Adaptive control universality of STATCOM for efficient wind energy conversion systems

Introduction

Despite the usage of alternative generators such as switching reluctance generators (El-Naggar et al., 2021), self-excited asynchronous generators (Bansal, 2005), and permanent magnet synchronous generators (Ibrahim et al., 2021), the Doubly Fed Induction Generator (DFIG) accounts for more than half of the generators used in wind energy (WE; Mosaad et al., 2022). Compared to other generators, DFIGs have notable attributes such as robustness, cost-effectiveness in terms of maintenance, and enhanced controllability in comparison to other generators (Hamid et al., 2020).

A wind system incorporating a DFIG exhibits a significant susceptibility to grid disturbances due to the lack of synchronous coupling between the stator windings and the grid. This is primarily attributed to the presence of power electronic converters (Xiang et al., 2006). These disturbances have the potential to impact the power quality of the WT system adversely, cause damage to the turbine, and result in the disconnection of the generator from the system.

The WE system is susceptible to several disturbances, such as fluctuations in wind speed, faults occurring at the point of connecting the WT to the system, voltage sag/swell situations, and occurrences of ferroresonance (Jabbour et al., 2020). Therefore, it is imperative to incorporate Fault Ride-Through (FRT) capability in the DFIG-WT system to ensure its efficient operation during fault occurrences. The FRT capacity is often recognized as the most demanding aim for a grid-connected wind turbine (Edrah et al., 2020). In order to ensure grid stability, the wind system must maintain its connection to the grid even in the event of a voltage drop. This can be achieved by maintaining a consistent energy output without experiencing significant current oscillations during and after clearing the faults. Additionally, the wind system should be capable of contributing to the restoration of voltage levels, thereby providing valuable help in the grid’s recovery process. On the contrary, the abrupt cessation of a significant quantity of wind power has the potential to exacerbate the repercussions of voltage dips, resulting in various ramifications for the network (Du et al., 2016; El-Naggar and Erlich, 2015). In addition to FRT support, it incorporates measures to mitigate overvoltage errors and stabilize voltage fluctuations caused by wind speed variations (Du et al., 2016; Gautam et al., 2009). Therefore, the integration of certain controlled devices is essential to enhance and optimize DFIG-WT system performance.

The utilization of various configurations of Flexible AC Transmission Systems (FACTS) holds significant importance in enhancing the performance of wind energy systems (Parastvand et al., 2020). The fundamental operating principle of FACTS devices is to enable efficient power transfer between these devices and the electrical network (Parastvand et al., 2020). This interaction provides support for the operation of WE systems in the presence of disturbances and climate variations (Nayak et al., 2021). The incorporation of FACTS devices has a substantial impact on the methodology employed in the design, establishment, and control of WE systems. This integration results in enhancements in system flexibility and overall performance. The selection of a particular type of FACTS is influenced not only by its performance but also by other factors such as cost, structural feasibility, and controllability. For more elaboration, it can be argued that a unified power flow controller (UPFC) exhibits greater efficacy compared to a Synchronous Compensator (STATCOM). This could be attributed to the inherent design of the UPFC, which incorporates a series controller that is absent in the STATCOM. UPFC was successfully employed in the DFIG-WT system to ameliorate the performance through wing gust and support FRT (Mosaad et al., 2020). However, the cost and complexity of control were not investigated.

The STATCOM is a highly responsive device that can provide/consume reactive power, so effectively controlling the voltage at the point of linking the WE system to the grid. Its operation is based on using Voltage Source Converters (VSCs) with semi-conductor valves arranged in modular multi-level Modular Multilevel Cascade Converters (MMCC). The use of the MMCC family may be a viable option for the implementation of STATCOM inside WE systems (Akagi, 2011; Peng and Wang, 2004). The STATCOM was implemented to enhance the stability and fault recovery capabilities of WT-DFIGs on a significant scale. During a state of steady-state operation, the STATCOM will actively inject/absorb reactive power in order to maintain the voltage at the bus and prevent any fluctuations. During transient events, the STATCOM is utilized to expedite the recovery of voltage and reinstate voltage stability by injecting a maximum amount of reactive current to assist the electrical grid (Molinas et al., 2008). When comparing Static VRr compensator (SVC) to STATCOM, it has been demonstrated that STATCOM offers a higher transient margin and the potential to incorporate overloading capability (Molinas et al., 2008). The utilization of STATCOM technology has been employed in offshore wind power plants to meet the requirements of grid codes during regular operation as well as in the event of grid faults (Tanaka et al., 2017). The occurrence of ferroresonance events is typically attributed to the interaction between capacitances and nonlinear inductances within a system. This phenomenon resulted in the occurrence of decelerated transient overvoltages characterized by non-sinusoidal/distorted waveforms, which had an impact on the various components of the power system. Hence, the implementation of ferroresonance overvoltage mitigation measures became imperative to safeguard the power system components from potential harm. STATCOM was implemented to mitigate ferroresonance in DFIG-WE system for the first time in Mosaad et al. (2022). Simulation results of employing a STATCOM to enhance the damping characteristics of an offshore WT integrated into a multi-machine system were investigated in Wang and Truong (2013). The performance of the observed offshore WT is conducted using an analogous aggregated DFIG. The proposed STATCOM system incorporates a PID damping controller as well as a hybrid controller that combines PID and fuzzy logic control (FLC) techniques (Wang and Truong, 2013).

In the context of a DFIG-WE system, effectively mitigating sub-synchronous oscillations using STATCOM was discussed in Wu et al. (2021). STATCOM was implemented to support low voltage ride-through (LVRT) in the DFIG-WE system in Kamel et al. (2020). To stabilize the rotor speed response of the DFIG under high-load operating conditions, a control strategy for the STATCOM was developed. This control strategy utilizes Pulse Width Modulation (PWM) voltage magnitude and Proportional-Integral (PI) phase angle controllers (Senthil Kumar and Gokulakrishnan, 2011). The evaluation presented highlights the utilization of STATCOM in the DFIG-WE system. The literature indicates that the investigation of STATCOM focused exclusively on a specific application, with limited exploration of its possibilities for additional uses.

The controller is specifically created and presented for this particular application. The primary objective of the present study was to fill the existing research void by investigating the utilization of STATCOM in various scenarios inside the DFIG-WE system while also assessing its viability as a universal controller.

The control of STATCOM is a significant area of research since numerous studies have been conducted on the implementation of controllers for it in WE applications. The selection and design of such controllers significantly impact the operation and objectives of STATCOM. The most commonly used controller used for the STATCOM is the PI controller. The abundant use of this type of control is due to the ease of use in modeling and practical implementation. PI and its other configurations, Proportional-Integral-Derivative (PID) were presented as a controller for STSTCOM in many applications (Hazrati and Jalilian, 2012; Senthil Kumar and Gokulakrishnan, 2011; Truong and Wang, 2012; Wang and Hsiung, 2011). There is a prominent and essential issue associated with using PI controllers. That is the tuning of the controller parameters, and this issue has been explored at length in many research articles and is still under research and improvement based on different optimization algorithms like genetic algorithms, particle swarm optimization, elephant handling, etc. (Mosaad et al., 2021; Senthil Kumar and Gokulakrishnan, 2011; Truong and Wang, 2012; Wang and Hsiung, 2011). Following the resolution of the issues pertaining to the tuning of PI controller parameters, more challenges have surfaced. One factor to consider is the duration required for tuning, which subsequently necessitated the utilization of optimized PI controllers in an offline manner. The second aspect pertains to the assurance of achieving these optimal parameters and subsequently optimal performance even when the operating conditions deviate partially or entirely from those under which the optimization process was done. This problem was solved by using an adaptive controller for STATCOM. Many adaptive controller techniques have been proposed for controlling the STATCOM to enhance its performance in the WE system as opposed to utilizing optimized PI controllers. Most of these adaptive controllers for STATCOM were used for one application only (Mosaad, 2018; Wu et al., 2021). The investigation of Model Predictive Control (MPC) as an adaptive control technique was conducted to regulate STATCOM for steady-state and startup conditions only (Kaymanesh et al., 2022). The study compared the performance of a seven-level STATCOM with a two-level STATCOM (Kaymanesh et al., 2022). To the knowledge of the author, no adaptive control method has been proposed thus far for addressing various fault situations or providing a universal control strategy for the STATCOM in WE systems.

The primary aim of this study is to modify the control of STATCOM to effectively regulate the WE-DFIG and mitigate a greater number of fault events by implementing adaptive control techniques.

The main contribution of this study may be delineated as:

System description

The system employed in this study comprises 6 × 1.5 MW DEIGs with a rated wind speed of 12 m/s, which are interconnected to the power grid. The generator’s output voltage is measured at 0.55 kV, and a step-up transformer is employed to elevate this voltage to 25 kV. A transmission line spanning a distance of 30 km is employed to establish a connection between the generator and the grid. The system is interconnected with the grid via 25/132 kV transformers, as seen in Figure 1, (Mosaad et al., 2020, 2022).

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Figure 1.

System description.

STATCOM control

The voltage level at POC will be impacted by any fault events, resulting in a deviation from the 1 pu value. The primary aim of implementing STATCOM at the POC is to efficiently regulate and sustain the voltage magnitude at this POC to a normalized value of 1 pu. In such cases, the regulated STACOM will inject/absorb the necessary reactive power to restore the voltage level back to 1 pu. The STATCOM consists of two converters, denoted as 1 and 2, which are interconnected via a DC-link. The initial converter, denoted as 1, is characterized by its lack of control and serves primarily to facilitate the transfer of power from the AC to the DC sides. The second converter, denoted as 2, is a controlled converter that comprises two layers of force-commutated gate turn-off thyristors (GTOs). This converter facilitates the transfer of electrical power from the DC link to the alternating current AC side. The STATCOM is regulated through the utilization of two controllers, namely Controller 1 and Controller 2, as shown in Figure 2.

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Figure 2.

Block diagrams of STATCOM.

The voltage magnitude at the POC will be influenced by any disturbance, which can be detected and mitigated by promptly injecting/absorbing the necessary amount of reactive power from the STATCOM. The regulation of reactive power exchange between the STATCOM and the system at the POC is achieved by manipulating the phase angle difference between the voltages at the STATCOM and the POC. The contribution of STATCOM during these disruptions, in conjunction with the operation of the two controllers, can be briefly stated as follows (Mosaad, 2018):

Figure 2 illustrates the block diagram representing the control mechanism for the STATCOM.

The controller proposed for the STSTCOM in this work is the MPC for both controller 1 and 2. A companion between the MPPC and the optimized PI controller will be elaborated.

Controller design

The optimized PI controller is widely employed in numerous applications, and the whale optimization technique has been proposed to tune the parameters of the PI controller. Following this, the use of adaptive controllers was implemented to tackle the inherent issues associated with the use of optimum PI controllers, as previously explained.

Whale optimization algorithm

WOA is utilized in this work to minimize an objective function J that represents the integral of the square of the error between the reference voltage (1 pu) and the measured voltage at the POT.

J = ∫ 0 t ( error _ v ( t ) 2 ) dt

(1)

Being one of the most intelligent creatures, WOA, a contemporary optimization approach, imitates whale behavior. Their brain cells have some similarities with human cells [Mosaad et al. (2021)]. When using such WOA, the solution begins by assuming random solutions for the four optimized parameters of both PI controllers, and the objective function J for that objective function, which was presented in (1) is established. In WOA, search agents are updated at each iteration location, and the goal function is chosen following this. The procedure is continued until the maximum number of iterations is reached, at which point the best answer is saved. Figure 3 depicts the WOA flow chart for adjusting PI control parameters to their ideal values. The WOA was presented for optimized the STATCOM in Mosaad et al. (2021).

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Figure 3.

Flow chart for WOA.

The process of WOA can be broken down into three distinct steps namely, surrounding prey whales, assaulting instruments of the WOA, and Hunting phase.

In the first step, surrounding prey whales, the humpback whales detect the location and then swim around the prey. The WOA computation predicts the current optimal value of the objective function as the solution that is near the best one. Once this solution has been identified, other search agents adjust their particular places to get the optimum arrangement. The mathematical representation of the process where whales surround their prey can be written as

F → = | B → . S P → ( i ) − S → ( i ) |

(2)

S → ( i + 1 ) = S P → ( i ) − G → . F →

(3)

where i represents the current iteration.

The vector coefficients F → and G → can be determined as:

B → = 2 r 2

(4)

G → = 2 g → . r 1 − g →

(5)

The value of G drops from 2 to 0, and the vector G → span the range of [ − g , → g → ] . The values of r₁ and r₂ are randomly generated within the range of 0–1.

Two techniques are defined in the second step: the shrinking encircling mechanism and the spiral updating position. The whale diminishing behavior is achieved by decreasing the magnitude of vector g. The second way relies on updating the position attitude and can be characterized as

S → ( i + 1 ) = T ' → . b el ( 2 π r ) + S P → ( i )

(6)

While pursuing, whales typically swim close to their prey, employing each of the aforementioned methods simultaneously. To update the positions of the whales, a chance of 50% is assigned to each of the two tactics, as stated in Kaymanesh et al. (2022)according to (3) and (6).

In the last step of Hunting, the searching step primarily depends on the variation of the vector. When humpback whales look for a spot, they randomly search for the best place among each other. To get an appropriate global location, the following steps are taken as:

T → = | DG → . S r a n d → − S → |

(7)

S → ( i + 1 ) = S r a n d → − G → . F →

(8)

Where S r a n d is a randomly chosen location vector of a whale from the present population. The flow chart of WOA for optimal tuning of PI controller parameters is shown in Figure 3.

Model predictive control design

The use of MPC methodologies has assumed a significant role in both theoretical frameworks and practical implementations within the field of control systems. The concept of MPC relies on the analysis of the system dynamics of the open-loop system and the characterization of the interdependencies among the system variables, including controlled variables (inputs), internal states, and measured variables (outputs). Expanding on the current observed or predicted states, an optimum control problem is addressed at each sample period in a receding horizon. The optimum problem is built using constraints, weights, beginning states, reference signals, and system dynamics (system model).Beginning with a future control signal prediction inside the prediction horizon or optimization window, which is specified as the number of samples N_p, is how MPC is designed. The vector of the changed variables, U, and the number of its values, N_c, have been used to derive the future control trajectory. Both in theory and in practice, MPC techniques now play a significant role in control systems. The idea of MPC is based on examining the open-loop system’s dynamics and describing the relationships between the system’s variables, which include controlled variables (inputs), internal states, and measured variables (outputs).

MPC has the capacity to forecast the plant’s reaction in the future, which sets it apart from conventional control algorithms. By using an online optimization technique that optimizes the tracking performance while taking into account specific limits, MPC makes an effort to forecast future plant behavior at each control interval. A simple block schematic of the MPC is shown in Figure 4.

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Figure 4.

Simple block diagram describing MPC: (a) MPC for controller A and (b) MPC for controller B.

The strategy that characterizes MPC can be described as follows:

In the initial step, a well-defined model is employed to forecast the output of a process over a certain period in the future. The estimated predicted outputs y ^ ( t + k ) , k = 1 , … , N for the prediction horizon are determined at each time instant t, taking into account the historical inputs and outputs, as well as the anticipated future control signal u ( t + k ) , k = 0 , … , N − 1 .

In the second step, a sequence of forthcoming control signals is calculated in order to enhance a performance measure through the minimization of a cost function. The cost function that is typically minimized consists of a weighted sum of the squared predicted errors and the squared future control values.

J ( N 1 , N 2 , N u ) = ∑ j = N 1 N 2 β ( j ) [ y ^ ( k + j ) − w ( k + j ) ] 2 + ∑ j = N 1 N u λ ( j ) [ u ( k + j − 1 ) ] 2

(9)

The weighting variables β(j) and λ(j) are utilized in this context, where N₁ and N₂ represent the lower and upper prediction horizons, respectively for the output. Additionally, N_u denotes the control horizon. The control horizon enables the reduction of the quantity of future control computations, as indicated by the equation. The equation Δu(k + j) = 0 is valid for j values more than or equal to N_u. In this context, w(k + j) represents the reference trajectory for the future horizon N. The cost function encompasses the constraints about the control signal, the change in the control signal, and the outputs can be presented as:

u min ≤ u ( k ) ≤ u max Δ u min ≤ Δ u ( k ) ≤ Δ u max y min ≤ y ( k ) ≤ y max

(10)

In the last step, the current control signal is allocated to the plant. In the subsequent time interval, the value is assessed, and the initial step is reiterated in accordance with the receding horizon technique to calculate. Consequently, at each successive interval, the horizon undergoes a displacement toward the future while retaining a consistent length. The tuning of MPC can be accomplished with relative ease, notwithstanding its effective handling of restrictions. Constraints can manifest either as limitations on the output of controlled processes, referred to as control variables, or as restrictions on the control signals that serve as inputs to the process, known as manipulated variables. The limitations manifest as saturation features, such as valves that possess a confined range of adjustment or control surfaces with restricted deflection angles. Rate constraints are another type of input constraint that can be observed in various systems. These constraints are typically associated with valves and other actuators, which have limitations on their maximum rates of operation.

Results and discussions

This study presents an adaptive controller for STATCOM, MPC, which is designed to achieve universal control of grid-connected DFIG in WE applications. Furthermore, this study presents a comparison between the MPC and optimized PI controllers for the STATCOM.

When considering several fault scenarios, such as a three-phase to ground fault at the POT, voltage sag or swell conditions of ±50%, and the ferroresonance, each fault exhibits a certain voltage level, as seen in Figure 7. The PI controller, which is widely used in many control applications, has substantial challenges in optimizing its parameters because of the different POT voltage levels corresponding to each fault event. In essence, when faced with faults events that differ from those for which the parameters were tuned, obtaining optimum performance becomes difficult. This constraint occurs due to the inherent restriction of the adjustment operation, which can only be performed for a singular kind of operating condition or fault event. This implies that the optimum PI controller parameters are computed individually for each fault event, so ensuring the optimal operation configuration specifically for this event. Nevertheless, if this controller is used in events or conditions other than the one it was initially optimized for, the attainment of optimal performance cannot be assured. Because voltage levels change based on the kind of problem, an ideal PI controller’s setting must be updated often, which is challenging to execute.

The problems associated with using an optimized PI controller for STATCOM will be investigated through different fault events: three-phase to ground fault at POT, ±50% voltage sag/swell conditions, and ferroresonance. The ferroresonance is simulated in this work by opening a single pole of the transmission line that connects the WECS to the grid, as shown in Figure 1. Without using STATCOM, the three-phase to ground fault, ferroresonance, and swelling conditions, the system will be disconnected from the grid as per the US LVRT and HVRT codes as illustrated in Figure 5.

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Figure 5.

POT voltage at different faults without STATCOM.

The WOA is used to determine the optimal PI controller parameters that drive the STATCOM to keep the voltage level at POT at 1 pu at different faulty conditions and consequently improve the system efficacy. The convergence of the WOA and the optimized controller parameters for three-phase fault at POT, 50% voltage sag/swell conditions are shown in Figure 6 and Table 1, respectively. The determination of the optimal settings for each group (four PI controllers) in Table 1 is based on specific fault condition situations. Group A is designed for three-phase faults, while groups B and C are tailored for 50% voltage sag and swell conditions, respectively. To further expound upon the limitations of the optimized proportional-integral (PI) controller in its ability to update and modify itself to handle faults beyond those it was initially designed for, many fault scenarios will be described.

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Figure 6.

Convergence of the objective function at different fault cases.

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Table 1.

Optimized PI controller parameters at different faulty cases.

Fault	Group	KP_A	KI_A	KP_B	KI_A
Three-phase SC	A	0.95	1.05	2.3	6.5
50% voltage sag	B	1.25	6.7	3.6	2.8
50% voltage swell	C	512.5	3.4	5.6	8.7

Assessment of the optimized PI controller for STATCOM under different faulty operating conditions

Initially, the parameters of the two PI controllers associated with the STATCOM will be employed to regulate the operation of the STATCOM during a three-phase fault occurrence. These parameters encompass the values pertaining to all groups, namely Group A, Group B, and Group C. Notably, group A is tuned at the same fault condition, a three-phase fault while groups B and C are tuned at 50% voltage sag and swell, respectively. The objective of this case is to assess the performance of the tuned PI controller parameters for groups B and C (at sag and swell conditions), in the event of a three-phase fault.

The POT voltage without incorporating STATCOM at a three-phase fault between 1 and 1.25 seconds ranges outside the US code that will call for disconnecting the generator from the system as shown in Figure 7.

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Figure 7.

Three-phase fault with and without STATCOM with different PI controller parameters.

An improved POC voltage profile was obtained by using the STATCOM in conjunction with the optimized PI controller and the values of the three groups A, B, and C independently. This improvement ensured that the voltage remained within the US code range, hence preventing the generator from experiencing disconnection during a three-phase fault scenario as shown in Figure 10. The results indicated that the controller settings from group A yielded the most favorable voltage profile, despite the fact that the other two groups (B and C) also showed improvements in the POT voltage profile.

The effectiveness of the tuned PI controller with the three groups of controller parameters (A, B, and C) will be evaluated once more separately in the presence of voltage sag and swell scenarios. The best POT voltage profile was achieved by using the parameters from group B for voltage sag situations and group C for voltage swell conditions, as seen in Figure 8(a) and (b), respectively. This indicates that the most outstanding performance is obtained when utilizing the parameters that are adjusted at the same conditions.

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Figure 8.

50% voltage sag and swell with STATCOM and different PI controller parameters: (a) sag and (b) swell.

In the context of voltage swell events, the utilization of parameters derived from groups A and B resulted in subpar performance compared to the utilization of parameters from group C. Furthermore, these parameters were unable to sustain the operation of the generator due to the voltage exceeding the designated continuous operating range, US HVRT as depicted in Figure 8(b).

Based on the analysis of these test cases and subsequent discussions, it is recommended that the parameters of the PI controller for the STATCOM be modified for each fault occurrence. This adjustment is necessary to guarantee that the controlled STATCOM runs following the grid codes, exhibiting improved performance and effectively handling various fault events. The returning process of the PI controller parameters is not appropriate in this context due to the need for offline execution and the considerable amount of time needed for tuning. In order to address these challenges, it is recommended to include an adaptive controller in the STATCOM system. This addition will enable the system to achieve universal control of the WE system while maintaining optimum or near-optimal performance in the presence of various fault conditions. This study introduces a MPC approach as the adaptive control technique for the STATCOM.

Three-phase fault

The proposed MPC capacity to activate the two controllers of the STATCOM and hence enhance the performance of the WE system is tested using the same three-phase to-ground failure simulation as in the previous section. The MPC and WOA-PI controllers, whose settings were optimally tuned this fault (group A), are compared.

The voltage profile at the POT is plotted for the MPC and WOA-PI controller for the STATCOM, Figure 9(a). It is clear that both controllers result in improved voltage with better performance of the MPC in terms of maximum overshoot and settling time. It is noteworthy that both controllers could keep the POT voltage levels during this fault within the continuous operating zone as per the US-LVRT code. This means that the generator will be in service during this fault.

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Figure 9.

System performance at three-phase fault with MPC for STATCOM: (a) voltage at POT, (b) rotor speed, (c) WE current, (d) DFIG power, and (e) DFIG electromagnetic torque.

The generator speed increased largely without integrating the STATCOM to the system to higher levels, which may cause damage of the generator shaft if it is not disconnected. Both MPC and WOA-PI controllers (group A) could enhance the speed profile and keep the speed in an acceptable range to keep the connection of the generator to the system as depicted in Figure 9(b). The MPC surplus the optimized PI controller for the rotor speed profile. The WECS current without using STATCOM increases to nearly 4.5 times the rated value that will call the protection devices to disconnect the WESC from the network with its complex consequences and procedures for reconnection. Adding the STATCOM to the system, the current profile is improved and reaches 1.5 and 1.75 times the rated current when applying MPC and PI controllers, respectively, as illustrated in Figure 9(c).

During this three-phase short circuit fault, the generator switches to motor mode without using the STATCOM. This can be observed in the DFIG power and electromagnetic torque profiles displayed in Figure 9(d) and (e) accordingly. It is important to note that for the DFIG to maintain stability during disturbance events, the synchronizing and damping components of the electromagnetic torque must be suitably large. The utilization of STATCOM, in conjunction with an improved PI controller (Group A) and MPC, enables effective dampening of both the DIG power and electromechanical torque.

50% voltage sag

This test case aims to examine the efficacy of the MPC approach for the STATCOM under a voltage sag condition of 50%. Furthermore, a comparison will be conducted between the MPC and the WOA-PI controller (group B). Figure 10(a) to (c) depict the voltage of the POT, the current of the WE system, and the speed profiles, respectively. Both controllers showed an improvement in system performance and were capable of maintaining the generator’s operational status amidst the occurrence of this sag condition.

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Figure 10.

System performance at 50% voltage sags with MPC for STATCOM: (a) voltage at POT, (b) rotor speed, and (c) WECS current.

Ferroresonance faults

In this case, the efficacy of the MPC will be assessed by simulating a ferroresonance event. Moreover, considering that the PI controllers in the experiment were not optimally tuned, a comparative assessment will be conducted to compare the performance of the MPC and the PI controllers using parameters from distinct groups (A, B, and C).

In the absence of a STATCOM, the POT voltage increased to values above 1.8 pu, resulting in the disconnection of the WE system from the grid, as seen in Figure 11(a). When using the PI controller parameters that were tuned during the occurrence of a three-phase fault (Group A), the voltage levels also exceed the limits specified in the US-HVRT code, leading to the disconnection of the generator from the grid. This implies that the PI controller is unable to ensure the proper functioning of the system during various fault occurrences. The voltage profile has been enhanced and remains within acceptable limits for grid connection throughout the ferroresonance event, using the PI controller settings established at 50% voltage swell (Group C) and MPC. The performance advantage of MPC over the WOA-PI controller is seen in the context of the STATCOM.

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Figure 11.

System performance at ferroresonance with and without STATCOM: (a) POT voltage at ferroresonance without and with controlled STATCOM and (b) the wind speed profile.

The speed of the generator rotor exhibited a significant rise, reaching high values, accompanied by substantial oscillations that have the potential to cause damage to the shaft without STATCOM, as seen in Figure 12(a). The implementation of MPC and PI controllers, specifically in the context of Group C, in the STATCOM leads to an enhanced generator rotor speed profile. This improvement is evident in Figure 12(b), where a decrease in overshoot and oscillations can be observed. The performance of the MPC surpasses that of the optimized PI controller.

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Figure 12.

STATCOM and WECS currents: (a) WECS current without STATCOM, (b) WECS current with STATCOM, MPC, and (c) STATCOM current.

Opening a single pole of the line connecting the WE system to the grid (ferroresonance) will increase the current of the two phases. Conversely, no current will flow through the phase that has been disconnected, as seen in Figure 12(a). This fault may necessitate the disconnection of the generator from the system. By incorporating the MPC-STACOM into the system, the electrical current is restored.

Conclusions

The parameters of the PI controller are determined based on specific operating conditions and may not be suitable or dependable to use under different operating situations. This work explores the application of an optimized PI controller utilizing WOA for achieving universal control of STATCOM in a DFIG-WE system. The results indicated that the optimized PI controller for STATCOM was not universally adaptable for control purposes. The resolution for this problem involves implementing the adaptive controller technique. This work successfully applies MPC to achieve universal control of STATCOM in a DFIG-WE system. This technique can effectively mitigate various fault events, regardless of the voltage level, whether it increases or decreases. This MPC has the capability to control the STATCOM to mitigate three-phase faults, sag/swell events, and ferroresonance. This particular MPC supports FRT, LVRT, and HVRT capabilities, and mitigates ferroresonance consequences.