Contribution of FACTS Devices to the Transient Stability Improvement of a Power System Integrated with a PMSG-based Wind Turbine

The increasing penetration of wind energy to the conventional power system due to the rapid growth of energy demand has led to the consideration of different wind turbine generator technologies. In fault conditions, the frequency of the power system decreases and eventually leads to speed differences between the grid and the interconnected wind generator. This can result to power system problems such as transient instability (TS). This paper focuses on enhancing the TS of a permanent magnet synchronous generator (PMSG)-based power system during 3ph fault conditions using FACTS devices. The power system considered is connected to a large wind farm which is based on PMSG. Critical clearing time (CCT) is used as an index to evaluate the transient state of the system. Under the study of an IEEE-14 bus system using PSAT as a simulation tool, the integrated CCT with PMSG-based wind turbine is improved with three independent FACTS devices. One of the synchronous generators in the test system has been replaced at random with the PMSG-based wind turbine which is meant to generate an equivalent power. Time domain simulations (TDSs) were carried out considering four study cases. Simulation results show that the (CCT) of the system with the FACTS devices is longer than the CCT without them, which is an indication of TS improvement. Keywords-critical clearing time; FACTS; generator; transient statbility; wind

INTRODUCTION Among renewable power sources, wind has been noted to be the fastest growing one due to its clear and numerous advantages [1]. Transient stability (TS) which is the tendency of synchronous generators remaining in synchronism following a severe disturbance [1][2][3][4], is one of the major aspects of a power system that gets affected with the integration of large wind turbines. Globally, Squirrel Cage Induction Generator (SCIG), Doubly Fed Induction Generator (DFIG), and Permanent Magnet Synchronous Generator (PMSG) are common wind generator technologies considered in wind energy conversion. Unlike DFIG, the PMSG has a full-scale power converter [5]. It enables more reliable operation of wind turbines and reduces the required maintenance [6]. These features make PMSG more advantageous than DFIG. Currently, most wind energy conversion technologies employ turbines with PMSG [7,8]. Even though the PMSG has a better reactive power capability, it is still not adequate as the principal precaution during transient conditions [9][10]. There is therefore a need to augment the dynamic reactive power capability of FACTS devices in order to strengthen the transient state of the system to which it is connected.
TS is considered one of power system's dynamic behaviors having been analyzed and improved by various approaches. However, since TS study can only be considered in the presence of a severe fault [4], there is need to mention the clearing time of faults which will keep the system transiently stable. For a particular given system, the critical clearing time (CCT) must be specified or stated to allow easy system operation during faults. In addition, TS study time is short and so faults need to be cleared as quickly as possible to prevent synchronism loss of the system generators, knowing the CCT can allow fault clearing within the time limit thereby maintaining the stability of the system. An impact study for PMSG-based wind generation on the TS was carried out in [7]. The study considered a method of equal area criteria theory. An active current control strategy taking into account a perturbation estimation was proposed in [11] for enhancing the TS of a power system connected with a PMSG-based turbine. A simulation study was conducted in [12] by using a TSSC to improve the efficiency of a wind turbine. Authors in [8] compared the TS augmentation between doubly fed induction generators and permanent magnet synchronous generators. It was deduced that the TS of the system with DFIG wind generator can be improved by including a permanent magnet synchronous generator in the same system. Authors in [13] investigated the effects of series compensation on the TS improvement for a DFIG wind turbine power system. In [14], a study of the assessment of wind energy based on SCIG penetration effect on TS was provided. Different penetration levels were considered and CCT was analyzed.
The current paper focuses on the TS analysis with consideration of critical clearing time index. Thus, conclusions on the improvement of the TS of the system are based on the CCTs of all the cases considered.

II. IMPLEMENTATION OF THE SYSTEM IN PSAT
This paper employed the IEEE-14 bus system for the simulation process. Power System Analysis Toolbox (PSAT) was used in implementing the considered system. PSAT is a MATLAB package which uses Simulink libraries for network designs. It is appropriate for analysis of small and medium size power systems [15]. PSAT also supports both dynamic and static power system analysis and control studies. Aside time domain simulations, PSAT also includes optimal power flow, continuation power flow and small signal analysis. The data used in implementing the system in PSAT are taken from [16] with 20s simulation time.

A. The IEEE 14-bus System Model
The implementation of the proposed test system is executed using PSAT 2.1.10. Synchronous generator models, wind turbine model, wind turbine generator model, constant loads, and FACTS devices are all inherent models adopted from MATLAB/Simulink library. The test system consists of 5 generator buses and 8 load buses. Out of the 5 generator buses, there is one slack (bus 1), one PV (bus 2) and 3 additional synchronous condensers (buses 3, 6, 8). Table I shows a summary of the system characteristics. Three different voltage levels were chosen for the whole system equipment with a power rating of 100MVA. Blue indicates a 13.8kV bus, green indicates an 18kV bus and red indicates a 69kV bus. Bus 1 is defined to be the reference bus (where the wind turbine is integrated). The purpose of integrating the wind at the slack is to allow the wind turbine generate a greater percentage of the whole system capacity.

B. Modeling of the PMSG-based Turbine
The PMSG, also referred to as direct drive synchronous generator (DDSG), is a type of synchronous generator whose rotor windings are replaced with a permanent magnet and hence the name permanent magnet synchronous generator (PMSG). Its excitation field is created by the permanent magnet in the rotor [10]. This arrangement has led to the elimination of excitation losses that will take place in the rotor during starting of the generator. Block diagram of the variable speed connected grid wind energy system based on PMSG Consequently, the PMSG has better performance and higher efficiency as compared to other wind turbine generators since the rotor losses contribute to about 20-30% of total generator losses [17]. Even though the PMSG is a synchronous machine, its contribution to the grid inertia is little compared to that of the conventional synchronous generators. This is due to the power electronic based converters through which it is interfaced with the grid as shown in Figure 1 [9].
The purpose of the power electronics based back-back converter equipment is to control the generator rotor angle and convert the electrical power available at the shaft of the generator into high quality power to be integrated to the power grid. The total power generated by the wind turbine is represented in (1) with ߣ defined in (2) [18]: where P is the active power generated by the turbine, ߩ is the air density, ‫ܣ‬ is the swept area of the turbine blades, ‫ܥ‬ is the power coefficient, ߣ is the tip speed ratio, v is the wind speed, and n is the generator rotor speed. Since there is no gearbox in the PMSG, the aerodynamic torque (N/m) is equal to the mechanical torque [19] transferred to the generating unit as represented in (3): The modified IEEE 14-bus system with the integration of the PMSG module is shown in Figure 3. The generator is connected to the entire grid via a fully-scaled back to back voltage source power converter (AC/DC/AC). Equations (4) and (5) are the state equations, (6) is the electrical equation, and (7) is the mechanical equation of the PMSG.
where d and q subscripts represent the physical quantities transformed to the d-q reference frame. ܴ ௦ is the stator resistance (Ω), ‫ܮ‬ ௗ and ‫ܮ‬ are d and q-axis inductances (H), ‫ܮ‬ ௗ is the leakage inductance, ߰ is the permanent magnetic flux (Weber), ܸ ௗ and ܸ are d and q-axis voltages, ‫ݓ‬ is the electromagnetic speed of the generator (rad/s) and p is the number of pole pairs. Figures 2 and 4 illustrate respectively the d and qaxis equivalent circuits of the PMSG.

C. Modeling of the FACTS Devices
Three FACTS devices were employed one from each of the three generations of FACTS [20]. Generally, FACTS devices have a unique feature of rapidly controlling the system by their reactive power management [18,21]. This characteristic was exploited for the system's TS improvement. Just like the wind generator, the simulation models of the thyristor controlled series capacitor (TCSC), unified power flow controller (UPFC) and the static synchronous compensator (STATCOM) were utilized. TCSC is an important FACTS device which is connected in series in the power system [3]. The total reactance of the TCSC (represented by ܺ ்ௌ ) is given in (8) with ܹ and ߙ representing the electrical angular frequency and the firing angle of the thyristor. The TCSC basically improves the power system's TS by adjusting the transmission line impedance: The makeup of a UPFC combines characteristics of static synchronous compensator together with static series compensator. It simultaneously acts as a shunt and phase shifting device [22]. STATCOM is a voltage source based converter and a shunt connected device. It controls the bus voltage at the place where it is connected [18,23,24]. Voltage stability index tool was used to analyze the weakness of the buses in the IEEE-14 bus test system for proper placement of the FACTS devices. The use of voltage stability index creates awareness of the closeness of a power system to voltage collapse or voltage instability [25][26]. Using Figure 5 as an example of the power system's line model (e.g. from bus a to bus b), the fast voltage stability index (FVSI) of any line in the IEEE-14 bus test system is calculated using (9): In (9), Z and X are the line impedance and reactance, ܸ and ܳ are the sending end voltage and receiving end reactive power respectively. The closest line to 1 is considered the weakest of all the lines in the system. From the FVSI calculation, line 3 which is found between bus 2 and 3 was identified as the weakest and hence appropriate for integration of FACTS devices. Figure 6 illustrates a plot of the FVSI of all the 20 transmission lines in the system with line 3 indicating the highest value of FVSI aside line 9 (transformer). This means that, more reactive power will be injected through line 3 in each case in order to boost the voltage level and hence improve the TS of the whole system. The modified IEEE-14 bus test system with the integrated PMSG-based wind turbine (at bus 1) and TCSC (between bus 2 and 3) is shown in Figure  7. • Power system integrated with PMSG-based wind turbine • Power system integrated with wind turbine and TCSC • Power system integrated with wind turbine and UPFC

• Power system integrated with wind turbine and STATCOM
The fault was created in bus 2 and was set to clear automatically by the system after some time. The fault clearing time varied until the system lost synchronism. The time immediately after the system lost its synchronism was noted and stated as the critical clearing time in each of the above systems. All the synchronous generators in the system were monitored and the critical clearing time in each case was noted with emphasis laid on the generator that was closer to the position of the three phase fault.  From the swings of both rotor angle and speed deviation, it is discovered that the G1 remains stable when the fault is cleared at or before 0.319s (Figures 8, 10) following the occurrence of the fault. On the other hand, delaying the fault by 0.320s after its occurrence causes the system to lose synchronism (Figures 9, 11). Thus, the speed of the synchronous generator deviates and continues to increase without returning to its original value. In this system, the maximum clearing time for which the synchronous generator remains in synchronism is 2.319s. Beyond this time, the system is unstable. Therefore the CCT of the system integrated with only PMSG-based wind turbine without any FACTS device is 0.319s after the fault.  However, delaying fault clearing time to 2.541s makes the system unstable. In other words, clearing the fault at 2.541s instead of 2.540 makes G1 lose synchronism with respect to other synchronous generators in the system. In this case, the CCT of the system is 0.540s following the fault.  (Figure 17, 19). This indicates that the CCT of this system is 0.435s following the occurrence of the three phase fault.   Figures 23 and 25 for rotor speed and angle respectively. With fault clearing time delayed to 2.417s the G1 does not regain synchronism, making the system unstable as shown in Figures 24 and 26 for speed deviation and rotor angle respectively. Therefore, in this system, clearing the fault at 0.417s instead of 0.416s after the occurrence makes the system totally unstable. Hence, the CCT is 0.416s.

IV. CCT EVALUATION AND IMPROVEMENT
It was concluded from the simulation results that CCT differs from one system to another for all FACTS devices. A summary of the CCT for each case is provided in Table II. The three phase fault was created at bus 2 and at 2s. It can be noted that the system with PMSG and TCSC has the longest CCT. In order to visualize clearly the individual contributions of the FACTS devices to the TS improvement in terms of CCT, the CCT of the PMSG-based system is subtracted from the CCT of the systems connected with each of the FACTS devices as shown in (10): where subscript a represents TCSC, UPFC or STATCOM. Subscript n represents the individual cases (cases 2, 3 and 4). This means that, the CCT of the system with the wind turbine only (case 1) which is 0.319s was subtracted from 0.540s, 0.435ss and 0.416s for systems with TCSC, UPFC and STATCOM respectively. The results are summarized in Table  III in descending order of improvement.
These results indicate that TCSC has the longest CCT among the three FACTS devices. Therefore, TCSC improves a system integrated with wind turbine better than UPFC and STATCOM. It is also observed that STATCOM has the shortest CCT, so is the weakest FACTS device regarding the TS improvement of the power system. This is in agreement with the findings in [15] for a larger power system. V. CONCLUSION This paper aimed at studying the transient stability improvement of a power system connected to a large scale wind turbine using FACTS devices based on the critical clearing time index. Three FACTS devices were considered and each of them was connected individually to investigate their respective contributions to the CCT improvement. In each case, the CCT was stated and the improvement time was identified. This study showed that all the three FACTS devices have different critical clearing times. Thus, they improve the system TS to different extents. It was also discovered that the best FACTS device for TS improvement is TCSC while STATCOM is the weakest FACTS device for transient stability improvement.