Wind power integration with high penetration in a power system is indispensable. However, wind power integration, especially with high level, raises the power system instability problems due to its natural variability and unpredictability, which increases system uncertainties. Thus, uncertainties and correlations amongst wind farms should be considered in a power system operation and planning. One of the best solutions for facilitating the wind power integration is the installation of an energy storage system (ESS). However, the location and sizing of ESSs should be optimally planned to achieve maximum benefits such as minimising total cost, time shifting, reliability and power quality enhancement, minimising power loss, improving the power factor and providing environmental support. In this paper, a new probabilistic discretising method is derived and developed to discretise the continuous joint power distribution of correlated wind farms. Combining the new probabilistic discretising method with a multi-objective hybrid particle swarm optimisation (MOPSO) and non-dominated sorting genetic algorithm (NSGAII), a new hybrid probabilistic optimisation algorithm is proposed. The proposed hybrid algorithm aims to search for the best location and size of energy storage system (ESSs) and considers the power uncertainties of multi-correlated wind farms. The objective functions to be minimised include a system's total expected cost restricted by investment budget, total expected voltage deviation and total expected carbon emission. IEEE 30-bus and IEEE 57-bus systems are adopted to perform the case studies using the proposed hybrid probabilistic optimisation algorithm. The simulation results demonstrate the effectiveness of the proposed hybrid method in solving the optimal allocation problem of ESSs and considering the uncertainties of wind farms’ output power and the correlation amongst them.

高渗透率的风电集成在电力系统中是必不可少的。然而，由于其自​​然的可变性和不可预测性，特别是具有高水平的风电集成提出了电力系统的不稳定性问题，这增加了系统的不确定性。因此，在电力系统的运行和规划中应考虑风电场之间的不确定性和相关性。促进风电集成的最佳解决方案之一是安装储能系统（ESS）。但是，应该对ESS的位置和大小进行最佳规划，以实现最大的收益，例如最小化总成本，时间转换，可靠性和电能质量增强，最小化功率损耗，改善功率因数并提供环境支持。在本文中，推导并发展了一种新的概率离散化方法，以离散化相关风电场的连续联合功率分布。将新的概率离散化方法与多目标混合粒子群算法（MOPSO）和非支配排序遗传算法（NSGAII）相结合，提出了一种新的混合概率优化算法。提出的混合算法旨在寻找能量存储系统（ESS）的最佳位置和大小，并考虑了多相关风电场的功率不确定性。要最小化的目标函数包括受投资预算限制的系统总预期成本，总预期电压偏差和总预期碳排放量。使用建议的混合概率优化算法，采用IEEE 30总线和IEEE 57总线系统进行案例研究。仿真结果证明了该混合方法在解决ESS最优分配问题，考虑风电场输出功率不确定性及其相互关系方面的有效性。