# Synchronous Generator Stability Characterization for Gas Power Plants Using Load Rejection Tests
## 1 Introduction  
Electrical power systems are by far one of the greatest achievements of engineering and, at the heart of them, electrical generators are found, which pump the electrical power into the network. Back in the old days, the power system was small and weakly interconnected, but with the industrial development and the increase in household consumptions, it has had to become larger and more interconnected. The expansion of the power system, such as the addition of new generators or transmission lines, can lead to increased stress on the system. This stress can result in an increased likelihood of incorrect operation, such as power outages or equipment failures, which can negatively impact the reliability of the power system. As a result, the predictability of the system's operation can be reduced, making it more difficult for operators to anticipate and respond to potential issues in a timely manner. Therefore, it is important to carefully plan and manage the expansion of the power system to ensure that it remains reliable and predictable even under increased stress. Additionally, interconnections with neighboring power systems make the network stronger. However, they expose the system to more interferences because of the larger covered area. This type of situation jeopardizes the system, causing it to face many disturbances simultaneously or within a short interval of time [1]. A default power system is meant to sustain N-I contingencies, i.e., the power system should be able to continue operating without one of the elements that compose it. However,it does not guarantee full security to the power system [2]. The main reason for the systems' blackouts in a power system is due to dynamic instability and voltage instability [3; 4; 5; 6]. In this field, many advances in improving the network interconnection stability and efforts in restoring the system after major disturbances have been carried out [7; 8]. Nevertheless, there are problems defining and classifying power system stability problems as they can be voltage, frequency or load angle stability problems. This is a task that aims to provide a systematic basis for the discussion on issues like power system security and reliability [9]. One important point that must be remarked is the protection system and its relationship with the system's stability, which can cause a major outage in the power system [10]. Protection relays are involved in about three out of four contingencies in the electric system [11] due to wrong system coordination or improper controllers' adjustments at power plants, which cause the cascade tripping of upstream relays. In order to solve this issue, power system operators (PSOs) require transient technical parameters from the different power plants in order to better fit their protections, perform contingencies simulations and deeply study the transient behavior of the grids. However, the estimation of these parameters is not a trivial task. For example, in synchronous generators (SGs), the automatic voltage regulator (AVR) voltage variation rates are quite slow in performing the emulated transients required to characterize the machines in compliance with the requirements of the PSO. In this paper, three real cases of the study and characterization of real gas power plants are exposed from more than 60 examined power plants, all coupled to the Spanish power grid, the product of a project carried out for the Spanish PSO. A load test rejection is proposed to solve the problem and provoke a fast rejection response similar to a real fault in order to study the transient behavior. Then, the transient power plant parameters are fitted through simulations to replicate the real load rejection response. The model used in this paper to replicate the power plant gas turbine and speed governor is the GAST model, as it is one of the most used for dynamic modeling [12; 13; 14]. The AVR model chosen was the simplified excitation system (SEXS) [15; 16] and, to represent the SG, the model used was GENSAL [17; 18; 19].