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Previous robust transmission expansion planning (RTEP) studies have rarely considered the important question of how large the uncertainty set should be, and hence, how the uncertainty budget can be determined objectively. This study addresses this issue by proposing a novel adaptive optimization method that optimizes the value of the uncertainty budget to minimize the size of the uncertainty set while considering the underlying risk for wind power generation (WPG) fluctuations residing outside of the proposed uncertainty set. As such, the proposed method ensures a good tradeoff between the robustness and costs of RTEP solutions. In addition, the proposed method optimizes investment strategies under forecasted WPG scenarios, while providing a security guarantee under extreme WPG scenarios. The variable-limit integral terms introduced by the proposed method are addressed in the solution process by applying the piecewise linearization approximation method combined with the quadratic Newton-Gregory interpolating polynomial technique, which allows the solution process to be cast as a mixed integer linear programming problem. The good performance and effectiveness of the proposed adaptive uncertainty set optimization method are verified by numerical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the interchange and generation scheduling problem of multi-area power systems, where decentralized decision procedure is preferred and the uncertainties of nodal injections should be considered. The problem is formulated as a multi-area robust security constrained unit commitment model, with a novel uncertainty set specified by the variance of system net load. We prove that such an uncertainty set can provide a more precise probabilistic guarantee than conventional budgeted sets. To solve the problem in decentralized manner, an upper-level robust convex optimization model is proposed to optimize the tie-line power flow and derive a generation interval for each area. Then through the coordinated uncertainty requirement decided by the generation interval, each regional system operator can solve a decoupled robust unit commitment problem independently. Besides, a modified outer approximation algorithm is developed to obtain higher-quality solution of the bilinear programming involved in the process. Simulation results on a two-area system demonstrate the effectiveness of the uncertainty set, and show the economic efficiencies of unit commitment solutions acquired from the hierarchical method. [ABSTRACT FROM AUTHOR]

Reactive power optimization is a special kind of optimal power flow for optimizing voltage profile and reactive power flow in the steady state based on deterministic sets of the demand load and generation values, thus minimizing the real power losses or improving the voltage quality of the power grid. However, the input data in power systems have a certain degree of uncertainty that requires the reactive power optimization be solved by means of uncertain nonlinear programming, as advocated in the literature. To address this problem, we represent the uncertain input data as intervals and establish a model of the reactive power optimization that incorporates the interval uncertainties to describe the problem. The linear approximation method is formulated using the interval Taylor extension to help solve this type of problem. To obtain more accurate intervals for the state variables, the affine arithmetic-based power flow calculation is used to solve the interval power flow equation instead of crude computation based on the interval arithmetic, and thus the modified linear approximation method is developed. The proposed methods are presented in detail and the numerical results are analyzed to demonstrate their effectiveness and applicability, especially in comparison to the previously proposed chance constrained programming method. [ABSTRACT FROM AUTHOR]

High penetrations of renewable energy sources incorporated into transmission systems pose a substantial challenge to transmission expansion planning operations due to both the strong uncertainty of these sources and their high variability. However, most current robust transmission expansion planning studies focus exclusively on the issue of uncertainty, and neglect to optimize system flexibility in an effort to cope with the high variability of these sources. The present work addresses this critical issue by proposing a flexibility-oriented robust transmission expansion planning method developed according to the unit commitment characteristics of coal-fired and gas-fired generation units that fully considers the short-term flexibility requirements of electric power systems while maintaining high robustness to the uncertainties of RES outputs in long-term transmission expansion planning problems. The proposed complex model with unit commitment constraints containing massive binary variables is solved by first reducing the number of binary variables via the application of clustering techniques to identify generator units with similar generation properties, and then decreasing the complexity of the model further by relaxing the integer variables in the unit-clustered model. Finally, we develop generalized column-and-constraint generation algorithms that can solve the clustered model and the relaxed simplified model with greatly enhanced efficiency. Comparisons of the numerical results obtained by the proposed approach with existing state-of-the-art methods when applied to a simple Garver 6-node system and a realistically-sized power system demonstrate that the proposed method produces optimal RTEP solutions that account for both the uncertainty and variability of RES outputs. Moreover, the total cost of the proposed approach is 2.22 × 1 0 6 $ less than that of the other state-of-the-art methods considered, which is of great significance in guiding practical transmission expansion planning applications. • Neglecting flexibility of units in robust transmission planning models can result in significant errors. • Existing algorithms fail to solve the flexibility-oriented planning model for large-scale systems. • Transmission planning schemes are significantly influenced by flexibility-related constraints. • The proposed generalized algorithm expedites the solution process of the model. • The relaxation technique facilitates the applicability of the flexibility-oriented model to large-scale systems. [ABSTRACT FROM AUTHOR]

The rapid incorporation of wind power resources in electrical power networks has significantly increased the volatility of transmission systems due to the inherent uncertainty associated with wind power. This paper addresses this issue by proposing a transmission network expansion planning (TEP) model that integrates wind power resources, and that seeks to minimize the sum of investment costs and operation costs while accounting for the costs associated with the pollution emissions of generator infrastructure. Auxiliary relaxation variables are introduced to transform the established model into a mixed integer linear programming problem. Furthermore, the novel concept of extreme wind power scenarios is defined, theoretically justified, and then employed to establish a two-stage robust TEP method. The decision-making variables of prospective transmission lines are determined in the first stage, so as to ensure that the operating variables in the second stage can adapt to wind power fluctuations. A Benders’ decomposition algorithm is developed to solve the proposed two-stage model. Finally, extensive numerical studies are conducted with Garver’s 6-bus system, a modified IEEE RTS79 system and IEEE 118-bus system, and the computational results demonstrate the effectiveness and practicability of the proposed method. [ABSTRACT FROM AUTHOR]