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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]

Renewable energy sources provide an important means of reducing reliance on conventional fuels. However, some renewable energy resources such as wind and solar energies are intermittent, and their uncertainty threatens the operating security of the power grid. To solve this problem, this study proposes the use of intervals to model the power output of renewable energy resources and the power load demand, and accordingly develops an interval voltage control model, i.e. interval reactive power optimisation model. The proposed model considers the control modes of renewable energy power generators and can safeguard the security of power grids by ensuring that the voltages reside within established limits. An adaptive genetic algorithm is employed to solve the proposed model, where a newly developed interval power‐flow (IPF) calculation is used to solve the IPF equations, and penalty functions are applied to express inequality constraints. The proposed method is introduced in detail, and simulation results are presented to demonstrate its performance in comparison with a previously proposed interval voltage control method, as well as its applicability to large systems with various fluctuations of input data. The proposed approach provides robust convergence, obtains lower system power losses, and substantially reduces the computation time. [ABSTRACT FROM AUTHOR]

The reactive power optimisation (RPO) is generally used to design an optimal profile of the voltage and reactive power of power systems in the steady state for deterministic sets of demand loads and generation values, and it is a significant procedure in voltage control. However, the input data of a power system is actually uncertain in practise, which makes RPO an uncertain non‐linear programme. To address this problem, the input data were considered as intervals, and the RPO incorporating interval uncertainties model was proposed. To solve this model, the genetic algorithm was employed as the solution algorithm, where the reliable power flow calculation was used to judge the constraints of the model. The Pareto front was established as the solution of the proposed model since it has two objective functions, i.e. the midpoint and radius of real power losses. The application of this technique to the uncertain RPO was explained in detail. Two numerical results were analysed to demonstrate the effectiveness of the proposed method, especially in comparison with the previously proposed chance‐constrained programming method. [ABSTRACT FROM AUTHOR]