## 1 Introduction  
The study of stability of electrical power systems (EPSs) is relevant for their operation and planning, as it thoroughly describes their behavior when facing events such as small and large perturbations [1]. The classical analysis assumes that the transmission grid is balanced and does not present large variations [2]. This allows making phase modeling suppositions and implementing simplifications and equivalent models. However, with the dependency of the world on electricity and the wide variety of users and loads in the distribution networks, it is not possible to assume that the power transmission through the lines is symmetric and that the charges will remain balanced. Furthermore, with the integration of new generation technologies with the distribution grid, the studies of the implementation and operation need to be more precise. This is why the model of the consumption loads can no longer be represented with the classical balanced method. The challenge for the new studies in electrical power system stability is to describe and model the systems considering these new scenarios in order create better analysis. Studies on this kind of analysis reported in the international literature consist of the proposition and practical verification of new models that accurately describe all the parameters of the system. Some works study transients [3; 4; 5; 6] and therefore need to solve the non-linear equations for power flow. In particular, concerning small signal stability, there is an additional problem not always considered, and it is the balance point that defines the linear model that is not fixed and varies with time [7]. Accordingly, the solutions proposed in the literature describe several types of approaches that solve this inconvenience [8]. Reference [9] was based on simulations and the use of estimation methods complemented with simulations so as to obtain the eigenvalues of the system. Additionally, mathematical modeling tools such as dynamic phasors are used to directly describe the system. Estimation methods just allow knowing the types of oscillation modes, oscillation frequencies, and the damping coefficient. However, having a mathematical model that analytically describes the behavior of the system enables carrying out more specific analyses such as the calculation of the participation factors. In References [10; 11], results were obtained by using the estimation model of a reduced system, which consists of a distributed generator under different load conditions. The results indicate that the more unbalanced the load of the system, the greater the possibility of losing the stability of the permanent regime is. Furthermore, multiple articles address small signal stability applied to power electronic interfaces in renewable generation systems [12; 13; 14]. In general, a dynamic phasors model is proposed based on \"dq\" coordinates, which are eventually validated through simulations. However, the techniques proposed are not applied to large-scale systems. Reference [2] proposed a model based on the phasors used in ZPNtransformation to solve the problem of the variant balance point. However, the model is only applied to a single machine infinite-bus system. Then, the case in [15] uses a derivation of this model applied to a small system with the inclusion of induction motors and photovoltaic modules. Reference [16] applied this concept to microgrid analysis. Despite the favorable results presented, there is no work that compares the classic mathematical models with those proposed in previous reports under real modeling conditions. This kind of study can verify the applicability of the models and can be possibly used to improve the studies of controllers applied to unbalanced system. In this article, we present a novel solution to the problem of small signal stability analysis for the multimachine systems under unbalanced conditions and compare it to the classical analysis in the search of a validation.