Enhancement of Transient Stability of the Nigeria 330 kV Transmission Network Using Fault Current Limiter

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.


Introduction
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 [1].These techniques include: reduction in system transfer reactance, use of breaking resistor, use of bundled conductor, use of fault current limiter and the placement of FACTS devices [2].As the power network becomes more complex, the consequence is that the fault current increases, and transient stability problem becomes more severe.The use of fault current limiter (FCL) has been identified as one of the necessary elements required to limit the fault current and invariably enhance the power system transient stability [3].On the other hand, superconductor fault current limiter (SFCL) plays a better role in limiting fault current during fault.SFCL offers low impedance (near zero) during normal operation, hence, does not interfere during steady state operation of the system.In the event of a fault, the SFCL quenches and this phenomenon causes a fast raise of the limiter impedance up to a value needed for limiting the fault current.The impedance of SFCL can change the transient stability of power system [4].The presence of SFCL in a power system can improve the system stability and distributed energy quality [5].
In the literatures, a number of studies have so far been done on transient stability improvement of power systems.Sheeba et al. [6] use FCL and SVC to enhance transient stability of IEEE 59-bus test system using ETAP Software.Masaki et al. [7] investigates the effect of FCL and Thyristor Controlled Braking Resistor (TCBR) on transient stability of IEEE 9-bus test system.Byung et al. [8], this paper describes the optimal sizing of a Resistive Superconducting Fault Current Limiter (RSFCL) applied to a multi-machine power system.The optimized SFCL generally gives the best damping performance for low-frequency oscillations.Heresh et al. [9] presents the application of FCL for reduction of fault current in a high voltage substation.Fereidouni et al. [10] evaluated the effects of the use of Solid-State Fault Current Limiter (SSFCL) unit on the transient stability of power systems and power quality.This paper focuses on the improvement of transient stability of the Nigeria 330 kV transmission network using Inductive-Type Superconductor Fault Current Limiter (ISFCL).

The Nigeria 330 kV Transmission Network
The Nigeria 330 kV transmission network used as the case study in this paper is shown in Figure 1.It consists of eleven (11) generators, twenty-one (21) load buses and thirty-six (36) transmission lines, which cut across the six (6) Geo-political zone (South-West, South-South, South-East, North-Central, North-West and North-East Region) of the country with long radial interconnected transmission lines as depicted in Figure 1.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 [11].Due to varying load demand, fragile nature of the transmission network, lack of sensitive equipment and frequent outages due to disturbances which result to instability.Assessing the network performance will involve system stability studies.System Stability may involve transient stability studies on the network.

Mathematical Modeling of a Multi-Machine Transient Stability Analysis
Consider a multi-machine n-bus power network consisting of m number of ge-nerators 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 gi ) 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 [12] * where X i is the equivalent reactance at bus i.
By converting each load bus into its equivalent constant admittance form, we have [13] 2 where Li P and Li Q are the respective equivalent real and reactive powers at each load bus.
The pre-fault bus admittance matrix [ bus Y ] can therefore be formed with the inclusion of generators reactance and the converted load admittance.This can be partition as [14]: where Equation ( 3) is formulated for the network conditions such as pre-fault, during fault and post-fault.The bus Y for the network is then formulated by elimi- nating 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 [15] 1 0 By expansion, Equation ( 4) can be expanded as and By combining Equation ( 5) and Equation ( 6) and some mathematical manipulations, the desired reduced admittance matrix can be obtained as reduced Y is the desired reduced matrix with dimension where m is the number of generators.
The electrical power output of each machine can then be written as [16] ( ) Equation ( 8) is use to determine the electrical power output of the generator during fault ei P The rotor dynamics, representing the swing equation, at any bus i, is given by All the parameters retain their usual meanings.
Consider a case when there is no damping i.e. 0 i D = , Equation ( 9) can be re-written as [17] ( ) ∴The swing equation for the during-fault condition can easily be express as Similarly, the swing equation for the post fault condition can be written as

Modeling of Inductive-Type Superconductor Fault Current Limiter
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.Figure 2 shows the variation of the limiting resistance with time.
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 Figure 3.The maximum power transferred from the generator to the system is given by a well-known expression: 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 Figure 3 as shown in Figure 4.The equivalent circuit is shown below in Figure 5.
Using Delta-star transformation, the equivalent reactance obtained during fault Journal of Power and Energy Engineering is given by Equation ( 14): ( ) When the fault is cleared after opening the breaker, the equivalent reactance obtained after fault is given by Equation (15): Furthermore, with ISFCL installed in the generator-transformer feeder, the equivalent circuit is shown in Figure 6.
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): 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 Figure 7 and Figure 8 that only the generator at Afam is the most severely disturbed, hence, the only generator considered for the investigation of the effect of ISFCL on the power system.It is

Conclusion
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

Figure 1 .
Figure 1.Single line diagram of the Nigeria 330 kV transmission network.

Figure 4 .
Figure 4. ISFCL installed in a line feeder.

Figure 5 .
Figure 5. Equivalent circuit when ISFCL is installed in line feeder.

Figure 6 .
Figure 6.Equivalent circuit when ISFCL is installed in generator-transformer feeder.

Figure 7 and
Figure 7 and Figure 8 shows the swing curves for all the ten generators in the Nigeria 330 kV transmission network when a three-phase fault occurs at Aiyede bus (Bus 16).