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The dynamic responses of generators when subjected to disturbances in an interconnected power system have become a major challenge to power utility companies due to increasing stress on the power network. Since the occurrence of a disturbance or fault cannot be completely avoided, hence, when it occurs, control measures need to be put in place to limit the fault current, which invariably limit the level of the disturbances. This paper explores the use of Superconductor Fault Current Limiter ( SFCL) to improve the transient stability of the Nigeria 330 kV Transmission Network. During a large disturbance, the rotor angle of the generator is enhanced by connecting a Fault Current Limiter (FCL) which reduces the fault current and hence, increases transient stability of the power network. In this study, the most affected generator was taken into consideration in locating the SFCL. The result obtained reveals that the Swing Curve of the generator without FCL increases monotonically which indicates instability, while the Swing Curve of the System with FCL reaches steady state.

Although, the occurrence of disturbances within power networks cannot be avoided, its impact which undermines the security margin of the system could be minimized. This usually resulted to the instability in the operation of power systems. This challenge therefore poses a great concern to power system researchers recently. In resolving this issue, there is the need to evaluate the ability and response of a power network when subjected to various disturbances with the aim of maintaining the network reliability. Instability in power system networks is of various types based on the duration. When a power system is subjected to a disturbance, the network may experience loss of synchronism which could result to total voltage collapse within the network. This explains why transient stability enhancement is of paramount importance in the operation of power system. Different techniques for enhancing transient stability of a multi-machine power system have been proposed in the literature [

In the literatures, a number of studies have so far been done on transient stability improvement of power systems. Sheeba et al. [

The Nigeria 330 kV transmission network used as the case study in this paper is shown in

The Nigeria 330 kV grid network is becoming more complex due to the recent deregulation in the Power Sector of the Economy to meet the ever-increasing energy demand [

Consider a multi-machine n-bus power network consisting of m number of generators such that n > m. At any bus i within the system, the complex voltages (V_{i}), generators real power (P_{gi}) and the generator reactive power (Q_{g}_{i}) can easily be obtained from the pre-fault load-flow analysis from which the initial machine voltages (E_{i}) can also be obtained. This relationship can be expressed as [

E i = V i + j X i [ P g i − j Q g i V i * ] (1)

where

X_{i} is the equivalent reactance at bus i.

By converting each load bus into its equivalent constant admittance form, we have [

Y L i = P L i − j Q L j | V i | 2 (2)

where P L i and Q L i are the respective equivalent real and reactive powers at each load bus.

The pre-fault bus admittance matrix [ Y b u s ] can therefore be formed with the inclusion of generators reactance and the converted load admittance. This can be partition as [

Y b u s = [ Y 11 Y 12 Y 21 Y 22 ] (3)

where Y 11 , Y 12 , Y 21 and Y 22 , are the sub-matrices of Y b u s . Out of these four sub-matrices, Y 11 , whose dimension is m × m is the main interest of this paper as it contains generator buses only with the load buses eliminated.

Equation (3) is formulated for the network conditions such as pre-fault, during fault and post-fault. The Y b u s for the network is then formulated by eliminating all nodes except the internal generator nodes. The reduction is achieved based on the fact that injections at all load nodes are zero. The nodal equations, in compact form, can therefore be express as [

[ 1 0 ] = [ Y m m Y m n Y n m Y n n ] [ V m V n ] (4)

By expansion, Equation (4) can be expanded as

I m = Y m m V m + Y m n V n (5)_{ }

and

0 = Y n m V m + Y n n V n (6)

By combining Equation (5) and Equation (6) and some mathematical manipulations, the desired reduced admittance matrix can be obtained as

Y r e d u c e d = Y m m − Y m n Y n n − 1 Y n m (7)

Y r e d u c e d is the desired reduced matrix with dimension m × m , where m is the number of generators.

The electrical power output of each machine can then be written as [

P e i = E i 2 Y i i cos θ i i + ∑ i = 1 j ≠ i m | E i | | E j | | Y i j | C o s ( θ i j − δ i + δ j ) (8)

Equation (8) is use to determine the electrical power output of the generator during fault P e i ( P e i ( d u r i n g − f a u l t ) ) and post-fault P e i ( P e i ( d u r i n g − f a u l t ) ) conditions.

The rotor dynamics, representing the swing equation, at any bus i, is given by

H i π f o d 2 δ i d t 2 + D i d i d t = P m i − P e i (9)

All the parameters retain their usual meanings.

Consider a case when there is no damping i.e. D i = 0 , Equation (9) can be re-written as [

H i π f o d 2 δ i d t 2 = P m i _ ( E i 2 Y i i cos θ i i + ∑ i = 1 j ≠ i m | E i | | E j | | Y i j | C o s ( θ i j − δ i + δ j ) ) (10)

\The swing equation for the during-fault condition can easily be express as

H i π f o d 2 δ i d t 2 = P m i − P e i ( d u r i n g − f a u l t ) (11)

Similarly, the swing equation for the post fault condition can be written as

H i π f o d 2 δ i d t 2 = P m i − P e i ( p o s t − f a u l t )

The FCL consist of a controller, a detector and a limiting resistance/reactance that helps to limit fault current during fault and improve the transient stability of power system.

The limiting resistance value is assume to be 1 p∙u and the fault detection time and starting of the limiting resistance are 2 ms and 1 ms respectively. This means FCL starts to operate at 0.102 sec, and then the limiting resistance increases linearly from 0.0 p∙u to 1.0 p∙u within 1ms.

Consider a synchronous generator connected to an infinite bus system as shown in

The maximum power transferred from the generator to the system is given by a well-known expression:

P max = | V | | E | X e q S i n δ (12)

X e q = X d + X t + X L 2 (13)

where X_{d} = reactance of generator, X_{t} = reactance of transformer, X_{L} = reactance of line.

Note that the values of resistances are small when compared with inductances; hence, all resistances are negligible.

Also, consider ISFCL installed in a line feeder of

The equivalent circuit is shown below in

Using Delta-star transformation, the equivalent reactance obtained during fault is given by Equation (14):

X e q = X d + X t + X L + ( X d + X t ) + X L X S F C L (14)

When the fault is cleared after opening the breaker, the equivalent reactance obtained after fault is given by Equation (15):

X e a = X d + X t + X L (15)

Furthermore, with ISFCL installed in the generator-transformer feeder, the equivalent circuit is shown in

In the case of a 3-phase fault at point A, the power transfer during fault is equal to zero. The equivalent reactance obtained after fault is cleared by opening of breaker is given by Equation (16):

X e q = X d + X t + X S F C L + X L (16)

Comparing Equation (15) and Equation (16) shows that installation of ISFCL in the line feeder enhances transient stability better than ISFCL installed in generator-transformer feeder.

It is observed from the swing curve of

clearly seen from

In this paper, an investigation of the effectiveness of superconductor fault current limiter in enhancing transient stability of the Nigeria 330 kV grid network is presented. The result reveals that when a three-phase fault is created at Aiyede bus, the generator at Afam generating station was found to loss synchronism at 850 ms, but with the installation of SFCL, the critical clearing time was improved to 1390 ms, which shows an improvement of 65.48%. Thus, there is considerable improvement in the generator rotor angle and rotor speed.

Okakwu, I.K. and Ogujor, E.A. (2017) Enhancement of Transient Stability of the Nigeria 330 kV Transmission Network Using Fault Current Limiter. Journal of Power and Energy Engineering, 5, 92-103. https://doi.org/10.4236/jpee.2017.59008