Abstract-Matching demand to supply is one of the key features of smart grid infrastructure. Transforming conventional static customers into active participants who interact with the electrical utility in real time is the central idea of Demand Response (DR)\Demand Side Management (DSM) in smart grid. In this paper, we decouple utility cost minimization and customer social welfare maximization into two stages. Since the utility is usually more risk averse than risk neutral in real life, this decoupling approach is more realistic than the usually adopted optimization setup, in which the two objectives are combined in a single weighted sum. With a block processing model introduced, in the first stage a convex optimization problem is formulated to minimize utility's generation cost and delay operation cost. An optimal load demand scheduling solution, of the form of waterfilling, is derived analytically. Based on the optimal load profile generated in this first stage, repeated Vickrey auctions over time intervals are adopted to allocate load demands among customers while maximizing the social welfare. Despite the fact that truthful bidding is a weakly dominant strategy for all customers in the auctioning game, collusive equilibria do exist and jeopardize utility's profit severely. Analysis on the structure of the Bayesian Nash equilibrium solutions shows that by introducing a positive reserve price the Vickrey auction can be made to be more robust against such collusion by customers. Moreover the corresponding Bayesian Nash equilibrium is essentially unique and guarantees the basic profit of the utility. We further discuss how customers' valuations and bidding strategies change over time for the repeated Vickrey auction model. Simulation results emphasizing the influences of reserve price and time interval size on utility's profit is also presented.

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The Virtual Telescope for X-ray Observations (VTXO) will use lightweight Phase Frensel Lenses (PFLs) in a virtual X-ray telescope with 1 km focal length and with nearly 50 milli-arcsecond angular resolution. Laboratory characterization of PFLs have demonstrated near diffraction-limited angular resolution in the X-ray band, but they require long focal lengths to achieve this quality of imaging. VTXO is formed by using precision formation flying of two SmallSats: a smaller, 6U OpticsSat that houses the PFLs and navigation beacons while a larger, ESPA-class DetectorSat contains an X-ray camera, a charged-particle radiation monitor, a precision star tracker, and the propulsion for the formation flying. The baseline flight dynamics uses a highly-elliptical supersynchronous geostationary transfer orbit to allow the inertial formation to form and hold around the 90,000 km apogee for 10 hours of the 32.5-hour orbit with nearly a year mission lifetime. The guidance, navigation, and control (GN&C) for the formation flying uses standard CubeSat avionics packages, a precision star tracker, imaging beacons on the OpticsSat, and a radio ranging system that also serves as an inter-satellite communication link. VTXO's fine angular resolution enables measuring the environments nearly an order of magnitude closer to the central engines of bright compact X-ray sources compared to the current state of the art. This X-ray imaging capability allows for the study of the effects of dust scattering nearer to the central objects such as Cyg X-3 and GX 5-1, for the search for jet structure nearer to the compact object in X-ray novae such as Cyg X-1 and GRS 1915+105, and for the search for structure in the termination shock of in the Crab pulsar wind nebula. The In this paper, the VTXO science performance, SmallSat and instrument designs, and mission description is be described. The VTXO development was supported as one of the selected 2018 NASA Astrophysics SmallSat Study (AS3) missions.

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