Assignment on Small Signal Stability

Introduction of Small Signal Stability

Small signal stability is a capacity of power system which also maintains the synchronism below the small disturbance. Therefore the disturbance is efficient for small linearization of the equations of the system which is permissible for the analysis of power. The small-signal stability also depends on the initial operating states for the power system. There are two forms of instability (Persson, 2004)

·         Increment of rotor angle due to lack of the synchronizing torque

·         The oscillation of the rotor is increased due to amplitude and by the lack of damping torque.

Oscillations of the power system could also be local mode, where the inter-area mode, and the torsional mode along with the control mode. The improvement of small-signal stability is also created for the inter-area mode and the local mode oscillations which could also determine by the various states of generators. The model of a small signal is for the multi-machine of power system which is also developed and involves the linearized model of different power systems by the component of exciter, generators, load and PSS.  When the linearized model is formed the analysis of Eigenvalue is carried which is also identified by the low frequency of inter-area and local modes of oscillation. The factor analysis participation is also carried which decided the optimal placement of PSS input speed (Bhowmik et al , 2011).

Generator classical model of Small Signal Stability

The below model is the UPFC model (“Unified Power Flow Controller”) and the performance of this model is tested on two areas of the four generators of the power system which is shown in below figure 1. A 230km interconnecting tie line carries 400MW from area 1 like (generator 1 and generator 2 ) to area 2 (generator 3 and generator 4). At bus 8, the UPFC is inserted in order which sees an influence for the power flow by those lines on the bus voltage phases (BEKRI et al , 2009). The system also contains the two areas and eleven buses which are connected through the weak tie among bus 7 and 9. And the total two loads which are also applied to the system and on bus 7 and 9. There are two shunt capacitors which are also connected to a bus 7 and bus 9 as shown in the below figure 1. And the fundamental frequency of this system is 60Hz.

 

Figure 1:  single-line diagram of the two-area test system

Exciter generators of Small Signal Stability

In this assignment according to the requirement, the exciter generators which are used are the IEEE AC4 model and also considered in the test.

The exciter model is given below;

                             Figure 2:  Exciter model IEEE AC4 (Neplan.ch, 2019)     

Calculation of the small-signal model of Small Signal Stability

Power system behavior could also be explained through a set of group of the non-linear first order of differential equations as well as a set group of the non-linear algebraic equations which could also be expressed as;

Here the x is the vector for state variable which also involves the generators variables and Power system stabilizer and exciters. The column vectors “w” is the voltage vector, and thus “u” as well as “y” are the output and input vectors of the variables. If the supposed for the equilibrium point of the power system and the linearized model of the power system could also be expressed as;

Whereas  also represent the state of output and input vector. And A, B .C and D is expressed the states, output, control and the feedforward of the matrix (Acharya et al , 2018).

Power System Stabilizer (PSS) of Small Signal Stability

                   At high load when generators are operated as well as it also connected to the weak external grid of voltage regulator which is created negative damping of torques as well as it gave rise of oscillation along with the instability. The stabilizing signal is introduced like the input of voltage regulator where the signal is also improved the damping rotor of oscillations along with the devices is known as the power system stabilizer (PSS) (Choo, 2015).

Washout circuit of Small Signal Stability:

                   It acts like the high pass filter which is also passed from all frequency and the area of interest. It eliminates steady states biased as the input of the PSS that would also modify the terminal voltage of generators.

Dynamic Compensator of Small Signal Stability:

It also contains the two-lag lead block by the gain block which provides phases of lead system, and the PSS gain also provides the damping for the operating conditions.

                   The signal input of the small-signal PSS model is also working where the speed of rotor deviations is used as the input signal. The below figure is the vernalized structure of the PSS diagram. The PSS also acts by the excitation system which also provides the damping and it’s required to compensate for the phases lag among synchronous machine and excitation system. The deviation for the rotor speed is also used as the input signal to the PSS block.

Figure: Generalized structure of PSS

Figure: Blok diagram of PSS

                   By using  the PSAT software tool analysis of figure 1 which is given is done, and there also have some time-domain response, PSS model, and the Eigenvalue analysis

References on Small Signal Stability