Pricing storage operation in the real-time market under demand and generation stochasticities is considered. A scenario-based stochastic rolling-window dispatch model formulated for market, consisting of conventional generators, utility-scale storage, distributed energy resource aggregators. We show that uniform pricing mechanisms require discriminative out-of-the-market uplifts, making settlem...

The time evolution of quantum fields is shown to be equivalent a time-symmetric Fokker-Planck equation. Results are obtained using Q-function representation, including fermion-fermion, boson-boson, and fermion-boson interactions with linear, quadratic, cubic, quartic Hamiltonians, typical QED many other cases. For local boson-boson coupling, the resulting probability distribution proved have po...