Recent developments in multiscale computation allow the solution of "coarse equations" for the expected macroscopic behavior of microscopically/stochastically evolving particle distributions without ever obtaining these coarse equations in closed form. The closure is obtained "on demand" through appropriately initialized bursts of microscopic simulation. The effective coupling of microscopic simulators with macrosocopic behavior embodied in this approach requires certain decisions about the nature of the unavailable "coarse equation". Such decisions include (a) the determination of the highest spatial derivative active in the equation, (b) whether the coarse equation satisfies certain conservation laws, and (c) whether the coarse dynamics is Hamiltonian. These decisions affect the number and type of boundary conditions as well as the nature of the algorithms employed in good solution practice. In the absence of an explicit formula for the temporal derivative, we propose, implement and validate a simple scheme for deciding these and other similar questions about the coarse equation using only the microscopic simulator. Microscopic simulations under periodic boundary conditions are carried out for appropriately chosen families of random initial conditions; evaluating the sample variance of certain statistics over the simulation ensemble allows us to infer the highest order of spatial derivatives active in the coarse equation. In the same spirit we show how to determine whether a certain coarse conservation law exists or not, and we discuss plausibility tests for the existence of a coarse Hamiltonian or integrability. We argue that such schemes constitute an important part of the equation-free approach to multiscale computation.

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Outage recovery is important for reducing the economic cost and improving the reliability of a distribution system (DS) in extreme weather and with equipment faults. Previous studies have separately considered network reconfiguration (NR) and dispatching mobile power sources (MPS) to restore the outage load. However, NR cannot deal with the scenario of an electrical island, while dispatching MPS results in a long power outage. In this paper, a resilient outage recovery method based on co-optimizing MPS and NR is proposed, where the DS and traffic network (TN) are considered simultaneously. In the DS, the switch action cost and power losses are minimized, and the access points of MPSs are changed by carrying out the NR process. In the TN, an MPS dispatching model with the objective of minimizing power outage time, routing and power generation cost is developed to optimize the MPSs’ schedule. A solution algorithm based on iteration and relaxation methods is proposed to simplify the solving process and obtain the optimal recovery strategy. Finally, numerical case studies on the IEEE 33 and 119-bus systems validate the proposed resilient outage recovery method. It is shown that the access point of MPS can be changed by NR to decrease the power outage time and dispatching cost of MPS. The results also show that the system operation cost can be reduced by considering power losses in the objective function.

Reasonable planning of flexible power sources is crucial for the reliable operation of new power systems based on new energy sources. However, in the long-term planning, how to consider the shortterm ramping capability of the flexible power supply to meet the capacity demand of the net load and the flexible ramping requirement at the same time is still an unsolved problem. Therefore, this paper conducts research on generation expansion planning based on flexibility balance. Firstly, the flexibility balance are modeled based on the flexible supply domain and the net load fluctuation domain, which are used as the flexible supply and demand constraints in the planning stage. Then, a two-layer expansion planning model is constructed, including two modules of investment decision and production simulation. Flexibility index is proposed to quantify the system's ability to adjust at different levels of payload, and incorporated into the planning model for iterative optimization. Finally, an example is verified on the improved IEEE-39 node system. The test results show that the long-term generation expansion planning scheme based on the balance of flexible supply and demand can effectively meet the net load demand and its ramping demand.INDEX TERMS Flexible requirements, flexible supply domains, flexible supply and demand balance, generation expansion planning. NOMENCLATURE A. INDICES AND SUPERSCRIPTSi M planned capacity of resource i i l expected service life of resource i v discount rate k N sum of the initial units and new units added for the planning year max D maximum load for the planning year D M capacity reserve factor.