The randomness and fluctuation of wind turbines and photovoltaics affect the optimal operation of the power system. This paper aims to mitigate wind and solar fluctuations by integrating energy storage systems (ESS). One crucial metric for assessing the performance of energy storage systems is state of charge (SOC). Therefore, this paper proposes a power flow optimization method based on SOC characteristics. Firstly, we consider the uncert. The randomness and fluctuation of wind turbines and photovoltaics affect the optimal operation of the power system. This paper aims to mitigate wind and solar fluctuations by integrating energy storage systems (ESS). One crucial metric for assessing the performance of energy storage systems is state of charge (SOC). Therefore, this paper proposes a power flow optimization method based on SOC characteristics. Firstly, we consider the uncertainties on both the generation and load sides of the power system and establish a source load model. Subsequently, an analysis of the SOC characteristics of the ESS is conducted, and associated constraints are provided. Then, a power flow model for the AC-DC system with voltage source converter (VSC) is developed based on the source load storage configuration. The optimization model is formulated as a multi-objective problem, utilizing penalty functions to minimize the overall economic cost, system losses, and line voltage deviations. Finally, the proposed method is validated through simulation analysis using an enhanced IEEE 30-node system as a case study. The simulation results confirm the correctness and effectiveness of the presented approach.••••Establish a source-load dual-side uncertainty model and consider the correction of customer responsiveness under time-of-use price for the load side••Consider the SOC characteristics of the energy storage system and perform nodal equivalence••Establish the power flow calculation model of source grid load storage AC/DC system••Introduce penalty function to establish a multi-objective optimization model for probabilistic optimal power flow and improve the power flow distribution at time tsource network load storageenergy storage systemsstate of chargeprobabilistic power flowWith the increasing shortage of non-renewable energy and the prominent environmental degradation caused by traditional thermal power generation, China has proposed the goal of striving to achieve carbon peak before 2030 and carbon neutrality before 2060. Renewable energy sources represented by wind and solar power are gradually showing their value, and new energy power generation has been accepted by the power system,,,. However, due to the uncertainty of wind and solar power output and the increasing randomness of the load side at this stage, the imbalance between supply and demand is exacerbated, and voltage limit problems are prone to occur, posing huge challenges to the safe and stable operation of the power system,,. In addition, with the widespread application of ESS, the wind-solar-storage system has become mainstream, and SOC is also a necessary consideration in ESS. Therefore, it is urgent to recalculate the operation optimization problems of new power systems at this stage.With the uncertain increase of both supply and demand sides and the deployment of energy storage systems in the new power grid, traditional deterministic power flow calculation methods are no longer suitable for system planning, scheduling, and evaluation,,. The traditional power flow calculation methods do not consider the uncertainty of supply and demand, w. 2.1. Source-Side Uncertainty ModelWind speed has strong uncertainty and is influenced by multiple factors such as season, region, temperature, and pressure. Due to the similarity between the characteristics of the Weibull distribution and wind speed variation, a combination of Weibull distribution and Monte Carlo method is used to sample and simulate wind speed changes. The probability density function and distribution function of wind speed distribution can be expressed as:(1)f(v)=kc(vc)k−1exp(−(vc)k)(2)F(v)=1−exp(−(vc)k)In equation (1): v represents the actual wind speed, k represents the shape parameter of the Weibull distribution function, and c represents the scale parameter.The uncertainty of wind turbine output is realized through the uncertainty of wind speed. The operating state of the wind turbine can be divided into rated operation, below-rated operation, and shutdown state according to the different wind speeds, which results in the uncertainty of the turbine's output power. The active output power PW of the wind turbine is expressed as:(3)PW={0,v<vinorv≥voutk1v+k2,vin≤v<vNPN,vN≤v<vout}In equation (3), k1=PNvN−vin,k2=−k1vin,vin and vout are the cut-in and cut-out wind speeds, respectively, and vN is the rated wind speed. PW and PN represent the wind turbine's output power and rated power, respectively.The probability model fo.
