## 5 Discussion and Conclusions  
The problem of economic dispatch is a classic problem in the planning of the generation and expansion of electricity networks. There are multiple representations of the problem according to its objectives, including the inclusion of renewable energy, the emissions generated as well as restrictions on fuel availability, among many other nuances. Similarly, the method of solving the problem has had various approaches to achieve more efficient solutions. To be able to test the algorithms for solving the problem of economic dispatch, it is necessary to have a large amount of test data information, which reflects the real behavior of the electricity grid and permits the consideration of stress scenarios. There are some approaches in this regard in the literature; however, the proposals are limited to the representation of reference architectures and the availability of historical data for specific networks.  
It has been documented that the demand for electricity has a particular behavior, with peak demand and seasonal effects during the day and during the year. The objective of the hybrid model using alpha stable distribution is to admit the simulation of demand peaks and seasonality. This lets us simulate demand data in specific time intervals according to the objective of planning or solution required for the problem of economic dispatch.  
This work covers a conceptual framework that includes the use of predefined architectures and historical data, consolidating the unlimited generation of test data and stress scenarios through the application of alpha stable distributions and generalized additive models. The proposal contemplates the generation of as many test cases as necessary for the validation of the optimization algorithms, as well as consenting exposure to stress scenarios. The results of the application of the model show the generation of test cases for long periods that maintain the seasonality and impulsivity of demand. The combination of heavy tail distributions and generalized additive models presents a better fit, as well as unlimited test case generation.  
The proposed model integrates three stages of analysis: (1) collection of historical information of specific network architecture, (2) fitting of the alpha stable distribution to be able to simulate as much data as necessary, and (3) estimation of a generalized additive model to fit test data required, according to a specific time interval capturing the seasonality and non-linearity. These generated data will be the input used to test the optimization algorithms for the economic dispatch problem posed.  
According to the data used in the case study, it is shown that the demand data for electrical energy show impulsivity and heavy tails that are consistent with the presence of demand peaks. Similarly, the fitting of the GAM model shows that the energy demand has a non-linear behavior, so the use of an additive model is a good alternative to have a better fit to the data. The use of smoothing splines functions showed a good fit to the data.  
One of the main advantages of the proposal is that it is possible to use information from different available electrical networks and thereby check the efficiency of the optimization algorithms for different scenarios and not only for a particular case. This will strengthen the proposed solutions and contemplate real-life cases.  
This research received no external funding.  
The author acknowledges the International Conference on Intelligent Computing and Optimization (ICO) for generating a forum for the discussion and dissemination of ideas.  
The authors declare no conflict of interest.