# Power system stabilty

HI guys,
I am grasuate student, i am planning to work on power system stability of Smart grid, i went through different books and papers and other sources and still i am confused to decide what is the basic measure of the stability of distribution system. I have this confusion over different things, like whether to go for Transeint Stability, steady state or dynamic, and finally decides to go for Transient stability. There i have problem, while going through different books and sources i found that transeint stability is deals with the prime mover and governor angle of the generator and different machine level factors, but i need to analyze the stability of the transmission&distribution system.

thanq

In a simplified stability analysis each generator is modeled by employing the classical model, that is by using the swing equation and constant emf behind the transient reactance. Transient reactance of generators is included in the network model. All the network elements (lines and transformers) are modeled by their π equivalents. For the simplified power system transient stability analysis, the transmission network is modeled explicitly while power injected from/to the distribution network is modeled as a load. Each such load is replaced by constant nodal shunt admittance. Indeed transient or steady state stability study of distribution/transmission network is subjected to new required power system stability study due to variation of passive characteristics of power system such as lines and transformers connection and/or disconnection.
When assessing the performance of an induction generator embedded within the system, the system reactance Xs and resistance Rs impact on the operation of the induction generator and modify the equivalent circuit. The system impedance as seen by the induction generator is affected by a number of factors:
1. The ‘strength’ of the network. If the network is strong the reactance between the generator and the system will be small, leading to a large short-circuit level. The short-circuit level being defined at the point of common connection as Vs/Xs. On the other hand, a weak system will have a large reactance and low short-circuit level.
2. For distribution networks, resistance affects are more apparent than at the transmission or
subtransmission level with the X /R ratio changing from typically 10 for transmission networks to 2 for distribution networks.

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Creative thinking is breezy, Then think about your surrounding things and other thought products. http://electrical-riddles.com

I dont want to consider the machine characteristics as you said because my system will consist of a number of PV cells (solar) besides with the regular power supply. So is there any way that i can do this project with out considering the machine parameters, and could you suggest any software?

thank you once again

Last edited by a moderator:
I apologize for delay, I was very busy last week, our second daughter (Ava) was born and we involved it.
Attached Figure is a typical circuit diagram of the grid-connected PV power system. It interfaces with the local utility lines at the output side of the inverter as shown. A battery is often added to meet short-term load peaks. In recent years, large building-integrated PV installations have made significant advances by adding grid connections to the system design. The PV systems interface the grid at the output terminals of a synchronizing breaker after the inverter. The power flows in either direction depending on the site voltage at the breaker terminals. The synchronizing breakers in Figure have internal voltage and phase-angle sensors to monitor the site and grid voltages and signal the correct instant for closing the breaker. As a part of the automatic protection circuit, any attempt to close the breaker at an incorrect instant is rejected by the breaker. A small unavoidable difference between the site and grid voltages results in an inrush current flowing between the site and the grid. The inrush current eventually decays to zero at an exponential rate that depends on the internal resistance and inductance. Once synchronized, the voltage and frequency of the PV system need to be controlled.
Indeed the output voltage of PV system have same role of generator emf in conventional system and interconnection impedance have same role of generator internal impedance. Also the link connecting a renewable power site with the area grid introduces an operating limit in two ways, the voltage regulation and the stability limit. In most cases, the link can be considered as an electrically short transmission line. The ground capacitance and the ground leakage resistance are generally negligible. The equivalent circuit of such a line, therefore, reduces to a series leakage impedance Z.
The direction of power flow depends on the sending- and receiving-end voltages and the electrical phase angle between the two. However, the maximum power the line can transfer while maintaining a stable operation has a certain limit. We derive in the following text the stability limit, assuming that the power flows from the renewable site to the grid, although the same limit applies in the reverse direction as well. The series resistance in most lines is negligible and hence is ignored here.
The power transferred to the grid via the link line is as follows:

P = (Vs.Vr).sind/X

Thus, the magnitude of the real power transferred by the line depends on the power angle d. If d> 0, the power flows from the site to the grid. On the other hand, if d< 0, the site draws power from the grid.
The reactive power depends on (Vs - Vr). If Vs > Vr, the reactive power flows from the site to the grid. If Vs < Vr, the reactive power flows from the grid to the site. Obviously, the power flow in either direction is maximum when d is 90°. Beyond Pmax, the link line becomes unstable and falls out of synchronous operation. That is, it loses its ability to synchronously transfer power from the renewable power plant to the utility grid. This is referred to as the steady-state stability limit. In practice, the line loading must be kept well below this limit to allow for transients such as sudden load steps and system faults. The maximum power the line can transfer without losing the stability even during system transients is referred to as the dynamic stability limit. In a typical system, the power angle must be kept below 15 or 20° to maintain dynamic stability at all times.

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Creative thinking is breezy, Then think about your surrounding things and other thought products. http://electrical-riddles.com

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