Stochastic AC Transmission Expansion Planning: A Chance Constrained Distributed Slack Bus Approach With Wind Uncertainty

Abstract

Integrating more renewable energy sources into the grid leads to a more vulnerable power system and presents challenges for power system planners. This paper proposes a probabilistic overload constraint based AC transmission expansion planning model. In terms of economic dispatch, generation adequacy and network constraints are assessed using a probabilistic participation factor power flow. Generation participation factors, which are handled in the AC power flow equations, are used to manage mismatch power that comes from uncertainties as well as transmission loss of the system in a distributed slack bus concept. Combinations of load, wind and N-1 contingency uncertainties are evaluated with Monte Carlo Simulation and the loading limits for the existing and candidate lines and violations on bus voltages are enforced as probabilistic constraints using chance constraint programming. The investment decisions taken under various operating conditions are re-evaluated under a new set of wind power uncertainty that differs from those utilized in the optimization process, and the resulting TEP decisions are analyzed from a risk perspective. The proposed method allows for the uncertain operating conditions to be easily and accurately adapted to the ACTEP optimization. The optimization results show that the participation factor power flow is a promising tool for evaluating probabilistic operating conditions, which can be used to explore the possibility of violations under different uncertainty conditions. INDEX TERMSChance constrained programming, distributed slack bus, participation factor, transmission expansion planning, wind power. NOMENCLATURE 𝑖, 𝑘 Bus no 𝑐 Contingency 𝛽 Not overload probability 𝑁 Total number of buses Ω Total set of candidate lines Ω 𝐶 Total set of contingency 𝑃 𝐺𝑖 Real power output of a generator at bus i 𝑃 𝐷𝑖 Load at bus i 𝑃 𝐼𝑀𝐵 Imbalance power 𝐶 𝑖 Quadratic cost function of generator at bus i 𝐶 𝑖 (𝑃 𝐺𝑖 ) Total generation cost 𝑎 𝑖 , 𝑏 𝑖 , 𝑐 𝑖 Cost coefficients of generator at bus i 𝑃 𝐺𝑖_𝑠𝑐ℎ Scheduled real power output of a generator at bus i 𝑃 𝐺𝑖_𝑢𝑝𝑑 Updated real power output of a generator at bus i 𝑃𝑓 𝑖 Participation factor of generator at bus i 𝑃 𝑖 Injected active power at bus i 𝑄 𝑖 Injected reactive power at bus i 𝑃 𝑠𝑝,𝑖 Specified (known) active power at bus i 𝑄 𝑠𝑝,𝑖 Specified (known) reactive power at bus i ∆𝑃 Mismatch active power vector ∆𝑄 Mismatch reactive power vector 𝑉 𝑖 Voltage magnitude at bus i 𝜃 𝑖 Voltage angle at bus i 𝑉 𝑖 𝑐 Voltage magnitude at bus i at contingency operating condition c 𝜃 𝑖 𝑐 Voltage angle at bus i at contingency operating condition c 𝑔 𝑖𝑘 Conductance of line i-k 𝑏 𝑖𝑘 Susceptance of line i-k 𝑏 𝑖𝑘 𝑠ℎ

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

“…A robust optimization model for ESS and transmission line investment co-planning, considering binary variables related to ESS statuses in the recourse problem, is established in [17], where an enhanced nested column and constraint generation technique is used to solve the problem. A scenario-based AC transmission investment model is put forth in [18], where combinations of load, wind, and N-1 contingency uncertainties are assessed with Monte Carlo simulation and the loading limits for the existing and candidate lines. A stochastic transmission and generation expansion planning model is formulated in [19] to increase the hosting capacity of networks and satisfy future load demands, in which two algorithms, namely, the weighted mean of vectors optimization and sine cosine algorithms, are used to solve the problem.…”