# Research on Interval Optimal Scheduling Strategy of Virtual Power Plants with Electric Vehicles
###### Abstract  
The operation process of a virtual power plant is affected by many uncertainties, and how to ensure its comprehensive operation quality is a pressing challenge. For the virtual power plant incorporating electric vehicles, the interval number is used to describe the stochastic fluctuation of system uncertainties, and the optimization objectives are to (1) improve the operating economy, environmental protection, and grid load smoothing, (2) build a multi-objective interval optimal dispatching model considering the constraints of power balance and equipment operating characteristics, (3) solve the Pareto solution set by adopting the improved NSGA-II algorithm incorporating extreme scenario analysis, and (4) determine the optimal dispatching solution by the hierarchical analysis method. The median values of the determined optimal target intervals are 6456.11 yuan, 9860.01 kg, and 2402.56 kW. The algorithm shows that the proposed optimal dispatching strategy can effectively improve the economy of the virtual power plant and ensure that environmental protection and grid load smoothing requirements are met. virtual power plant; electric vehicle; interval optimization; NSGA-II algorithm +
Footnote †: journal: 2022, 13, 235. [[https://doi.org/10.3390/weyl3120235](https://doi.org/10.3390/weyl3120235)]([https://doi.org/10.3390/weyl3120235](https://doi.org/10.3390/weyl3120235))  
a two-stage day-ahead dispatch model. Reference [12] formed a typical scenario set based on Kantorovich distance for reduction of the original scenario, and this type of method can describe uncertainty better. However, it requires a known probability distribution or its affiliation function, which is often difficult to obtain in engineering practice. Secondly, there are methods based on time-domain rolling optimization or multiple time scales. In [13], a hybrid time-scale strategy was used to optimize the system intra-day and day-ahead. In [14], a hybrid seasonal autoregressive integrated shift-averaging model SARIMA model and Kalman filter KF algorithm were proposed to predict the uncertain parameters of the system and optimize the scheduling of the virtual power plant based on rolling time-domain optimization and feedback correction. In [15; 16], a virtual power plant day-ahead and real-time optimal scheduling model was established and an adaptive particle swarm algorithm was used to solve it in the real-time stage, which gives better results but has the disadvantages of a complex process and high dependence on power prediction results. Thirdly, there are robust optimization methods based on multiple scenarios. In [17], by calculating the correlation covariance matrix of power output at different moments of the scenery and using the simultaneous backgeneration elimination method to reduce the number of scenarios, a typical set of scenarios is generated to characterize the uncertainty, and a virtual power plant optimization model is established to verify its effectiveness. In [18], by generating continuous-time scenarios through Latin hypercube sampling and using the simultaneous backgeneration elimination method to reduce the generated scenarios, a virtual power plant optimal scheduling model was built. Reference [19] used robust optimization to find the optimal solution that makes the system worst in the fluctuation range of uncertain variables and transformed it into a deterministic problem by pairwise comparison. Reference [20] used an adaptive neuro-fuzzy inference system and spectral clustering method to generate scenarios, established the concept of uncertainty measure to characterize uncertainty, and built a two-stage robust schedulable model. References [21; 22] used robust optimization to deal with the uncertainty parameter scenario set described by confidence interval and solved by an improved fuzzy equilibrium coordination model. Reference [23] considered the user endowment effect and environmental awareness established an uncertainty scenario set and built a two-stage robust optimization model.