Abstract
Wind turbines (WTs) are a desirable alternative to traditional nonrenewable power resources as a result of recent environmental concerns. Some of them are fixed speed wind generator (FSWG) and have been integrated to power system by squirrel cage induction generator (SCIG). Induction machine absorbs reactive power during all operating conditions, especially at fault condition may result in severe voltage drop which can lead to generator outage. This outage disconnects a significant amount of active power and consequently leads to frequency instability. In order to prevent induction generator (IG) outages in short circuit failures, this paper investigates thyristor-controlled series capacitor (TCSC) device as a candidate solution. TCSC compensates the IG terminal voltage drop by adjusting transmission line impedance at fault condition. In the proposed method, a metaheuristic technique means that shuffled frog leaping algorithm (SFLA) has been utilized to optimize the TCSC controller gains. The proposed scheme can be applied for both SCIGs and wound rotor induction generators (WRIGs) which is another advantage of this method. Single-machine infinite bus system is considered as case study, and various operating conditions and disturbances have been considered to verify the effectiveness of the proposed method.
1. Introduction
1.1. Background
Renewable energy resources are environmentally beneficial and cost-effective power resources, and their penetration level is notably increased in power systems in recent years. In the past decade, wind energy has grown rapidly among these resources [1]. Most WTs are connected to power grid using IGs. There are two primary forms of IG that are regularly utilized. Wound rotor induction generator is connected to power grid by electronic converter and is known as a doubly fed induction generator (DFIG). This type of IG usually has variable speed and includes an external mechanism to control electrical characteristics via rotor circuit [2]. SCIG is another form which is directly connected to the power grid and known as fixed speed WT. Over the former years, due to simplicity and inexpensiveness, SCIGs were installed in large proportions in power grids, but they have stability problems such as the transient stability of synchronous machines [3]. SCIGs absorb reactive power during normal and fault operating condition that may result in voltage collapse and rotor speed instability [4]. If there is no stabilization solution, this event may lead to generator outage, and consequently, a significant amount of active power may be lost [5]. So, it is important to analyze the transient stability of SCIGs.
1.2. Literature Review
There are many researches related to the stabilization of FSWG as an interesting topic. It is reported in literatures that static synchronous compensator [6–8] can stabilize the FSWG. Braking resistor has been proposed as another method for transient stability improvement of synchronous generators for a long time [9, 10]. According to [11, 12], braking resistor can be recognized as a candidate for wind generator stabilization as well. Generally, wind turbine blades are equipped with a pitch angle controller. Although the primary purpose of this controller is to keep output power of WTs at the rated level, it can also improve the transient stability of the IG by verifying the rotor speed in emergency condition [13, 14]. Superconducting magnetic energy storage is an alternative solution for WT stabilization problem. It consists of large superconducting coil which can save electric energy in the magnetic field. The real and reactive power can be supplied or absorbed by the coil related to grid necessities [15–17]. Smart loads are another choice for improving the fault-ride-through capability of FSWGs in microgrids which is reported recently [18].
1.3. Research Gap, Challenges, and Motivation
The aforementioned solutions of transient stability for FSWGs implies the importance of this issue. TCSC as a series flexible AC transmission system (FACTS) device is able to change transmission line impedance rapidly and continually [19, 20]. It can control the power flow of transmission lines and improve the transient stability of the power system during the large disturbances such as short circuit faults [21]. The application of TCSC to improve voltage stability [22], transient stability [19, 23], and small signal stability [24, 25] of power systems including synchronous generators has been previously reported. This paper proposes an application of TCSC for power system transient stability including IGs. This paper is aimed at filling this gap and provides a well-documented dynamic modeling of WTs and fixed speed IGs for transient stability study. The method comprises TCSC designing, controller tunning, and stability analyzing.
1.4. Contribution
Different control strategies have been used for FACTS devices. PID control [26], fuzzy logic control [20, 24], lead-lag control [23], and neural network-based control [27] have been studied in the literature. Despite modern control methods, the classical PID controller is mostly used in industrial applications as a simple, reliable, and low-priced controller [26]. The most important issue in this controller is related to the complexity of tuning its gains [28]. In this study, a method to tune controller gains in an optimal way is proposed. In this regard, a metaheuristic technique, shuffled frog leaping algorithm, is used to optimize the controller gains of TCSC integrated to power system with WT. The proposed scheme can be applied for both SCIGs and WRIGs.
1.5. Paper Organization
The rest of the paper is organized as follows. The dynamic modeling of WTs and IGs and dynamic response of them at fault condition are presented in Section 2. The controller scheme is introduced in Section 3. The SFLA formulation and application for the problem are explained in Section 4. Time-domain simulations of the proposed controller are presented in Section 5, and the results for two scenarios show that SCIGs can ride through the fault without disconnecting from network by well-organized use of TCSC. The paper finally concludes in the last section.
2. System Model
2.1. Dynamic Model of Induction Machine
The 5-order dynamic model of the three-phase induction machine is known as the Park model [29]. The Park model expression in reference frame system is shown in equations (1)–(12):
Stator voltage equations:
Rotor voltage equations:
Electromechanical equation:
Electromagnetic torque:
Stator flow equations:
Rotor flow equations:
By referring all the values to the stator in these equations, we will have
In these equations, and are the stator and rotor resistors, and are the stator and rotor inductance, and are the stator and rotor leakage inductance, is the magnetizing inductance, and are the current and voltage of -component of the stator, and are the current and voltage of -component of the stator, and are the current and voltage of the -component of rotor, and are the current and voltage of -component of rotor, is the stator field speed, is the rotor mechanical speed, is the slip, is the electromagnetic torque, is the mechanical load torque, and is the inertia constant which all are expressed in per unit.
2.2. Dynamic Model and Characteristics of WT
The details of the WT in this paper are based on the model presented in [30]. Figure 1 shows the main components of the rotating part including the blades, hubs, low speed shaft, high speed shaft, gearbox, and generator rotor. The dynamics of this model can be presented as the following equations:
In these equations, , , and are the inertia moment of the generator, hub, and blades in which . Moreover, , , and are the mechanical speed of the blades, hub, and gears. , , and are the mechanical angle of the blades, hub, and generator. , , and are self-damping coefficients of the blades, hub, and generator. and are damping coefficients between blade-hub and hub-generator. and are blade-hub and hub-generator stiffness coefficients. Moreover, is the gearbox ratio unit, is the angular speed, and is the number of generator poles. All parameters are expressed in per unit.
The mechanical torque is equal to wind aerodynamic torque which is calculated from where is the air density, is the radius of the blades, is the wind speed, and is the power factor of the turbine. is the ratio of the wind speed to the angular speed of the blades calculated from equation . represents the blade rotation angle. There is a pitch angle control system in WTs to maintain the output power in the generator terminal in constant acceptable range using the angle of the turbine blades when the wind speed changes around the rated speed [31]. Although the main purpose of pitch angle controller is to regulate output power when the wind speed is over the rated value, it can enhance the transient stability of wind generator by controlling the rotor speed. The pitch control system used in this work for controlling the rotor speed is shown in Figure 2.
Figure 3 shows the curve for different values of which is referred to the WT characteristic curve [32]. This curve is calculated by the following nonlinear:
2.3. Analysis of IG during Fault Condition
Figure 4 illustrates the FSWG as a single machine connected to infinite power bus by two power lines. One line is equipped with a three-phase TCSC, and the other one is candidate for fault condition.
Considering the steady-state equivalent circuit of induction machine, the output active and reactive powers of the IG are calculated based on the following equations [33]: where is the stator terminal voltage, is the stator leakage reactance, is the rotor leakage reactance referred to the stator, and is the magnetizing reactance. These equations show the dependency of the active and reactive powers of SCIG on terminal voltage and slip.
The output active power and reactive power vs. slip characteristics for a typical IG that show the steady-state behavior of the generator are shown in Figures 5 and 6, respectively.
According to Figure 5, the slip value is about -0.01 during the normal operation of IG based on the prefault curve. When a fault occurs, the terminal voltage of the generator, , drops sharply, and according to equation (20), the output active power of the IG () will be decreased. In this regard, the postfault active power-slip curve is followed in Figure 5. In this situation, as is lower than mechanical input power (), the rotor speed will be increased continuously, and the absolute value of slip will be increased consequently. If the ultimate rotor speed of the generator after the fault exceeds the critical speed, the IG will lose its stability [34]. Therefore, to prevent the generator from tripping, it is necessary to make a condition in which the generator tracks the postfault curve as soon as possible. Accordingly, increasing the terminal voltage of the generator helps to achieve this goal. Consequently, the stability of the IG in permanent fault conditions depends on the recovering time of terminal voltage as well as the critical speed after fault. If this time is less than a specific value, the IG rotor speed does not exceed the critical speed and its stability will be guaranteed. On the other hand, increasing the critical speed range of the postfault curve will result in increasing stability, and thus, the IG will ride through the fault.
Output reactive power vs. slip characteristic shown in Figure 6 confirms that the IG absorbs reactive power in both generator and motor modes. For each curve, it is obvious that when the absolute value of slip is increased, the amount of absorbed reactive power is also increased. When a fault occurs, the terminal voltage of the generator, , drops sharply, but the speed does not immediately change because of the rotor inertia. Therefore, in the fault condition, the amount of reactive power absorbed by the generator decreases initially, but with the increase in the absolute value of the slip, the amount of absorbed reactive power increases, and it may exceed its previous value in the prefault condition. This will lead to a worse voltage drop at the generator terminal, and as a result, the instability of the rotor speed will be aggravated.
2.4. TCSC Model and Parameter Design
TCSC consists of a fixed capacitor paralleled by thyristor-controlled reactor in order to provide a variable reactance. The electrical model of TCSC is shown in Figure 7.
The thyristor-controlled reactor is a variable reactor with respect to its firing angle () which is represented by . This reactance has continuous changes which could be shown in
The equivalent impedance of the TCSC includes and which can be calculated as follows: where is the delay angle between the peak current of the capacitor and its voltage or the delay angle by zero-crossing line current [35].
By varying the from its maximum value () to its minimum value (), will change from to . To have both capacitive and inductive operations, should be selected smaller than . Table 1 shows the reactance behavior of TCSC by varying firing angle on this basis.
Based on the above description, variation vs. is shown in Figure 8.
The appropriate values for the inductor and capacitor in TCSC are selected based on the equivalent reactance of the transmission line. In this regard, the series compensating degree of transmission line is described as follows: where is the degree of compensation and is the equivalent reactance of the transmission line. To avoid resonance phenomenon, should not be selected. In practical applications, the maximum degree of compensation must not exceed 70%. The other assumption is that in the capacitive region, the maximum value of for must not exceed . Moreover, of TCSC is chosen such that the ratio be in the range between 0.1 and 0.3 to have both capacitive and inductive operation modes [36, 37].
3. Proposed Control Scheme
3.1. Structure
Figure 9 depicts the controller structure used for TCSC to have the appropriate firing angle. Since the capacitive operating mode is considered in this paper, the PID controller is configured to provide the appropriate response in the entire capacitance zone. The linearization block is a lookup table that matches the input reactance values to the corresponding proper firing angle. The firing angle should not exceed its maximum value in and minimum value in . Therefore, a limiter is used to restrict the linearization block output. Finally, for each phase, the firing angle is compared with the line current using a comparator, which results in a square pulse at the comparator output that can be applied to each thyristor.
This controller can also be activated if there are transients corresponding to rotor relative speed. It should not affect original slow control function in which TCSC acts as a line power flow management. The output of the proposed controller has to be slowly bypassed in steady state by a washout filter with zero static gain.
3.2. Optimum Design
After a disturbance, the TCSC controller must be able to limit and stabilize the transient of the rotor’s speed, . In other words, the swings reflected in the speed deviations must be damped and settled down as soon as possible. It means that the settling time and overshoot of must be minimized. In this regard, an optimization problem given in (24) must be solved.
In (24), is the objective function as well as and are the weighing factors. The first part of relates to the overshoot, and the second part relates to the settling time. Variables that must be optimized are PID gains, i.e., , , and . The problem constraints are the limitations of TCSC controller gains.
To calculate the objective function, the time-domain simulation of the studied power system is carried out. The major problem is to find the optimal set of , , and .
4. Shuffled Frog Leaping Algorithm
Eusuff et al. developed SFLA to solve optimization problems [38]. This algorithm is a metaheuristic population-based solution to seek the global optimal answer. In SFLA, frogs as solution candidate members are divided in several groups and improve their positions by communicating information with each other and shuffling to other groups.
The SFLA steps are as follows: (i)Initialization: random initial population of solution possible members is generated. Each one has dimension based on the number of decision variables(ii)Sorting and division: the members are sorted in descending order according to their finesses. These sorted members are divided into groups known as memeplexes; each has members such that . The division is done in such a way that the first sorted member goes to the first group, the second one goes to the second group, the -th one goes to the -th group, the -th one goes back to the first group, etc. Figure 10(a) demonstrates this process. The members with the best and worst fitness for each group are identified as and , respectively. Moreover, the first sorted member with the global best fitness is identified as (iii)Local search: the worst member in each group is propelled toward or as follows:where is a random -dimensional number each in the range [0, 1]. If the fitness of is better than the fitness of , the worst member is replaced by the new one. Otherwise, is replaced by in equation (26), and the process is repeated. If no improvement becomes possible in these two cases, the worst member is replaced by a new random one and its fitness is evaluated. The local search is done for all worst members in all groups [39] (iv)Shuffling: after local search step, all members in all groups are mixed into one group. The algorithm is returned to sorting and division step. This process is repeated until termination criterion such as finishing specific number of iterations or reaching relative tolerance of global best fitness less than a predefined value. Figure 10(b) demonstrates the SFLA flowchart
(a)
(b)
5. Simulation Results and Discussion
The case study is shown in Figure 4. The grid components are modeled in three phases, and the distribution feeders are modeled as resistive-inductive () series impedances. The output power is delivered to a 33 kV bus at 50 Hz through two parallel feeders and a transformer. The parameters of the system have been listed in Tables 2 and 3.
The system also comprises a WT coupled to a 3 MVA SCIG.
To show the effectiveness and validation of the proposed method, the following cases are considered.
5.1. Scenario 1
In this scenario, it is supposed that a three-phase fault to ground is occurred in the middle point of transmission line at s and cleared by circuit breaker after 200 ms as depicted in Figure 4. Although the speed of wind is a stochastic variable, during the short time interval of the transient stability analysis, the change of the wind speed can be ignored, so in this study, the wind speed is assumed to be constant.
This scenario consists of three cases as follows:
Case 1. Without control.
Case 2 (conventional scheme (pitch angle control)). Pitch angle control system is considered as conventional solution for fault ride through of WTs. In this regard, the time constant, , of the pitch control system depicted in Figure 2 is considered 1.0 second. Moreover, the parameters of the PI controller, and , are considered 98 and 3, respectively, by trial and error.
Case 3 (proposed scheme (TCSC with optimal control)). In this case, based on the discussion in Section 2.4, the maximum degree of line compensation by TCSC is assumed to be 70%. In this regard, TCSC capacitor and inductor values in each phase are obtained 1554 μF and 1.32 mH, respectively.
The SFLA is used to minimize the objective function introduced in Section 3.2. The initial parameters of the SFLA are as follows:
Population size: 100 members
Number of iterations: 100
Number of groups: 20
As a result, the optimum PID controller gains, , , and , are obtained as 0.43, 0.08, and 0.09, respectively. The convergence plot of the SFLA is shown in Figure 11.
5.1.1. Rotor Speed Evaluation
The rotor speed of IG for all cases is shown in Figure 12. As can be seen, in without control case, the rotor speed continually increases and fault clearance by breaker cannot make the IG stable. In conventional and proposed schemes, rotor speed is recovered. However, the maximum speed and settling time of the proposed scheme are better as detailed in Table 4.
5.1.2. Active and Reactive Power Evaluation
The active and reactive powers of IG are depicted in Figures 13 and 14, respectively. When there is no control scheme, after fault occurrence, generated active power of the IG converges to zero. In conventional and proposed schemes, the IG continues to inject active power into the grid, but the steady state in proposed method is achieved faster than conventional scheme.
As can be seen in Figure 14, the IG absorbs reactive power from grid in all cases, but in conventional and proposed schemes, the absolute value of absorbed reactive power is recovered and converged around the previous fault condition.
5.1.3. Terminal Voltage Evaluation
The response of IG terminal voltage is illustrated in Figure 15. When there is no control scheme, the voltage drops to almost 0.8 p.u. after fault occurrence. This voltage drop occurs because of significant amount of absorbed reactive power. The voltage drop in both the conventional and proposed schemes is lower in comparison to no-control scheme. Moreover, the proposed scheme's settling time is better than the conventional scheme. The results are presented in detailed in Table 5.
5.1.4. Electromagnetic Torque Evaluation
The electromagnetic torque of IG is displayed in Figure 16. When there is no control scheme, the torque almost converges to zero. In conventional and proposed schemes, the induction machine recovers its normal operation. However, the response of the proposed scheme is better in which the torque converges to the steady-state value with less fluctuations.
5.1.5. Harmonic Analysis
Although TCSC injects harmonics to power system, it is acceptable if the generated harmonic is less than the standard. The generator terminal bus is taken under study to evaluate the effect of harmonic on the IG operation because it is close to the wind turbine. Figure 17 shows the harmonic component and total harmonic distortion (THD).
It is remarkable that the most generated harmonic is related to frequency of 66.67 Hz whose value does not exceed 1.79%. Moreover, it can be seen that the THD is almost 2.83% that is acceptable based on IEEE 519 standard.
5.2. Scenario 2: Variable Fault Location and Clearance Time
In this scenario, different fault location and clearance time have been considered to verify the control methods. In this regard, both conventional and proposed schemes are applied to ride through the faults, and the simulation results are shown in Table 6. In this table, TP shows that both TCSC and pitch angle methods can ride through the IG from fault. T shows that only TCSC method can return the IG back to stable operation. Finally, P shows that only pitch angle method can stabilize the IG operation.
Generally, the shorter the clearance time, the higher the stability. Therefore, while clearance time is less than 155 ms, IG can maintain its stability independent of the fault location in both conventional and proposed schemes. On the other hand, if clearance time is higher than 220 ms, the IG cannot return to stable condition in any fault location for both schemes. As can be seen from Table 6, in some marginal conditions, only TCSC can stabilize the IG. Indeed, the faster response of TCSC enables it to stabilize the IG in more situations. Moreover, there is no situation in which pitch angle solution can ride through the IG from fault merely.
6. Conclusion
In this paper, a new control method for thyristor-controlled series capacitor was proposed to enhance fault ride through of wind turbines equipped with the FSIG. The dynamic behavior of IG and WT was introduced to study the stability of power system. Furthermore, the TCSC modelling and integration for fault ride through of IG were investigated. In order to obtain the optimal PID controller gains of TCSC, shuffled frog leaping algorithm was utilized. For comprehensive study, the clearance time and fault location were considered as variable parameters to study different conditions. Simulation results show that proposed method can stabilize the IG rotor speed in more conditions in comparison conventional method. In the other words, marginal clearance time was improved in the proposed scheme. In fact, adjusting transmission line impedance with TCSC results in IG voltage compensation and more possible restoration to normal operating mode after fault occurrence. For future work, it is needed to apply the TCSC to the larger power networks, including more fixed speed wind generators. Also, more research is necessary to study the effect of the TCSC on variable speed wind generator. Moreover, the effect of the shunt FACTS devices for stabilizing the fixed and variable speed wind generators can be investigated as future work.
Data Availability
There is no data supporting this study.
Conflicts of Interest
The authors declare that they have no conflicts of interest.