the term power system stability is of utmost importance in this field, and is used to

define the ability of the of the system to bring back its operation to steady state

condition within minimum possible time after having undergone some sort of

transience or disturbance in the line. the power system stability is also referred to as

synchronous stability and is defined as the ability of the system to return to

synchronism after having undergone some disturbance due to switching on and off of

load or due to line transience. To understand stability well another factor that is to be

taken into consideration is the stability limit of the system. The stability limit defines

the maximum power permissible to flow through a particular point or a part of the

system during which it is subjected to line disturbances or faulty flow of power.

Having understood these terminologies related to power system stability let us now

look into the different types of stability.

The synchronous stability of a power system can be of several types depending upon

the nature of disturbance, and for the purpose of successful analysis it can be

classified into the following 3 types as shown below:

1) Steady state stability.

2) Transient stability.

3) Dynamic stability.

Steady State Stability of a Power SystemThe steady state stability of a power system is defined as the ability of the system to bring itself back to its stable configuration following a small disturbance in the network (like normal load fluctuation or action of automatic voltage regulator). It can only be considered only during a very gradual and infinitesimally small power change.

In case the power flow through the circuit exceeds the maximum power permissible, then there are chances that a particular machine or a group of machines will cease to operate in synchronism, and result in yet more disturbances. In such a situation, the steady state limit of the system is said to have reached. Or in other words the steady state stability limit of a system refers to the maximum amount of power that is permissible through the system without loss of its steady state stability.

Transient Stability of a Power SystemTransient stability of a power systemrefers to the ability of the system to reach a stable condition following a large disturbance in the network condition. In all cases related to large changes in the system like sudden application or removal of load, switching operations, line faults or loss due to excitation the transient stability of the system comes into play. It infact deals in the ability of the system to retain synchronism following a disturbance sustaining for a reasonably long period of time.

And the maximum power that is permissible to flow through the network without loss

of stability following a sustained period of disturbance is referred to as the transient

stability of the system. Going beyond that maximum permissible value for power

flow, the system would temporarily be rendered as unstable.

Dynamic Stability of a Power SystemDynamic stability of a system denotes the artificial stability given to an inherently unstable system by automatic controlled means. It is generally concerned to small disturbances lasting for about 10 to 30 seconds.

Steady State Stability studies are restricted to small and gradual changes in the system operating conditions. In this we basically concentrate on restricting the bus voltages close to their nominal values. We also ensure that phase angles between two buses are not too large and check for the overloading of the power equipment and transmission lines. These checks are usually done using power flow studies.

Transient Stability involves the study of the power system following a major disturbance. Following a large disturbance the synchronous alternator the machine power (load) angle changes due to sudden acceleration of the rotor shaft. The objective of the transient stability study is to ascertain whether the load angle returns to a steady value following the clearance of the disturbance.

The ability of a power system to maintain stability under continuous small disturbances is investigated under the name of Dynamic Stability (also known as small-signal stability). These small disturbances occur due random fluctuations in loads and generation levels. In an interconnected power system, these random variations can lead catastrophic failure as this may force the rotor angle to increase steadily.

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Fig. 2e. Equivalent circuit of a PV Cell

The characteristic equation of the output current can be expressed as:

I=I pv−I 0 {e(V + I R sV t∗a )−1}−V + I RS

Rp

Where,

Ipv =Current generated by the incident solar radiation Io=Reverse saturation or leakage current of the diode Vt =Thermal voltage of PV module with Ns number of PV cells connected in series = NsKT/Q K=Boltzmann constant=1.3806503 x 10-23J/K Q=Electron Charge=1.60217646 x 10-19 C T=Temperature in Kelvin a=Diode ideality constant (1<a<1.5)Rp , Rs = parallel and series resistances provided by manufacturer after MPPT(maximum power point tracking)

Applications:

Power generated from solar energy can be used either as off-grid (stand-alone) or grid connected. Both applications have own importance in power system. In off-grid the required power is generated by the solar farm itself. In grid connected it can be used in two ways, either to supply continuous power to particular defined loads or to supply power to loads during peak load hours only.