**Small Signal Stability with the Householder Method in Power Systems**

### **Asghar Sabati 1,\*, Ramazan Bayindir 2, Sanjeevikumar Padmanaban 3,\*, Eklas Hossain 4 and Mehmet Rida Tur 5**


Received: 1 August 2019; Accepted: 30 August 2019; Published: 4 September 2019

**Abstract:** Voltage collapse in power systems is still considered the greatest threat, especially for the transmission system. This is directly related to the quality of the power, which is characterized by the loss of a stable operating point and the deterioration of voltage levels in the electrical center of the region exposed to voltage collapse. Numerous solution methods have been investigated for this undesirable degradation. This paper focuses on the steady state/dynamic stability subcategory and techniques that can be used to analyze and control the dynamic stability of a power system, especially following a minor disturbance. In particular, the failure of one generator among the network with a large number of synchronous generators will affect other synchronous generators. This will become a major problem and it will be difficult to find or resolve the fault in the network due to there being too many variables, consequently affecting the stability of the entire system. Since the solution of large matrices can be completed more easily in this complex system using the Householder method, which is a small signal stability analysis method that is suggested in the thesis, the detection of error and troubleshooting can be performed in a shorter period of time. In this paper, examples of different rotor angle deviations of synchronous generators were made by simulating rotor angle stability deviations up to five degrees, allowing the system to operate stably, and concluding that the system remains constant.

**Keywords:** rotor angle; small signal stability; householder algorithm; power systems
