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To address the issue that Lagrangian dual-function-based algorithms cannot guarantee convergence and global optimality for decentralised multi-area security constrained unit commitment (M-SCUC) problems, a novel decomposition and coordination method using mixed-integer linear programming (MILP) value functions is proposed. In the proposed solution method, first, each regional system operator sets the tie-line power injections as variational parameters in its regional SCUC model, and utilises a finite algorithm to generate an MILP value function, which returns the optimal generation cost for any given interchange plan. Then, with the value functions available from all system operators, theoretically, a coordinator is able to devise a globally optimal interchange plan. After the problem is solved, considering that power exchanges may alter the financial position of each area considerably from what it would have been via scheduling independently, the authors then propose a fair savings allocation method using the value functions derived above and the Shapley value in cooperative game theory. Numerical experiments on a two-area 12-bus system and a three-area 457-bus system were carried out. The validity of the value-function-based method was verified for the decentralised M-SCUC problem. The outcome of savings allocation was compared with that of the locational marginal cost-based 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]

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]