Closure to Discussion on “Approximate Linear Power Flow Using Logarithmic Transform of Voltage Magnitudes With Reactive Power and Transmission Loss Consideration”

The discusser raised insightful discussions on our previous paper about an approximate linear power fl ow model using the logarithmic transform of voltage magnitudes (LTVM). The following includes our responses to those discussions. About the reasons of applying Q
_i
e
^-2lnVi
for reactive power equations and P
_i
e
^-1nVi
for active power equations. About the numerical results in Table I of [1]. To conduct a fair comparison among the linear power fl ow model mentioned in [1], we update the codes of [1] by involving the nodal shunt admittances and using the consistent rules for setting bus types. Then the numerical simulations in the discussion of [1] are run again using the standard dataset package in [3] with the updated codes. The updated codes together with the dataset is provided in [4]. The simulation results presented in Table I indicate that the method corresponding to the second column is of the least root-mean-squared errors of voltage magnitudes in most cases except two. Therefore, the proposed linear power fl ow model in [2] is still advantageous in approximating voltage magnitudes.