Due to environmental and fuel cost concerns more and more wind- and solar-based generation units are embedded in distribution networks (DNs). However, a part of such an embedded generation would be curtailed due to system constraints and variations of the energy penetration. This part of energy can be recovered by introducing energy storage systems (ESSs) and an optimal dispatch of both active and reactive powers. Therefore, we propose a combined problem formulation for active-reactive optimal power flow (A-R-OPF) in DNs with embedded wind generation and battery storage. The solution provides an optimal operation strategy which ensures the feasibility and enhances the profit significantly. Results of a 41-bus distribution network are presented. It can be demonstrated that more than 12% of energy losses and a large amount of reactive energy to be imported from the transmission network (TN) can be reduced using the proposed approach in comparison to the operation strategy where only active OPF is considered.

Solution approaches to chance constrained programming (CCP) have been recently developed and applied in many areas for optimization under uncertainty. Due to the nonlinear model with multiple uncertain variables as well as multiple output constraints, CCP has not been directly applied to optimal power flow (OPF) under uncertainty. The objective of this paper is twofold. First, we introduce the CCP approach to OPF under uncertainty and analyze the computational complexity of the chance constrained OPF. Second, the effectiveness of implementing a back-mapping approach and a linear approximation of the nonlinear model equations to solve the formulated CCP problem is investigated. Load power uncertainties are considered as multivariate random variables with correlated normal distribution. Based on both the nonlinear and the linearized model, results of a five-bus system and the IEEE 30-bus test system are presented to demonstrate the scope of chance constrained OPF.

The interest in installing PV-based microgrids has increased significantly in the last years due to the urgent need for reducing greenhouse gas emissions and improving the reliability as well as the quality of power supply, in particular in developing countries. The design of a microgrid is challenging since multiple components and complicated operating conditions have to be taken into account. In this paper, a comprehensive method for optimal design of a class of residential PV-battery microgrids is proposed to determine the optimal number of lead-acid batteries and PV-panels, the optimal battery bank depth of discharge (DOD) value, and the optimal tilt angle of the PV-panels. The aim of the optimization is to minimize the levelized cost of energy (LCOE) where the limitation of the annual total loss of the power supply (TLPS) and the operational constraints are considered. In addition, a detailed model for battery lifetime estimation is introduced based on the physico-chemical mechanism of the lead-acid battery. Moreover, the effect of design parameters, e.g., the size and DOD of the battery bank on the battery capacity degradation, the PV-Panel number and battery lifetime on LCOE, is investigated. Computation results demonstrate that the proposed method is capable of optimizing the size of the microgrid components and the other design parameters while satisfying all technical and operational constraints.

This study presents a probabilistic analysis to consider the impact of uncertain system parameters on optimal power flow (OPF). A general OPF under uncertainty is formulated as a chance-constrained programming model and its stochastic features are investigated. The impact of the uncertain variables is addressed by the probabilistic analysis with the method of Monte-Carlo simulation (MCS) combined with a deterministic optimisation. In this way, relations between the optimality and reliability in power systems under uncertainty can be achieved. The information derived from the statistical results can be applied in the system risk assessment and operation performance evaluation, which is helpful for making decisions in power system optimal dispatch under uncertainty. Case studies of a 5-bus system and the IEEE 30-bus system are presented to illustrate the probabilistic analysis.