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In this paper, firstly, a formulation for Multi-Period AC Optimal Power Flow is developed to incorporate intertemporal constraints and, specifically, equations representing energy storage systems. Secondly, a solution method for the resulting optimisation model is proposed based on the primal-dual interior point method and the mathematical details underlying the solution approach are explicitly and extensively elaborated. The developed solver is tested on a simple 3 bus system. Finally, the computationally efficiency is compared with similar GAMS-and MATLAB-based non-linear commercial solvers. The main contributions of our proposed method can be summarised as follows: a) Shorter computational time is observed in the test due to the merit of using analytical differentiation in the solution method rather than numerical, which is typically used by commercial solvers. b) The formulation and solution method provides the basis of an open-box flexible solver that can be extended to include other components of power systems.

This paper proposes an accurate and efficient probabilistic method for modeling the nonlinear and complex uncertainty effects and mainly focuses on the Electric Vehicle (EV) uncertainty in Peer-to-Peer (P2P) trading. The proposed method captures the uncertainty of the input parameters with a low computational burden and regardless of the probability density function (PDF) shape. To this end, for each uncertain parameter, multitude of random vectors with the specification of corresponding uncertain parameters are generated and a fuzzy membership function is then assigned to each vector. Since the most probable samples occur repeatedly, they are recognized by the superposition of the generated fuzzy membership functions. The simulation results on various case studies indicate the high accuracy of the proposed method in comparison with Monte-Carlo simulation (MCs), Unscented Transformation (UT), and Point Estimate Method (PEM). It also scales down the computational burden compared to MCs. Also, a real-world case study is employed to examine the ability of the method in capturing the uncertainty of EVs' arrival and departure time. The studies on this case reveal that involving EVs in P2P trading augments the amount of energy traded within the prosumers.