange relaxation method for the unit commitment problem is that it can relax (ignore) each generator's output dependency caused by demand-supply balance constraint so that an unit commitment of each generator is determined independently by Dynamic Programming. However, when we introduce the transmission loss into the demand-supply balance constraint, we cannot decompose the problem into the partial problems in which each generator's unit commitment is determined independently and have to take some measures to get an optimal schedule by Lagrange relaxation method directly. In this paper, we present an algorithm for the unit commitment schedule using the Lagrange relaxation method for the case of taking into account transmission losses.