A Joint Optimization Model for Transmission Capacity and Wind Power Investment Considering System Security

Abstract

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: Ω Set of buses indexed by 𝑖, 𝑗. Ω Set of scenarios indexed by s. B. Parameters: 𝑔 , 𝑏 Conductance and susceptance of a transmission line. 𝐴 , 𝐵 , 𝐶 Constant parameters used to approximate a circle by a regular polygon. 𝑎 , 𝑏 , 𝑐 Production cost coefficients of a thermal unit. 𝐼 ,𝐼 Annualized investment cost of a wind farm and a transmission line. 𝑀 , 𝑀 , 𝑀 , 𝑀 Big-M parameters. 𝑃 Active power demand. 𝑄 , 𝑄 , 𝑄 Reactive power generation of thermal units in the main problem, VSM assessment problem and OPF problem. 𝑃 , 𝑃 , 𝑃 Active power generation of wind farms in the main problem, VSM assessment problem and OPF problem. 𝑄 , 𝑄 𝑄 Reactive power generation of wind farms in the main problem, VSM assessment problem and OPF problem. 𝑃 Capacity of a wind farm. 𝑢 Binary variable indicating the installation status of a transmission line. ∆𝑣 , ∆𝑣 , ∆𝑣 Voltage deviation in the main problem, VSM assessment problem and OPF problem. 𝛿 ,𝛿 𝛿 Voltage angle in the main problem, VSM assessment problem and OPF problem. 𝛿 , Voltage angle at the reference bus.

Analysis of Wind Turbine Equipment Failure and Intelligent Operation and Maintenance Research

“…However, this study focused only on the granularity modeling of individual data centers and the flexible planning of energy systems in their surrounding areas, without considering detailed energy networks. Alshamrani et al [198] proposed a transmission expansion planning model that considers the voltage stability assessment of a grid with embedded wind farms under uncertainty conditions, which is unique in that it incorporates the voltage stability margin (VSM) into the planning model. The model is a two-tier model in which the first tier minimizes the total investment and operating cost minus the weighted VSM and the second tier evaluates the optimal expan-sion plan given by the VSM from the first tier.…”