Due to continuous growth in electric demand and increasing connection of renewable energy, the power systems are being operated with smaller stability margins. Therefore, a sufficient loading margin is essential to maintain the system secure and ensure voltage stability. To this end, this paper studies the joint optimization of transmission capacity and wind power investment problem, the unique feature of which is incorporating voltage stability margin (VSM) in the planning model. A bi-level model has been formulated whose upper level minimizes the total investment and operation cost minus the weighted VSM. The lower level evaluates the VSM given the optimal expansion plan from the upper level. In addition, the stochastic nature of wind power and load can impact voltage stability. Thus, uncertainties related to intermittent wind generation and demand must be modeled. We use an approximated linear representation to model the AC power system at both levels of the problem. The duality theory (primal-dual formulation) is utilized to transform bi-level programming into single-level mathematical programming. The validity of the constructed methodology is demonstrated on the IEEE 24-bus RTS, which indicates the efficacy and feasibility of the presented model.
INDEX TERMSBi-level programming, Primal-dual formulation, Transmission and wind investment, Voltage stability. NOMENCLATURE A. Indices and sets: Ξ© Set of buses indexed by π, π. Ξ© Set of scenarios indexed by s. B. Parameters: π , π Conductance and susceptance of a transmission line. π΄ , π΅ , πΆ Constant parameters used to approximate a circle by a regular polygon. π , π , π Production cost coefficients of a thermal unit. πΌ ,πΌ Annualized investment cost of a wind farm and a transmission line. π , π , π , π Big-M parameters. π Active power demand. π , π , π Reactive power generation of thermal units in the main problem, VSM assessment problem and OPF problem. π , π , π Active power generation of wind farms in the main problem, VSM assessment problem and OPF problem. π , π π Reactive power generation of wind farms in the main problem, VSM assessment problem and OPF problem. π Capacity of a wind farm. π’ Binary variable indicating the installation status of a transmission line. βπ£ , βπ£ , βπ£ Voltage deviation in the main problem, VSM assessment problem and OPF problem. πΏ ,πΏ πΏ Voltage angle in the main problem, VSM assessment problem and OPF problem. πΏ , Voltage angle at the reference bus.