Correct the Piecewise Linearization Error of Quadratic Objective Function in DC OPF Model

In power industries and academia, piecewise linearization methods are widely used in optimal power flow (OPF) problems to approximate the nonlinear objective functions. Better computational performance can be achieved. However, limited attention has been paid to the approximation error. In electricity markets, this error could cause distortions of market clearing results and deficits in social welfare. To address this issue, we provide a criterion for the desired number of piecewise segments. We then propose an efficient method for correcting the piecewise linearization error of the DC OPF problems.