Forecasted output of wind electric generators (WEGs) in a 24-h horizon has large uncertainties. These uncertainties pose a challenge while computing optimal bids necessary for participating in the day-ahead unit commitment process (DACP) thus limiting their integration and success. This study proposes a new optimal participation strategy for a WEG that employs an energy storage device (ESD) for participating in the DACP. The WEG is modelled to function as a price-taker. The proposed formulation has two objectives: (a) maximise returns from the market considering the best forecast; and (b) minimise risks considering the forecast uncertainties. Risk in the participation strategy is quantified by computing expected energy not served (EENS). The multiobjective mixed integer linear programming formulation is transformed into a fuzzy optimisation problem and solved. Through suitable examples, the ESD is shown to play two important roles: (a) it helps to shift wind energy produced during hours with low marginal prices to those hours with higher marginal prices by appropriately storing and releasing it. This shift can be forward or backward in time. (b) The second crucial role played by ESD, upon minimising EENS, is to maintain an energy reserve akin to spinning reserve such that the risk of the optimal participation schedule is the least.

Electric vehicles (EVs) will be dominating the modes of transport in the future. Current limitations discouraging the use of EVs are mainly due to the characteristics of the EV battery and lack of easy access to charging stations. Charging schedules of EVs are usually uncoordinated, whereas coordinated charging offers several advantages, including grid stability. For a solar photovoltaic (PV)-based charging station (CS), optimal utilization of solar power results in an increased revenue and efficient utilization of related equipment. The solar PV and the arrival of EVs for charging are both highly stochastic. This work considers the solar PV forecast and the probability of EV arrival to optimize the operation of an off-grid, solar PV-based commercial CS with a battery energy storage system (BESS) to realize maximum profit. BESS supports the sale of power when the solar PV generation is low and subsequently captures energy from the solar PV when the generation is high. Due to contrasting characteristics of the solar PV and EV charging pattern, strategies to maximize the profit are proposed. One such strategy is to optimally size the BESS to gain maximum profit. A mixed integer linear programming (MILP) method is used to determine the optimal solution.

Capacitor planning in a distribution system (DS) must account for forecasted load and planned wind generators (WGs). In some DSs with large penetration, WGs support a significant part of the total load on an average and the power flow reverses to the substation during high-wind-low-load conditions. With annual forecasts of peak loads and generations being probabilistic in nature with differing probability distribution functions, their proper representation in a capacitor planning exercise is imperative. In this work, using probabilistic models of load and wind generation, we propose a stochastic capacitor planning formulation for DSs. The proposed formulation minimizes the total cost of newly located and sized capacitors and the annual energy loss in a DS while considering limits on load bus voltages. The starting state of the optimization process has forecasted loads, planned WGs, and inadequate capacitors that results in lower voltage limit violations. In order to handle this infeasible state in a stochastic optimization formulation, fuzzy models are used to represent load bus voltage constraints. The proposed fuzzy stochastic programming method that combines stochastic programming and fuzzy optimization procedure is solved using a robust mixed integer linear programming solver. Results on a 70-bus system are reported, compared, and discussed.

This paper formulates a set of equations (SOE) to describe a radial distribution system with high R/X ratio. The SOE comprises 3(N - 1) second-order equations and an equal number of variables for an N-bus system. The proposed method solves this SOE using the first-order Newton-Raphson technique. The SOE model accounts for elements such as transformers, transmission lines, shunt capacitors, constant PQ loads, and constant impedance loads. Irrespective of the R/X ratio values of the lines in the system, the SOE preserves a strong diagonal characteristic. As well, this SOE is devoid of bus phase angles, unlike the 2(N - 1) ac power flow equations used to describe transmission systems. The proposed method is compared with other methods reported in the literature for distribution systems, such as Newton-based methods and recursive methodologies that use forward and reverse sweeps. Tests conducted on radial distribution systems with 43, 69, and 5002 buses show the new method to be more accurate than other methods reported in the literature.

One of the key strategies for decarbonization and green transportation is using electric vehicles (EVs). However, challenges like limited charging infrastructure, EV battery characteristics, and grid integration complexities persist. This study proposes a mixed-integer linear programming (MILP) approach to optimize a grid-connected solar PV-based commercial EV charging station (SPEVCS) with a battery energy storage system (BESS) for profit maximization. The MILP model efficiently manages SPEVCS operations, considering solar power fluctuations, EV charging patterns, and BESS usage. By coordinating charging schedules, grid stability is reinforced, and excess solar power can be lucratively managed. Comparing grid-connected and off-grid SPEVCS scenarios highlights grid integration benefits. Solar power mismatches with optimal charging periods pose a challenge, addressed here by BESS utilization and import/export of deficit/surplus power from/to the grid. The proposed framework incorporates solar power forecasts and probabilistic EV arrival predictions, enhancing decision accuracy. This approach fosters viable commercial EV charging, promotes green transportation, and reinforces grid resilience.