The probabilistic and intermittent output power of Wind Turbines (WT) is one major inconsistency of these Renewable Energy Sources (RES). Battery Energy Storage Systems (BESS) are a suitable solution to mitigate this intermittency by smoothening WT's output power. Although the main benefit of BESSs mentions as peak shaving and load-shifting, but in this research, it will verify that optimal placement and sizing them jointly with WTs can lead to more benefits like compensating the required system's reactive power support from WTs. The reactive power size of WTs and BESSs will be derived from the result of the joint sizing and placement in this study, as well as their active power output to meet the load demand. This can facilitate WTs and BESSs contribution to cover the system's required reactive power and their participation in the reactive power market and ancillary services. This paper also proposes new cost functions for both WTs and BESSs and minimizes their cost while ensuring minimal total loss (active and reactive) in the power distribution system. This can benefit both WTs' and BESSs' owners as well as system operators. Suitable placement and sizing of the WTs and BESSs can also improve the load bus voltage profiles, which can benefit the end-users, and will verify using the proposed optimization by different case studies on the 33 bus distribution system. The results of case studies ascertain the consistency of the proposed formulation for placement and sizing BESSs and WTs jointly, as well as other benefits to the power system, the power plant owners, and system operators.

风力涡轮机（WT）的概率性和间歇性输出功率是这些可再生能源（RES）的主要矛盾之一。电池能量存储系统（BESS）是通过平滑WT的输出功率来减轻这种间歇性的合适解决方案。虽然BESS的主要优点是削峰和负载转移，但是在本研究中，它将验证与WT一起优化放置和调整大小可以带来更多的好处，例如补偿WT所需的系统无功功率支持。WT和BESS的无功功率大小将根据本研究的联合尺寸和放置结果以及满足负载需求的有功功率输出得出。这可以帮助WT和BESS做出贡献来覆盖系统的 所需的无功功率及其在无功市场和辅助服务中的参与度。本文还为WT和BESS提出了新的成本函数，并在确保配电系统的总损耗（有功和无功）最小的同时，将其成本降至最低。这可以使WT和BESS的所有者以及系统运营商受益。WT和BESS的合适放置和尺寸设置也可以改善负载总线电压曲线，这可以使最终用户受益，并且将通过对33个总线配电系统进行不同案例研究，使用建议的优化进行验证。案例研究的结果确定了用于BESS和WT的放置和尺寸调整的拟议配方的一致性，以及对电力系统，电厂所有者和系统运营商的其他好处。