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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 paper 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. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) have been well recognized as a deferrable load with the flexibility to shift their energy demands over time. Although this one-dimensional flexibility has been extensively investigated both by research and industrial implementations, the expanding energy demand and the associated uncertainties still make the integration of a large population of EVs into power system reliably and economically greatly challenging. In this paper, we design an auction scheme via mechanism design to elicit two additional flexibilities from EVs, namely energy flexibility and deadline flexibility. An offline mechanism is firstly designed as a benchmark based on the famous Vickrey–Clark–Groves mechanism. Then based on the primal-dual approach, we propose an online auction, in which all bids are truthful, the loss of social welfare is bounded by competitive ratio, and the mechanism can be implemented in polynomial time. By the numerical results, we quantitatively show that both the power system operators and individual EVs can benefit from the integration of the multi-dimensional flexibilities through our proposed mechanisms. [ABSTRACT FROM AUTHOR]

By the introduction of competitive supply, modern electric utilities are forced to operate their systems closer to their security limits. Under such fragile conditions, any disturbance could endanger system security and lead to system collapse. There is, therefore, a need to develop new methods which could evaluate optimal scheduling of operating reserve and forewarn the system operators to take necessary preventive actions in case need arises. An effective method is proposed in this paper to optimally allocate spinning reserve based on a well-being model. The method used in conventional well-being framework for classifying power system comfort zone into healthy and marginal states is initially revised. The optimal value of health index and system spinning reserve requirements are then evaluated on the basis of a trade off between the total cost of spinning reserve and the expected cost of energy not served. The effectiveness of the proposed method is examined using the IEEE-RTS. [ABSTRACT FROM AUTHOR]