Robust Transmission Network Expansion Planning Under Correlated Uncertainty

Abstract

This paper addresses the transmission network expansion planning problem under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby the worst-case operating cost is accounted for under a given user-defined uncertainty set. This work differs from previously reported robust solutions in two respects. First, the typically disregarded correlation of uncertainty sources is explicitly considered through an ellipsoidal uncertainty set relying on their variance-covariance matrix. In addition, we describe the analogy between the corresponding second-stage problem and a certain class of mathematical programs arising in structural reliability. This analogy gives rise to a relevant probabilistic interpretation of the second stage, thereby revealing an undisclosed feature of the worst-case setting characterizing robust optimization with ellipsoidal uncertainty sets. More importantly, a novel nested decomposition approach based on results from structural reliability is devised to solve the proposed robust counterpart, which is cast as an instance of mixed-integer trilevel programming. Numerical results from several case studies demonstrate that the effect of correlated uncertainty can be captured by the proposed robust approach.

Robust generation expansion planning considering high penetration renewable energies uncertainty

“…When applying the Mixed Integer Linear Programming (MILP) optimization technique on the robust GEP model through modified constraints (24), (25), (26), and (27), it is expected that the number of RES units X RE will be increased to maintain the decrease in CF(i) due to the RES uncertainty based on the preselected confidence level.…”

“…Capacity margin is proposed to deal with the RES uncertainty. So that previous power balancing constraint (15) is modified and utilized as (24), (26), and (27). The RES uncertainty is represented in the power balancing constraint (15) only in this method and not represented in the integration of high sharing RES constraint (16).…”

“…The RES uncertainty is represented in the power balancing constraint (15) only in this method and not represented in the integration of high sharing RES constraint (16). The reason behind that the goal of this method is to deal with the RES uncertainty impact via increasing the number of thermal units X CS only as clarified in (24), (26), and (27). Hence, the reserve margin will be increased.…”

“…The demand and available generation capacity uncertainties are modeled through an ellipsoidal uncertainty set. 27 The level of conservativeness is controlled by proposing a conservativeness parameter defined by the network planner. The uncertainty boundaries are modeled as a polyhedral uncertainty set.…”

Reliability-constrained dynamic transmission expansion planning considering wind power generation

“…The second case study is performed in the IEEE 118-bus system with 40 conventional generators, 40 wind farms, 91 loads and 179 corridors containing existing transmission lines. The used transmission data can be found in [34], each candidate corridor can receive up to 3 new reinforcements, and the bus data is available in [29]. At the end of planning horizon, the system comprises a total of 18.05 GW of conventional power capacity, 7.74 GW of wind power capacity and 15.73 GW of load demand.…”