Stability of Power System (May 2011)
Vladimír KRIŠTOF, 2Stanislav KUŠNÍR, 3Matúš KATIN
Dept. of Electric Power Engineering, FEI TU of Košice, Slovak Republic Dept. of Electric Power Engineering, FEI TU of Košice, Slovak Republic 3 Dept. of Electric Power Engineering, FEI TU of Košice, Slovak Republic 2 1
email@example.com, firstname.lastname@example.org, email@example.com change rapidly, but the mechanical power into the machine is relatively slow to change. Because of this difference in speed of response, there exists a temporary difference in the balance of power. This power unbalance causes a difference in torque applied to the shaft, which causes it to accelerate or decelerate, depending on the direction of the unbalance. As the rotor changes speed, the relative rotor angle changes. Fig. 2 shows the relationship between the rotor (torque) angle δ, the stator magnetomotive force (MMF) F1, and the rotor MMF F2. The torque angle δ is the angle between the rotor MMF F2 and the resultant of the vector addition of the rotor and stator MMFs R, as shown in Fig. 2
Abstract— Due to increase of electric power demands, power systems are larger and more complicated, and the dependence of people on electricity increases. Outages in electric supply have an increasing social and economic impact. Therefore it is necessary to minimize the effect of disturbances that arise in the power system so as to have minimum impact on the reliable and safe supply of electricity. Stability of power system is one of the most important area of power system operation. Loss of stability (loss of synchronism) can lead to outages of transmission lines, loss of loads, cascading failures, and eventually to black-out. This paper discusses power-system instability and the importance of fast fault-clearing performance to aid in reliable production of power.
Keywords—power system, steady-state stability, transient stability, fault-clearing time
I. INTRODUCTION Power system stability has been recognized as an important problem for secure system operation since the 1920s , . Many major blackouts caused by power system instability have illustrated the importance of this phenomenon . The term stability of the power system is connected with transient phenomena associated with changes in generator rotor angle, changes in frequency and voltage. Given the wide range of issues there is need for classification of power system stability according to Fig.3.  This article deals mainly with steady-state and transient stability. II. BASIS FOR STEADY-STATE STABILITY In an interconnected power system, the rotors of each synchronous machine in the system rotate at the same average electrical speed. The power delivered by the generator to the power system is equal to the mechanical power applied by the prime mover, neglecting losses. During steady-state operation, the electrical power out balances the mechanical power in. The mechanical power input to the shaft from the prime mover is the product of torque and speed (P M = T M ω). The mechanical torque is in the direction of rotation. An electrical torque is applied to the shaft by the generator and is in a direction that is opposite of the rotation, as shown in Fig. 1. When the system is disturbed due to a fault or when the load is changed quickly, the electrical power out of the machine changes. The electrical power out of the machine can
Fig. 1. Mechanical and electrical torques applied to the shaft .
Fig. 2. Stator, rotor, and resultant MMFs and torque angle .
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Fig. 3. Classification of power system stability according to IEEE and CIGRE [3,7]
Fig. 4 shows a circuit representation of a synchronous generator connected through a transmission system to an infinite bus. The synchronous machine is modeled by an...