Improvement of Transient Stability of Power System by Thyristor Controlled Phase Shifter Transformer

Problem statement: The improvement of transient stability of the powe r system was one of the most challenging research areas in power engine er. Approach: This study presents the method to improve transient stability of power system by Thyr istor Controlled Phase Shifter Transformer (TCPST). The mathematical model of power system equ ipped with a TCPST was systematically derived. The parameters of TCPST are modeled into p ower flow equation and thus it was used to determine control strategy. The swing curves of the three phase faulted power s ystem without and with a TCPST are tested and compared in various cases. Results: The swing curve of system without a TCPST gets increases monotonically and thus the sys tem can be considered as unstable whereas the swing curves of system with a TCPST can return to s table equilibrium point. Conclusion: From the simulation results, the TCPST can increase transien t tability of power system.


INTRODUCTION
Transient stability improvement is one of the important aspects in modern power system. The innovative Flexible AC Transmission System (FACTS) devices have been proposed during the last three decades for improving transient stability of power systems (Barbuy et al., 2009). There are various forms of FACTS devices such as Static Synchronous Series Compensator (SSSC), Static Synchronous Compensator (STATCOM), Unified Power Flow Controller (UPFC) and Inter line Power Flow Controller (Bhownick et al., 2009;Hannan et al., 2009;Magaji and Mutafa, 2009;Zhang, 2003;Leon and Zanetta, 2008;Parimi et al., 2008;Azbe and Mihalic, 2008).
A Thyristor Controlled Phase Shifter Transformer (TCPST) consists of a shunt transformer, a series transformer and a converter. The classification of TCPPS depends on the type of converter used. The converter can be of ac-ac bridge type, Pulse-Width Modulation (PWM) type, ac controller type (Badran et al., 2008;Daut et al., 2006). To verify the capability of TCPST on transient stability improvement, its suitable mathematical model and control strategy are needed to be presented.
This study presents the mathematical model of power system equipped with a TCPST. The presented mathematical model is applied to design control strategy of a TCPST. The simulation results are tested on a Single Machine Infinite bus system.

MATERIALS AND METHODS
Mathematical model: Figure 1a shows the schematic diagram of the Thyristor Controlled Phase Shifter (TCPS). The series transformer injects the voltage in series in the system. The active and reactive power injected by the series transformer is taken from the shunt transformer. For sake simplicity of analysis, the insignificant losses from transformer and converter is neglected. Thus the net complex power (real and reactive power) exchange between the TCPS and the system is zero. The injection of this complex power depends on the injection of a series voltage controlled by a converter. Figure 1b shows the equivalent circuit of Fig. 1a. V s and V sh are represented by the synchronous voltage sources in series and shunt, respectively. X sh is the leakage reactance of the shunt transformer. s X′ is the leakage reactance seen from primary side of series transformer is given by 2 s s sh X X n X ′ = + where n is the turn ratio number of the shunt transformer and X s is the leakage reactance of the series transformer. The shunt synchronous voltage source with leakage reactance can be represented by a shunt injected current model (I sh ) as shown in Fig. 1c. A shunt injected current is composed of in phase current (I p ) and in quadrature current (I q ) which respect to the V m . Thus I sh is given by: Consider the single machine infinite bus system equipped with a TCPS at bus m as shown in Fig. 2a and 2b shows the equivalent circuit of Fig. 2a. Note that X 1 is the sum of generator transient reactance, transformer leakage reactance and equivalent reactance of line 1 and 2; X 2 is the equivalent reactance of s X′ , line 3 and 4. The complex power injected by the series transformer can be written as: Here b = 1/X 2 . The active (P sh ) and reactive (Q sh ) powers drawn by the shunt transformer are given by: As mentioned earlier that the net complex power exchange between a TCPST and the system is zero. The equality of real power balance between series and shunt transformer is given by: The in phase current (I p ) of a shunt current injection can be written as: The size of a is related to the rating of a TCPS (0<a<a max ). The range of α depends on the type of TCPST. Now let the rage of α is π α π − ≤ ≤ . Figure 3 shows the phasor diagram of a series injected voltage and shunt injected current.
Thus in phase current as given Eq. 8 is written as: Similarly, the balancing of reactive power exchange is given by: Thus the in quadrature current of a shunt current injection (I q ) can be written as: The series injected voltage V s with X 2 of Fig. 2b can be transformed into the current I s as shown in Fig. 4a.
The value of I s is given by: The current source connected between bus m and the infinite bus can be replaced by two shunt current source as shown in Fig. 4b. The net injected current (I inj ) at bus m can be written as: The injected current inj I can further be replaced by a fictitious load inj S as shows in Fig. 4c. The value of the fictitious load is given by: The complex power of fictitious load power are given by: Similarly, the reactive power balance at bus m of Fig. 4c is: where, After some mathematical manipulation, the voltage magnitude at bus m is given by: It can be seen from the Eq. 18 and 20 that the TCPST placed at bus m impacts on both the voltage magnitude and the angle. It indicates that the voltage and the angle at bus m can be controlled by a series injected voltage. The electrical output power of generator (P e ) is given by: The generator dynamics, in classical model of system, can be represented by following two first order differential equation: Here δ, ω, P m , P e and M are the rotor angle, speed, input mechanical power, output electrical power and inertia, respectively, of the generator. Solving the Eq. 22 and 23 yields the variation of δ and ω that can be used to study the dynamic behavior of the generator. Equation 23 clearly indicates that the output electrical power (P e ) of the generator is the main factor that dictates the dynamic behavior of the generator because both P m and H are usually considered as constant. The proposed model of the TCPST indicates clearly that the V m can be controlled by a series injected voltage. Thus this proposed model of the TCPST is very easy to implement it to study its behavior on transient stability improvement of the simple system. However, the TCPST can help the system improve transient stability of the system when a series injected voltage is properly controlled. Thus the control strategy of a TCPST should be carefully designed.

Control strategy:
This study uses the machine speed control parameters on a TCPST. When the speed deviation is positive (ω>0), the P e is raised by controlling parameters on TCPST; When the speed deviation is negative (ω<0), the P e is raised by controlling parameters on TCPST.

RESULTS
The presented mathematical model and control strategy is used to study the effect of TCPST on transient stability improvement of the system of Fig. 3. In all cases, it is considered that a three phase self clearing fault appears at bus m and the fault is cleared without changing the network configuration. Figure 5 shows the swing curve of the system without a TCPST for clearing time (t cl ) = 144 msec. Figure 6 shows the swings curve of the system with and without an TCPST for t cl = 145 m sec.

DISCUSSION
From the results in Fig. 5 and 6, we found that the critical clearing time of the system without a TCPST is144-145 msec. It can be seen from the Fig. 5 that with fault clearing time (t cl ) = 144, the system is considered as stable and the system is considered as unstable with t cl = 145 msec as can been in Fig. 6. : Rotor angle of the system without and with an TCPST for t cl = 145 msec However, the system with a TCPST control can stabilize the system with t cl = 145 msec. The simulation results indicate that a TCPST can improve stability of the system.

CONCLUSION
This study investigates the capability of the Thyristor Controlled Phase Shifter Transformer (TCPST) on transient stability improvement of the system. The mathematical model is systematically derived. The presented mathematical model has shown that power flow and stability of system can be regulated by TCPST. This study uses machine speed to control parameters on TCPST. The speed deviation is the main factor to decrease and increase power flow of the system. The simulation results are tested on Single Machine Infinite Bus (SMIB) system. From the simulation results, it indicates that a TCPST can improve transient stability of the system.