Power transmission expansion planning based on voltage stability indexes

This paper proposes an approach to select configurations for power transmission system planning based on voltage stability criteria. The strength and robustness of a particular bus in a power system can be characterized by the stability index, i.e. the bus eigenvalue. This eigenvalue reflects how the bus voltage magnitude changes corresponding to reactive power variations. If the eigenvalue is small, that bus is sensitive to a change and is a weak bus. On the other hand, if the eigenvalue is large, the corresponding bus is strong and robust. Thus, the robustness of a power system can be determined and estimated based on its eigenvalues. Different connections for a number of buses in a power system result in different values of eigenvalues, and our algorithm is oriented to find the configurations that have large eigenvalues. In each constraint scenario, all the possible power system configurations are considered, and the proposed algorithm calculates the performance index for each case. A configuration with small performance index is considered a strong and robust one. A typical five-bus power system is used to demonstrate the effectiveness of the introduced algorithm. Simulation results show that this method can find many networks that are more voltage stable than the original one.

I. Introduction

Power transmission expansion planning has been widely studied in the literature for a several decades; the main target is to guarantee the power system still operate properly with changes in load demand, the generation sources, the availability of power devices, or future policy. A transmission expansion planning (TEP) problem is considered as a nonlinear mixed-integer constrained optimization problem [1]–[3]. Depending on the formulation, the objective function can aim to optimize reactive power planning, uncertainty, reliability, etc. For example, in [4], [5] minimizing reactive power planning is considered. The reactive power flows on the transmission lines are reduced significantly by relocated the reactive power sources close to the loads to supply demands. This rearrangement also results in less power losses and thus increases the power system network capacity without building more transmission lines. Another example of TEP problem is considered uncertainties in the objective function. The uncertainties in the power system can be the changes in loads, new integration of renewable energy sources such as wind farms and photovoltatic inverters, or the availability of power components in the future [1], [6], [7]. This formulation relies on statistical and probabilistic models to design the power network [8]–[10].