  This paper presents a sensitivity-based approach for the placement of
distributed energy resources (DERs) in power systems. The approach is based on
the fact that most planning studies utilize some form of optimization, and
solutions to these optimization problems provide insights into the sensitivity
of many system variables to operating conditions and constraints. However, most
of the existing sensitivity-based planning criteria do not capture ranges of
effectiveness of these solutions (i.e., ranges of the effectiveness of Lagrange
multipliers). The proposed method detects the ranges of the effectiveness of
Lagrange multipliers and uses them to determine optimal solution alternatives.
Profiles for existing generation and loads, and transmission constraints are
taken into consideration. The proposed method is used to determine the impacts
of DERs at different locations, in the presence of a stochastic element (load
variability). This method consists of sequentially calculating Lagrange
multipliers of the dual solution of the optimization problem for various load
buses for all load scenarios. Optimal sizes and sites of resources are jointly
determined in a sequential manner based on the validity of active constraints.
The effectiveness of the proposed method is demonstrated through several case
studies on various test systems including the IEEE reliability test system
(IEEE RTS), the IEEE 14, and 30 bus systems. In comparison with conventional
sensitivity-based approaches (i.e., without considering ranges of validity of
Lagrange multipliers), the proposed approach provides more accurate results for
active constraints.
