# STATCOM Controller Tuning to Enhance LVRT Capability of Grid-Connected Wind Power Generating Plants

Authors: Irene Ndunge Muisyo; Christopher Maina Muriithi; Stanley Irungu Kamau
Journal: Journal of Electrical and Computer Engineering
 (2022)

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## Abstract

This paper investigates the utilization of a STATCOM to enhance the LVRT capability of wind power plants (WPPs) during grid faults. The STATCOM under investigation is tuned using the Water Cycle Algorithm (WCA), Particle Swarm Optimization (PSO), and a hybrid algorithm of both WCA and PSO. Simulations are conducted in MATLAB programming software, using the SimScape power system toolbox, where two test systems are investigated: a 9 MW WPP and the IEEE 39 bus test system. Performance analysis is done by investigating the ability of the WPPs to ride through grid voltage sags, with the incorporation of the STATCOM, independently tuned using WCA, PSO, and further with the hybrid WCA-PSO algorithm. To confirm the effectiveness of the proposed algorithm, simulation results for the three scenarios are compared. Results show that the LVRT capability of the German power system was met for L-G faults, for the 9 MW test system, whereas during LLL-G faults, the WPP only remained online for WCA and WCA-PSO tuned STATCOM. For the IEEE 39 bus system, the WPPs were able to ride through the LLL-G fault. In all scenarios, the WCA-PSO tuned STATCOM resulted in the least voltage, active, and reactive power overshoots.


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## Body

## 1. Introduction

Over the last three decades, the utilization of renewable energy resources has been on the rise. This is attributed to the depletion of fossil fuel reserves, increase in energy demand, and environmental concerns. Wind energy is among the fastest-growing renewable energy resources [1]. The installed capacity of wind power generation globally was 743 GW by the end of 2020, which represented about 26% of renewable energy generation. China and US remain the world’s largest onshore wind markets, together accounting for more than 60% of the new capacity in 2020 [2, 3]. Wind Energy Conversion Systems (WECSs) are either based on Fixed Speed Wind Turbines (FSWTs) or Variable Speed Wind Turbines (VSWTs). The FSWT configuration is simple but is unable to extract maximum power at varying wind speeds since its slip can only be varied over a small range. Most wind turbines today are based on the Variable Speed Wind Turbine (VSWT) technology, which utilizes power electronics to achieve improved efficiency and reduced mechanical stress for a wide range of wind speeds [4, 5].The most common VSWT is the Doubly Fed Induction Generator (DFIG), due to its advantages such as variable speed capability, independent active and reactive power control, lower converter cost, and lower active power losses [4, 5]. However, the DFIG is sensitive to grid faults since its stator is directly connected to the power system. During grid faults, the transient stator flux sets up a surge current in the rotor circuit which can destroy the Power Electronic Converter (PEC). Voltage dips at the Point of Common Coupling (PCC) also reduce the converter capability to transfer power to the grid, which leads to increased DC link capacitor voltage [6, 7]. The PEC is usually protected by a crowbar, which short-circuits the rotor once triggered by a fault. If the fault persists, the wind power generating plant is eventually disconnected from the grid [5, 6].Previously, wind farms were allowed to disconnect from grids during power system faults. With increasing levels of wind power injection into grids, disconnecting wind power generation during faults can negatively affect the stability of a power system [1]. Therefore, power system operators worldwide have revised their Grid Code Requirements (GCRs) to incorporate the Low Voltage Ride Through (LVRT) capability of wind farms. LVRT capability is the ability of power plants to remain connected to the grid for a specific period during grid voltage sag conditions [8, 9]. Various techniques have been proposed in the literature to improve the LVRT capability of DFIG-based WPPs. These techniques include the following:(i)
The use of a crowbar which provides an additional path for the rotor current, thus the DFIG stays connected to the grid [10, 11]. The crowbar can also be integrated with an R–L circuit to confine both the rotor inrush current and DC link overvoltage within their predefined threshold [12, 13].(ii)
A DC chopper connected in parallel with the PEC to dissipate excess power in the DC bus, protecting semiconductor switches from an overvoltage [12, 14].(iii)
Series Dynamic Braking Resistors (SDBRs) activated during fault conditions to limit the rotor current, thus avoiding DC link capacitor overvoltage [10, 12].(iv)
Fault Current Limiters (FCLs) used to regulate the terminal voltage by injecting resistance into a circuit, limiting fault current [10, 12].(v)
Flexible AC Transmission System (FACTS) devices such as Dynamic Voltage Restorer (DVR) [15, 16], Static VAr Compensator (SVC) [8], and Static Synchronous Compensator (STATCOM) [17, 18].Due to their reliability and fast response, FACTS devices are gaining popularity in their use to enhance the large-scale integration of renewable energy into grids. The DVR and STATCOM are the most utilized FACTS devices to enhance the performance of grid-connected WPPs. The DVR is seen to be robust; however, its rating should be the same as the rated output of the Wind Turbine Generator (WTG). Moreover, DVRs are expensive due to many ancillary components needed during installation [19, 20]. The STATCOM on the other hand can control output voltage independently of the AC system voltage, with a very fast response, and it is also easy to integrate into an existing power system [17, 18].The STATCOM controller is based on a Proportional Integral (PI) controller which provides a simple design structure at an affordable cost. STATCOM controller tuning can be done using conventional methods such as Ziegler-Nichols (Z-N) and graphical tuning, or by intelligent optimization algorithms such as fuzzy logic (FL) based control, Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) methods [21, 22]. With the advancement of artificial intelligence technologies, various optimization algorithms are increasingly being applied in controller parameter tuning and optimization. Intelligent optimization algorithms have merits of robustness and universality, but they also have challenges such as premature convergence or slow convergence rate [23].This paper investigates the LVRT capability of DFIG-based, grid-connected WPPs with STATCOM utilization. The STATCOM controller is independently tuned using three algorithms, namely, the Water Cycle Algorithm (WCA), Particle Swarm Optimization (PSO), and a hybrid algorithm of both WCA and PSO. The main contribution of this research is the simultaneous tuning of all three STATCOM controllers, using the newly proposed Water Cycle Algorithm (WCA) and the hybridization of WCA and PSO algorithms which has not been applied previously in the dynamic tuning of STATCOM controllers. From the literature, LVRT capability enhancement of the IEEE 39 bus test system with wind power generation has not been conducted before.The organization of the rest of this paper is as follows. Section2 presents Wind Energy Conversion Systems (WECS) operation, whereas in Section 3, the STATCOM operation and tuning are explained. Section 4 presents the test system and simulation results, while conclusions and recommendations are given in Section 5.


## 2. Wind Energy Conversion Systems (WECS)

Wind Energy Conversion Systems (WECSs) convert the kinetic energy in wind into mechanical energy, using wind turbine rotor blades. The mechanical power developed by a wind turbine depends on the wind velocity and air density [1], expressed as(1)Pm=12ρArvw3Cpλ,β,where ρ is the air density kg/m3, ArπR2 is the area swept by rotor blades (m2), vw is the wind speed (m/s), Cp is the power coefficient which is a function of Tip-Speed Ratio (TSR) λ, and the blade pitch angle (β) [6, 24]. The mechanical energy is then converted into electrical energy, which is fed to the grid. The Double Fed Induction Generator (DFIG) is investigated in this work, due to its advantages such as variable speed capability, independent active and reactive power control, lower converter cost, and lower active power losses [4, 5].


### 2.1. The Mathematical Modeling of DFIG

The DFIG has its stator directly connected to the grid, while its rotor is connected to the grid through a Power Electronic Converter (PEC), as shown in Figure1 [8].Figure 1
DFIG wind turbine [8].From Figure1, the Rotor Side Converter (RSC) controls active and reactive power flow from the stator to the grid while the Grid Side Converter (GSC) maintains the DC link voltage constant, thus controlling the grid current [6, 8]. The equivalent circuit of a DFIG in the d-q reference frame is shown in Figure 2.Figure 2
DFIG equivalent circuit [19].In Figure2, subscripts d and q indicate direct and quadrature axis components, while s and r indicate stator and rotor quantities, respectively [19]. The d and q stator and rotor flux components are given by(2)Ψsd=Lsisd+Lmird,Ψsq=Lsisq+Lmirq,Ψrd=Lmisd+Lrird,Ψrq=Lmisq+Lrirq,where Ls and Lr are the stator and rotor inductances, respectively, obtained using(3)Ls=Lsσ+Lm,Lr=Lrσ+Lm.Lsσ and Lrσ are the stator leakage and rotor self-inductances, respectively, and Lm is the mutual inductance [19, 25]. The dq stator and rotor voltages are(4)vsd=Rsisd+dΨsddt−ωeΨsq,vsq=Rsisq+dΨsqdt+ωeΨsd,vrd=Rrird+dΨrddt−ωe−ωrΨrq,vrq=Rrirq+dΨrqdt−ωe−ωrΨrd,where v and i denote voltage and current, respectively, R is the resistance Ω, Ψ is the flux linkage (Vs), ωe is the supply angular frequency (rad/sec), and ωr is the rotor angular frequency (rad/sec) [26, 27].During normal operating conditions with constant stator voltage (Vs), the stator flux linkage (Ψs) stays almost constant; therefore, dΨs/dt can be neglected. However, during voltage sags, Vs dips and Ψs decreases proportionally with the grid voltage. The magnitude of the natural component of Ψs depends on the amplitude of voltage dip, and during faults, it generates a large EMF in the rotor windings. Thus, the more severe the voltage dip, the higher the induced EMF, which results in an overcurrent in the rotor windings. This can damage the PEC. In addition, low voltage at the PCC reduces the capacity of the GSC to transfer active power to the grid. This leads to excess power in the DC link capacitor, resulting in increased DC link voltage [25, 28].Conventionally, the PEC is protected from rotor overcurrents using a crowbar, as shown in Figure1. The crowbar in Figure 1 consists of a set of switches usually implemented between the rotor circuit and the RSC to provide a bypass for the high transient rotor current during faults [27]. Once triggered by DC capacitor overvoltage or rotor overcurrent, the crowbar short-circuits the RSC; thus, control of active and reactive power is lost. During this period, the DFIG absorbs reactive power from the grid, which negatively affects voltage at the PCC. If the fault persists, the DFIG is finally disconnected from the grid. Disconnecting large WPPs during grid faults contributes to active power imbalance, which may lead to cascading outages [25, 27].


### 2.2. Grid Codes for Wind Power Plants

Many countries have recently revised their grid codes to address the challenges of increased penetration of large wind power generation in modern power systems. Grid codes refer to technical specifications which describe the standards a power generation plant connected to a grid must meet, to ensure the safe and secure operation of the power system [10, 27]. Grid Code Requirements (GCRs) for wind power generating plants define the specifications wind power plants must satisfy when connecting to a power system. GCRs consist of static and dynamic specifications. Wind power static GCRs confer the steady-state behavior of wind power generating plants. On the other hand, the desired wind power generating plant's behavior during grid faults is stated in the dynamic requirements. These dynamic requirements include active power regulation and frequency operating range, voltage variation limits, Fault Ride Through (FRT) requirements, and grid support capability. A detailed description of the grid connection requirements for WPPs has been given in [27].Power system operators have identified FRT capability during disturbances and reactive power control during steady-state conditions as the most important GCR in wind power integration into grids. FRT refers to the capability of wind power plants to remain connected to the grid during faults and provide reactive power support during such grid disturbances [14, 29]. FRT indicates the capability of large wind farms to stay connected to the grid for a brief period during faults. This ensures that for faults that can be cleared within a short duration, there is no loss of wind generation. FRT grid codes differ for each country based on the Transmission System Operator (TSO) requirements and grid strength. The minimum immunity of wind power plants to voltage fluctuations is denoted by voltage versus time characteristic curves, describing FRT requirements [19, 30].FRT capability has two aspects i.e., High Voltage Ride Through (HVRT) during voltage swells, and Low Voltage Ride Through (LVRT) during voltage sags [19, 29]. Voltage sags are the most common in power system faults; hence, LVRT capability is the most significant GCR for wind power generation. Voltage sags result from a sudden loss of large generating units, switching in large loads such as induction motors, energizing of transformers, and system faults [14, 29]. Recently, some countries have also included voltage-time profiles for conditions of swells in voltage in the grid codes. This requirement is referred to as the High Voltage Ride Through (HVRT) capability. Voltage swells result from single-phase short-term interruptions, reactive power overcompensation from capacitor banks, lightning strikes, or switching off large loads such as in response to voltage sag [30]. Since voltage sags are more frequent than swells, the LVRT capability of grid-connected wind power generating plants will be investigated in this work.


### 2.3. Review of Grid Code Requirements for LVRT of Wind Farms

Low Voltage Ride Through (LVRT) capability is demonstrated by profiles of voltage and time duration for which a generator must stay connected or disconnected from the grid based on a reduction in the voltage levels during faults. LVRT characteristics for various countries are shown in Figure3 [19].Figure 3
LVRT capability requirements for various countries [19].From Figure3, grid-connected WPPs must stay in operation if the voltage at the PCC remains above the solid line [15, 19]. From Figure 3, for instance, all wind farms connected to the German electric utility must withstand voltage dips up to 0% of nominal voltage at the PCC, for a duration of 150 ms. When the fault is cleared, the voltage at the PCC should recover to 0.9 p.u. within 1500 ms. To satisfy the Denmark grid code requirement, the WPP should remain connected for 100 ms when the terminal voltage drops to 20% of the nominal level, while the generator voltage should recover to 75% of the nominal level within about 700 ms. A summary of LVRT capability requirements for various countries is given in Table 1 [18, 31].Table 1
LVRT capability requirements for various countries.
S. No.CountryVoltage levelLVRT capabilityFault duration (ms)Voltage drop level (%)Recovery time (s)1.DenmarkDS/TS1002512.IrelandDS/TS6251533.GermanyDS/TS15001.54.Great BritainDS/TS140151.25.SpainTS5002016.Italy>35 kV500200.37.United StatesTS625152.38.OntarioTS6251539.QuebecTS15000.18DS: Distribution System, TS: Transmission System [31].In the literature, several methods are being investigated for LVRT capability enhancement of DFIG-based WPPs. These methods can be broadly classified into protection circuit-based or reactive power injection-based LVRT schemes [13]. Protection circuits (crowbars, SDBRs, DC choppers, and FCLs) are applied to limit the rotor overcurrent and undesirable DC link overvoltage during grid disturbance. On the other hand, reactive power injecting devices inject or absorb reactive power, thus improving the transient performance of the DFIG-based WT. Reactive power injection schemes vary from simple techniques such as fixed capacitor/inductor to power electronic-based compensating devices [32].With the ongoing advancement of power electronics, Flexible AC Transmission System (FACTS) devices are increasingly being adopted in modern power systems. FACTS devices consist of power electronic and static controllers which can be used to enhance controllability and increase power transfer capability in power systems. Depending on the desired compensation, FACTS devices can be connected in series such as the Dynamic Voltage Restorer (DVR) [10, 20], and the Static Synchronous Series Compensator (SSSC) [21], in shunt such as the Static Synchronous Compensator (STATCOM) [26, 33], or a combination of series and shunt such as Unified Power Flow Controller (UPFC) [21]. The Dynamic Voltage Restorer (DVR) and Static Synchronous Compensator (STATCOM) are the most utilized FACTS devices in enhancing the performance of grid-connected WPPs [10, 13]. The DVR and STATCOM are Voltage Source Converter (VSC) based FACTS devices which can independently exchange active and reactive power with a grid. In this work, the STATCOM is investigated for enhancement of the LVRT capability of WPPs. The following section presents STATCOM operation and control.


## 2.1. The Mathematical Modeling of DFIG

The DFIG has its stator directly connected to the grid, while its rotor is connected to the grid through a Power Electronic Converter (PEC), as shown in Figure1 [8].Figure 1
DFIG wind turbine [8].From Figure1, the Rotor Side Converter (RSC) controls active and reactive power flow from the stator to the grid while the Grid Side Converter (GSC) maintains the DC link voltage constant, thus controlling the grid current [6, 8]. The equivalent circuit of a DFIG in the d-q reference frame is shown in Figure 2.Figure 2
DFIG equivalent circuit [19].In Figure2, subscripts d and q indicate direct and quadrature axis components, while s and r indicate stator and rotor quantities, respectively [19]. The d and q stator and rotor flux components are given by(2)Ψsd=Lsisd+Lmird,Ψsq=Lsisq+Lmirq,Ψrd=Lmisd+Lrird,Ψrq=Lmisq+Lrirq,where Ls and Lr are the stator and rotor inductances, respectively, obtained using(3)Ls=Lsσ+Lm,Lr=Lrσ+Lm.Lsσ and Lrσ are the stator leakage and rotor self-inductances, respectively, and Lm is the mutual inductance [19, 25]. The dq stator and rotor voltages are(4)vsd=Rsisd+dΨsddt−ωeΨsq,vsq=Rsisq+dΨsqdt+ωeΨsd,vrd=Rrird+dΨrddt−ωe−ωrΨrq,vrq=Rrirq+dΨrqdt−ωe−ωrΨrd,where v and i denote voltage and current, respectively, R is the resistance Ω, Ψ is the flux linkage (Vs), ωe is the supply angular frequency (rad/sec), and ωr is the rotor angular frequency (rad/sec) [26, 27].During normal operating conditions with constant stator voltage (Vs), the stator flux linkage (Ψs) stays almost constant; therefore, dΨs/dt can be neglected. However, during voltage sags, Vs dips and Ψs decreases proportionally with the grid voltage. The magnitude of the natural component of Ψs depends on the amplitude of voltage dip, and during faults, it generates a large EMF in the rotor windings. Thus, the more severe the voltage dip, the higher the induced EMF, which results in an overcurrent in the rotor windings. This can damage the PEC. In addition, low voltage at the PCC reduces the capacity of the GSC to transfer active power to the grid. This leads to excess power in the DC link capacitor, resulting in increased DC link voltage [25, 28].Conventionally, the PEC is protected from rotor overcurrents using a crowbar, as shown in Figure1. The crowbar in Figure 1 consists of a set of switches usually implemented between the rotor circuit and the RSC to provide a bypass for the high transient rotor current during faults [27]. Once triggered by DC capacitor overvoltage or rotor overcurrent, the crowbar short-circuits the RSC; thus, control of active and reactive power is lost. During this period, the DFIG absorbs reactive power from the grid, which negatively affects voltage at the PCC. If the fault persists, the DFIG is finally disconnected from the grid. Disconnecting large WPPs during grid faults contributes to active power imbalance, which may lead to cascading outages [25, 27].


## 2.2. Grid Codes for Wind Power Plants

Many countries have recently revised their grid codes to address the challenges of increased penetration of large wind power generation in modern power systems. Grid codes refer to technical specifications which describe the standards a power generation plant connected to a grid must meet, to ensure the safe and secure operation of the power system [10, 27]. Grid Code Requirements (GCRs) for wind power generating plants define the specifications wind power plants must satisfy when connecting to a power system. GCRs consist of static and dynamic specifications. Wind power static GCRs confer the steady-state behavior of wind power generating plants. On the other hand, the desired wind power generating plant's behavior during grid faults is stated in the dynamic requirements. These dynamic requirements include active power regulation and frequency operating range, voltage variation limits, Fault Ride Through (FRT) requirements, and grid support capability. A detailed description of the grid connection requirements for WPPs has been given in [27].Power system operators have identified FRT capability during disturbances and reactive power control during steady-state conditions as the most important GCR in wind power integration into grids. FRT refers to the capability of wind power plants to remain connected to the grid during faults and provide reactive power support during such grid disturbances [14, 29]. FRT indicates the capability of large wind farms to stay connected to the grid for a brief period during faults. This ensures that for faults that can be cleared within a short duration, there is no loss of wind generation. FRT grid codes differ for each country based on the Transmission System Operator (TSO) requirements and grid strength. The minimum immunity of wind power plants to voltage fluctuations is denoted by voltage versus time characteristic curves, describing FRT requirements [19, 30].FRT capability has two aspects i.e., High Voltage Ride Through (HVRT) during voltage swells, and Low Voltage Ride Through (LVRT) during voltage sags [19, 29]. Voltage sags are the most common in power system faults; hence, LVRT capability is the most significant GCR for wind power generation. Voltage sags result from a sudden loss of large generating units, switching in large loads such as induction motors, energizing of transformers, and system faults [14, 29]. Recently, some countries have also included voltage-time profiles for conditions of swells in voltage in the grid codes. This requirement is referred to as the High Voltage Ride Through (HVRT) capability. Voltage swells result from single-phase short-term interruptions, reactive power overcompensation from capacitor banks, lightning strikes, or switching off large loads such as in response to voltage sag [30]. Since voltage sags are more frequent than swells, the LVRT capability of grid-connected wind power generating plants will be investigated in this work.


## 2.3. Review of Grid Code Requirements for LVRT of Wind Farms

Low Voltage Ride Through (LVRT) capability is demonstrated by profiles of voltage and time duration for which a generator must stay connected or disconnected from the grid based on a reduction in the voltage levels during faults. LVRT characteristics for various countries are shown in Figure3 [19].Figure 3
LVRT capability requirements for various countries [19].From Figure3, grid-connected WPPs must stay in operation if the voltage at the PCC remains above the solid line [15, 19]. From Figure 3, for instance, all wind farms connected to the German electric utility must withstand voltage dips up to 0% of nominal voltage at the PCC, for a duration of 150 ms. When the fault is cleared, the voltage at the PCC should recover to 0.9 p.u. within 1500 ms. To satisfy the Denmark grid code requirement, the WPP should remain connected for 100 ms when the terminal voltage drops to 20% of the nominal level, while the generator voltage should recover to 75% of the nominal level within about 700 ms. A summary of LVRT capability requirements for various countries is given in Table 1 [18, 31].Table 1
LVRT capability requirements for various countries.
S. No.CountryVoltage levelLVRT capabilityFault duration (ms)Voltage drop level (%)Recovery time (s)1.DenmarkDS/TS1002512.IrelandDS/TS6251533.GermanyDS/TS15001.54.Great BritainDS/TS140151.25.SpainTS5002016.Italy>35 kV500200.37.United StatesTS625152.38.OntarioTS6251539.QuebecTS15000.18DS: Distribution System, TS: Transmission System [31].In the literature, several methods are being investigated for LVRT capability enhancement of DFIG-based WPPs. These methods can be broadly classified into protection circuit-based or reactive power injection-based LVRT schemes [13]. Protection circuits (crowbars, SDBRs, DC choppers, and FCLs) are applied to limit the rotor overcurrent and undesirable DC link overvoltage during grid disturbance. On the other hand, reactive power injecting devices inject or absorb reactive power, thus improving the transient performance of the DFIG-based WT. Reactive power injection schemes vary from simple techniques such as fixed capacitor/inductor to power electronic-based compensating devices [32].With the ongoing advancement of power electronics, Flexible AC Transmission System (FACTS) devices are increasingly being adopted in modern power systems. FACTS devices consist of power electronic and static controllers which can be used to enhance controllability and increase power transfer capability in power systems. Depending on the desired compensation, FACTS devices can be connected in series such as the Dynamic Voltage Restorer (DVR) [10, 20], and the Static Synchronous Series Compensator (SSSC) [21], in shunt such as the Static Synchronous Compensator (STATCOM) [26, 33], or a combination of series and shunt such as Unified Power Flow Controller (UPFC) [21]. The Dynamic Voltage Restorer (DVR) and Static Synchronous Compensator (STATCOM) are the most utilized FACTS devices in enhancing the performance of grid-connected WPPs [10, 13]. The DVR and STATCOM are Voltage Source Converter (VSC) based FACTS devices which can independently exchange active and reactive power with a grid. In this work, the STATCOM is investigated for enhancement of the LVRT capability of WPPs. The following section presents STATCOM operation and control.


## 3. STATCOM Operation and Control

The STATCOM is a shunt FACTS device used to inject or absorb reactive power to a specified bus. It comprises a Voltage Source Inverter (VSI), DC source, and a coupling transformer, connected in shunt with the AC system [33], as shown in Figure 4.Figure 4
Equivalent circuit of the STATCOM [33].The VSI is the heart of a STATCOM consisting of self-commutating power electronic devices (GTO or IGBT), together with a reverse blocking diode in parallel. From Figure4, Vg is the bus voltage, Vst is the VSI voltage, P is the active power of the VSI, and Q is the reactive power of the VSI [33, 34]. The DC input voltage from the capacitor is converted into a set of controllable three-phase AC output voltages by the VSI. Thus, the fundamental component of Vst is proportional to Vdc. VSI controller operation starts with a measurement system which obtains DC capacitor voltage Vdc, STATCOM reactive current Iabc, and bus line voltage Vg,abc [28, 35], as shown in Figure 5.Figure 5
STATCOM control scheme [35].From Figure5, the Phase Locked Loop (PLL) system generates synchronizing signals (θPLL) for abc/dq transformation of Vg,abc and Iabc. In the voltage regulator loop, the actual PCC bus voltage (Vg) is compared with the reference value (Vref) and the difference is applied to the PI controller to generate the reference reactive current (Iq_ref). The current regulation loop compares injected or absorbed reactive current (Iq) with the reference value (Iq_ref) to produce the desired phase angle α. α is the phase shift of STATCOM voltage (Vst) with respect to the grid voltage (Vg). The positive and negative voltages of the DC capacitor are maintained equal using offset (Δα) from the DC voltage regulator [28, 35].The STATCOM control circuit uses zigzag transformers to filter all odd harmonics up to the 45th. The star/delta transformer cancels out5+12n5,17,29,41,.. and 7+12n7,19,31,43,.. harmonics. There is also a 150 phase shift between the two transformers, with the star side leading by 7.50 and the delta side lagging by 7.50, a shift that allows cancellation of 11+24n11,35,., and 13+24n13,37,. harmonics. All 3n harmonics are not transmitted by the transformers because of the delta and ungrounded star connection. The 23rd and 25th harmonics can also be minimized by adjusting the conduction angle (σ) to 172.501800−7.50. Thus, the first significant harmonics generated by the inverter will be 47th and 49th; an almost pure sine wave output is achieved [35, 36]. The switching pulses control the magnitude and phase of the VSI output voltage. The three regulators (voltage regulator, current regulator, and DC link voltage regulator) are based on a Proportional Integral (PI) controller [28, 35]. Their outputs are given by(5)Iqref=Vref−VgKP+KIs,α=Iqref−IqKP+KIs,Δα=Vdc2−Vdc1KP+KIs.The procedure of obtainingKp and KI which would result in the desired performance is called tuning. Controller tuning can be done using conventional methods such as Ziegler-Nichols (Z-N), pole placement, and graphical tuning or by intelligent optimization algorithms such as fuzzy logic (FL) based control, Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), among other methods [18, 34]. Intelligent optimization algorithms are increasingly being applied in controller parameter tuning and optimization. These algorithms have merits of robustness and universality, but they also have challenges such as premature convergence or slow convergence rate [22, 23].From the literature review, STATCOM controller tuning using intelligent optimization algorithms has not been investigated broadly. Rashad et al. in [17] use Artificial Neural Networks (ANNs) to tune a STATCOM, to improve the performance of a wind power plant during symmetrical faults. The performance of the wind farm with a STATCOM tuned by ANN was compared with that of a STATCOM tuned by the Multiobjective Genetic Algorithm (MOGA) and Whale Optimization Algorithm (WOA). From the results, ANN tuned STATCOM gave a better voltage profile for the wind farm during three-phase faults. The active power output of the wind farm with ANN tuned STATCOM was also greater than when the other two algorithms were used.Kamel et al. in [18] investigate the ability of a STATCOM to enhance the FRT capability of DFIG wind turbines. STATCOM PI regulators were tuned using classical methods, fuzzy logic, PSO, Ant Colony Optimization (ACO), and the hybrid PSO-ACO. It was seen that the fuzzy control method and metaheuristic methods (PSO, ACO, PSO-ACO) resulted in a better dynamic performance for the STATCOM as compared to the classical tuning method. The authors observe that the hybrid PSO-ACO method was able to obtain proper gains for the STATCOM in a short time, and the method can be exploited to realize the dynamic behavior needed in FACTS devices.Boulaoutaq et al. in [37] propose a scheme based on Active Disturbance Rejection Control (ADRC) strategy for a DFIG-based WT integrated with DVR. The DVR is connected in series with the DFIG output terminal and the utility grid to compensate for grid voltage disturbances, thus meeting LVRT requirements. The control scheme for DVR was designed using ADRC nonlinear control strategy. LVRT performance is investigated under a symmetrical voltage sag of 35% of the rated voltage which lasts for 150 ms. It is seen that the DVR controlled by the ADRC strategy effectively prevents the DFIG-based WT from experiencing transient voltages and currents and subsequently stays connected to the grid during the 35% voltage sag. Thus, a DVR controlled by the ADRC strategy can greatly enhance the LVRT capability of the DFIG-based WT under symmetrical voltage sag conditions. Despite its cost, DVR is highly recommended for already installed DFIG-WTs that do not have sufficient FRT capability.Bakir and Kulaksiz in [34] model a Solar PV-Wind Hybrid Microgrid and incorporate a Genetic Algorithm (GA) tuned STATCOM to increase the system voltage stability. With the conventional controller, voltage fluctuation between ±10% is observed, as opposed to by ±8% witnessed when GA is used.From the sample of ongoing research work, dynamic tuning of FACTS devices can be investigated for LVRT capability enhancement of WPPs. Little has been done on the dynamic tuning of STATCOM for LVRT enhancement of grid-connected WPPs. In this work, the Water Cycle Algorithm (WCA), Particle Swarm Optimization (PSO), and their hybrid technique WCA-PSO will be independently used to tune the three PI STATCOM regulators.


### 3.1. Problem Formulation

STATCOM controller tuning was converted to an optimization problem, with the aim of minimizing the error between the reference and measured values. Time domain integral error functions can be used as objective functions for metaheuristic optimization techniques. These include Integral of Squared Error (ISE), Integral of Absolute Error (IAE), and Integral of Time Absolute Error (ITAE) [18]. Control systems based on the ITAE function integrate the absolute error multiplied by time over a given period. Errors that exist for a long time are weighted more than those at the start of the response, which can reduce the settling time of the system.When optimizing the ITAE function, settling time and overshoots are reduced faster than IAE and ISE tuning methods. The ITAE index is emerging as a powerful optimization objective function in heuristic optimization techniques. The only drawback is that the first response might be slow [38, 39].The optimization problem was stated as follows:Minimize(6)JX=∫0TVref−Vgtdt+∫0TIqref−Iqtdt+∫0TVdc2−Vdc1tdtsubject to(7)Kmin≤K≤Kmax,where X=KP1,KI1,KP2,KI2,KP3,KI3, T is the time range of the simulation, and t is the discrete solver step time (50μs). The constraints were obtained from a conventional STATCOM as given in Table 2.Table 2
STATCOM PI gain constraints [35].
PI controllerConstraintsAC PI voltage regulator5≤KP1≤20,1000≤KI1≤2000AC PI current regulator0.3≤KP2≤10,10≤KI2≤20DC PI voltage regulator0.0001≤KP3≤1,0.02≤KI3≤1The optimization algorithms minimize the total ITAE error value and return the final objective function value and the corresponding six gains at the optimal output. STATCOM controller gains were evaluated using the algorithms independently, and a performance comparison was done. The WCA, PSO, and WCA-PSO algorithms are described in the following sections.


### 3.2. Water Cycle Algorithm (WCA)

The Water Cycle Algorithm (WCA) is a metaheuristic optimization algorithm inspired by the water cycle process. The algorithm is based on how rivers are created and how water travels to the sea. It was proposed by Hasanien and Matar in 2012 [40]. At the start of the WCA, an initial population of raindrops (Np) is generated. The cost function of each raindrop is evaluated using (6), and the costs are sorted in ascending order. The best raindrops (Nsr) are assigned to a number of rivers (Nr) and one sea, i.e.,(8)Nsr=Nr+1︸sea.In the optimization problem, the sea position is the optimal solution. The remaining population,Nst, includes streams that can flow to the rivers or directly to the sea, given by(9)Nst=Np−Nsr.Streams are allocated to rivers or the sea, based on the flow intensity of raindrops given by(10)NSn=roundCn∑i=1NsrCixNst,n=1,2,…,Nsr,where NSn is the number of streams flowing into certain rivers and seas [41, 42]. Streams move toward rivers and rivers toward the sea. Updated positions for the streams and rivers are given by(11)Xstreami+1=Xstreami+randxCxXriveri−Xstreami,Xriveri+1=Xriveri+randxCxXseai−Xriveri,where rand ∈01 and C is greater than 1. Costs of the new positions are evaluated again, and if the stream cost is less than the river cost, their positions are exchanged. If the cost of a river is less than that of the sea, their positions are exchanged. To avoid premature convergence, evaporation is conducted. We check whether the river or stream is sufficiently close to the sea to enable evaporation. Raining and evaporation are conducted if(12)Xseai−Xriveri<dmax,where i=1,2,…,Nsr−1 and dmax is a small number, updated as(13)dmaxi+1=dmaxi−dmaximax_iter,where i=1,2,…,max_iter. The optimization algorithm will continue with the search process until termination criteria are met. Raindrops at the optimal solution correspond to the optimal PI parameters [42, 43]. A flowchart of the WCA is given in Figure 6.Figure 6
Water Cycle Algorithm flowchart [42].The parameters used in WCA optimization in this work are given in Table3.Table 3
WCA parameters [43].
Parameter nameVariableValueNo. of variablesNvars6Population sizeNp50No. of rivers + seaNsr4Evaporation condition constantdmax10–16Maximum no. of iterationsMax_iter100The WCA has been observed to be efficient and simple compared to other methods. It has also shown superior performance in terms of convergence, computation, and precision [40, 43].


### 3.3. Particle Swarm Optimization (PSO)

Particle Swarm Optimization (PSO) algorithm is a biologically inspired computational search and optimization method developed in 1995 by Eberhart and Kennedy. The algorithm simulates the behavior of birds or fish when looking for the place with the most adequate food. The PSO algorithm starts by randomly generating particles in the search space. Next, the fitness value of each particle is evaluated, and the position corresponding to the best fitness value is called the local best position. The local best of all particles is compared and the best position in the swarm is defined as the global best. At every iteration, the termination criteria are checked, and if not met, an update of the velocity and position of all particles is done [44]. The velocity of particles is given by(14)Vk+1i=wVki+C1r1Pki−Xki+C2r2Pkg−Xkiwhile the position of individual particles is updated by(15)Xk+1i=Xki+Vk+1i,where Xki is the particle position, Vki is the particle velocity, Pki is the individual particle best position, Pkg is the swarm best position, w is the weight inertia used to ensure convergence, C1 and C2 are the cognitive and social parameters, and r1 and r2 are random numbers between 0 and 1 [45]. The flowchart of the PSO algorithm is shown in Figure 7.Figure 7
PSO flowchart [45].The PSO parameters used in this work are given in Table4.Table 4
PSO parameters [45].
Parameter nameVariableValuePopulation sizeNP100Maximum number of iterationsMax_iter100No. Of variablesNvars6Minimum inertia weightwmin0.4Maximum inertia weightwmax0.9Cognitive componentC11.4Social componentC21.4Random numbersr1,r2U (0,1)The PSO algorithm has been gaining popularity due to its simple structure and efficiency. Additionally, it outperforms gradient-based optimization methods which require the optimization problem to be differentiable. However, the PSO algorithm can result in suboptimal solutions in the event a particle gets stuck in a local optimum [46, 47].


### 3.4. WCA-PSO Hybridization

The WCA was hybridized with PSO to take advantage of the strengths of each algorithm. In this hybrid, the WCA first explores the search place to identify the most promising region, thus ruling out the challenge encountered by the PSO of particles being stuck in a local optimum. Next, starting with the solution obtained by WCA, the PSO is introduced to continue with the search until termination criteria are met. The flowchart of the hybridized WCA-PSO algorithm is shown in Figure8.Figure 8
WCA-PSO flowchart [42, 45].The parameters used in this work for the hybridized algorithm are given in Table5.Table 5
WCA-PSO parameters [42, 45].
Parameter nameVariableValueNo. of variablesNvars6Population sizeNpop50Maximum no. of iterations (PSO)Max_iter50Maximum no. of iterations (WCA)Max_iter50Minimum inertia weightwmin0.4Maximum inertia weightwmax0.9Cognitive and social componentsC1=C21.4Random numbersr1,r2U (0, 1)No. of rivers + seaNsr4Evaporation condition constantdmax10–16Each algorithm was independently used to tune the STATCOM. Different PI gains were obtained, and the test results are discussed in the following section.


## 3.1. Problem Formulation

STATCOM controller tuning was converted to an optimization problem, with the aim of minimizing the error between the reference and measured values. Time domain integral error functions can be used as objective functions for metaheuristic optimization techniques. These include Integral of Squared Error (ISE), Integral of Absolute Error (IAE), and Integral of Time Absolute Error (ITAE) [18]. Control systems based on the ITAE function integrate the absolute error multiplied by time over a given period. Errors that exist for a long time are weighted more than those at the start of the response, which can reduce the settling time of the system.When optimizing the ITAE function, settling time and overshoots are reduced faster than IAE and ISE tuning methods. The ITAE index is emerging as a powerful optimization objective function in heuristic optimization techniques. The only drawback is that the first response might be slow [38, 39].The optimization problem was stated as follows:Minimize(6)JX=∫0TVref−Vgtdt+∫0TIqref−Iqtdt+∫0TVdc2−Vdc1tdtsubject to(7)Kmin≤K≤Kmax,where X=KP1,KI1,KP2,KI2,KP3,KI3, T is the time range of the simulation, and t is the discrete solver step time (50μs). The constraints were obtained from a conventional STATCOM as given in Table 2.Table 2
STATCOM PI gain constraints [35].
PI controllerConstraintsAC PI voltage regulator5≤KP1≤20,1000≤KI1≤2000AC PI current regulator0.3≤KP2≤10,10≤KI2≤20DC PI voltage regulator0.0001≤KP3≤1,0.02≤KI3≤1The optimization algorithms minimize the total ITAE error value and return the final objective function value and the corresponding six gains at the optimal output. STATCOM controller gains were evaluated using the algorithms independently, and a performance comparison was done. The WCA, PSO, and WCA-PSO algorithms are described in the following sections.


## 3.2. Water Cycle Algorithm (WCA)

The Water Cycle Algorithm (WCA) is a metaheuristic optimization algorithm inspired by the water cycle process. The algorithm is based on how rivers are created and how water travels to the sea. It was proposed by Hasanien and Matar in 2012 [40]. At the start of the WCA, an initial population of raindrops (Np) is generated. The cost function of each raindrop is evaluated using (6), and the costs are sorted in ascending order. The best raindrops (Nsr) are assigned to a number of rivers (Nr) and one sea, i.e.,(8)Nsr=Nr+1︸sea.In the optimization problem, the sea position is the optimal solution. The remaining population,Nst, includes streams that can flow to the rivers or directly to the sea, given by(9)Nst=Np−Nsr.Streams are allocated to rivers or the sea, based on the flow intensity of raindrops given by(10)NSn=roundCn∑i=1NsrCixNst,n=1,2,…,Nsr,where NSn is the number of streams flowing into certain rivers and seas [41, 42]. Streams move toward rivers and rivers toward the sea. Updated positions for the streams and rivers are given by(11)Xstreami+1=Xstreami+randxCxXriveri−Xstreami,Xriveri+1=Xriveri+randxCxXseai−Xriveri,where rand ∈01 and C is greater than 1. Costs of the new positions are evaluated again, and if the stream cost is less than the river cost, their positions are exchanged. If the cost of a river is less than that of the sea, their positions are exchanged. To avoid premature convergence, evaporation is conducted. We check whether the river or stream is sufficiently close to the sea to enable evaporation. Raining and evaporation are conducted if(12)Xseai−Xriveri<dmax,where i=1,2,…,Nsr−1 and dmax is a small number, updated as(13)dmaxi+1=dmaxi−dmaximax_iter,where i=1,2,…,max_iter. The optimization algorithm will continue with the search process until termination criteria are met. Raindrops at the optimal solution correspond to the optimal PI parameters [42, 43]. A flowchart of the WCA is given in Figure 6.Figure 6
Water Cycle Algorithm flowchart [42].The parameters used in WCA optimization in this work are given in Table3.Table 3
WCA parameters [43].
Parameter nameVariableValueNo. of variablesNvars6Population sizeNp50No. of rivers + seaNsr4Evaporation condition constantdmax10–16Maximum no. of iterationsMax_iter100The WCA has been observed to be efficient and simple compared to other methods. It has also shown superior performance in terms of convergence, computation, and precision [40, 43].


## 3.3. Particle Swarm Optimization (PSO)

Particle Swarm Optimization (PSO) algorithm is a biologically inspired computational search and optimization method developed in 1995 by Eberhart and Kennedy. The algorithm simulates the behavior of birds or fish when looking for the place with the most adequate food. The PSO algorithm starts by randomly generating particles in the search space. Next, the fitness value of each particle is evaluated, and the position corresponding to the best fitness value is called the local best position. The local best of all particles is compared and the best position in the swarm is defined as the global best. At every iteration, the termination criteria are checked, and if not met, an update of the velocity and position of all particles is done [44]. The velocity of particles is given by(14)Vk+1i=wVki+C1r1Pki−Xki+C2r2Pkg−Xkiwhile the position of individual particles is updated by(15)Xk+1i=Xki+Vk+1i,where Xki is the particle position, Vki is the particle velocity, Pki is the individual particle best position, Pkg is the swarm best position, w is the weight inertia used to ensure convergence, C1 and C2 are the cognitive and social parameters, and r1 and r2 are random numbers between 0 and 1 [45]. The flowchart of the PSO algorithm is shown in Figure 7.Figure 7
PSO flowchart [45].The PSO parameters used in this work are given in Table4.Table 4
PSO parameters [45].
Parameter nameVariableValuePopulation sizeNP100Maximum number of iterationsMax_iter100No. Of variablesNvars6Minimum inertia weightwmin0.4Maximum inertia weightwmax0.9Cognitive componentC11.4Social componentC21.4Random numbersr1,r2U (0,1)The PSO algorithm has been gaining popularity due to its simple structure and efficiency. Additionally, it outperforms gradient-based optimization methods which require the optimization problem to be differentiable. However, the PSO algorithm can result in suboptimal solutions in the event a particle gets stuck in a local optimum [46, 47].


## 3.4. WCA-PSO Hybridization

The WCA was hybridized with PSO to take advantage of the strengths of each algorithm. In this hybrid, the WCA first explores the search place to identify the most promising region, thus ruling out the challenge encountered by the PSO of particles being stuck in a local optimum. Next, starting with the solution obtained by WCA, the PSO is introduced to continue with the search until termination criteria are met. The flowchart of the hybridized WCA-PSO algorithm is shown in Figure8.Figure 8
WCA-PSO flowchart [42, 45].The parameters used in this work for the hybridized algorithm are given in Table5.Table 5
WCA-PSO parameters [42, 45].
Parameter nameVariableValueNo. of variablesNvars6Population sizeNpop50Maximum no. of iterations (PSO)Max_iter50Maximum no. of iterations (WCA)Max_iter50Minimum inertia weightwmin0.4Maximum inertia weightwmax0.9Cognitive and social componentsC1=C21.4Random numbersr1,r2U (0, 1)No. of rivers + seaNsr4Evaporation condition constantdmax10–16Each algorithm was independently used to tune the STATCOM. Different PI gains were obtained, and the test results are discussed in the following section.


## 4. Test System and Results

### 4.1. 9 MW Test System

LVRT capability investigation is done for a power system integrated with a 9 MW DFIG-based wind power generating plant. The test system was developed by aggregating six, 1.5 MW DFIG wind turbines into a 9 MW WPP. The output of the wind power generating plant is injected into a 25 kV distribution system through a three-phase 12 MVA transformer. The wind turbine and induction generator parameters are presented in Tables6 and 7, as obtained from [18]. A single line diagram of the test system is shown in Figure 9.Table 6
Wind turbine parameters [18].
Wind turbine parametersRated capacity9 MW (6 turbines × 1.5 MW)Cut-in wind speed3.5 ms/Cut-out wind speed25 m/sRated wind speed12 m/sNo. of blades3Rotor diameter82.5Area swept5346m2Rotor speed10.1–18.7 rpmTable 7
Wind generator parameters [18].
DFIG parametersPrated9 MWVrated575 Vrs0.00706rr0.005lls0.171llr0.156Lm2.9pf0.9Figure 9
Single line diagram of test system [35].A medium transmission line of 30 km length connects the WPP to a 120 kV grid through a three-phase 47 MVA transformer at the bus feederB2. The transmission line parameters are found in Table 8. During normal operating conditions, the reactive power output of the DFIGs is regulated at zero MVAr to maintain a unity power factor connection. The wind turbines have a protection system monitoring voltage, current, and machine speed.Table 8
Transmission line parameters [19].
Transmission line parameters (π) modelrl0.1153Ω/kmr00.413Ω/kmll0.00105 H/kml00.00332 H/kmCl11.33e−9F/kmC05.01e−9F/kmThe test system was independently subjected to L-G and LLL-G, 100% voltage sags on the grid side for 150 ms, to investigate the German utility LVRT capability requirement. The German LVRT GCR is investigated since it is very tough to satisfy, as it demands WPP LVRT capability at a voltage level of 0 p.u., at the PCC. LVRT GCRs for other utility grids given in Table1 can also be investigated. A constant wind speed of 12 m/s is assumed since the fault duration is short, for noticeable wind speed variations. Simulation time was taken to be 20 seconds, and faults were introduced at t = 15 seconds and cleared at t = 15.15 seconds. The implementation was conducted in MATLAB 2018b programming software, using the SimScape power system toolbox. Simulations were done on a Lenovo ThinkPad P53s, powered by Intel Core i7-8th gen, 48 GB RAM, 512 GB SSD.A STATCOM was installed at busesB1 and B2 independently, as voltage profile and reactive power injection were monitored, to determine the optimal location and size of the STATCOM. B2 was obtained as the most optimal location, while the optimal size of the STATCOM was obtained as ±100MVA. A conventional 25 kV, 100 MVA STATCOM was adopted, whose classical gains and parameters obtained from [35] were used, presented in Table 9. Utilizing random streams/particles within the search space as initial inputs, and constraints for the search space previously given in Table 2, WCA, PSO, and WCA-PSO algorithms were used to tune the STATCOM, based on the objective function previously given in (6). The PI gains obtained for the three tuning algorithms are presented in Table 10.Table 9
Conventional STATCOM parameters [35].
S.NoSpecificationsQuantity1Nominal voltage andfrequency500 kVL-LRMS, 60 HZ2Converter rating100 MAV3Converter impedanceR1 = 0.00733 puL1=0.22 pu4DC link nominal voltage40 kV5DC link nominal equivalentcapacitanceC = 3000 µF6Reference voltage1 p.u7Droop0.003 p.u8AC voltage regulator gainsKP = 5K1 = 10009DC voltage regulator gainsKP = 0.0001K1 = 0.0210AC current regulator gainsKP = 0.3K1 = 10Table 10
PI controller gains.
STATCOM controllerGainConventional STATCOMPSO tunedWCA tunedWCA-PSO tunedFF = 0.2395CT = 2052FF = 0.2391CT = 2007FF = 0.238CT = 2063AC PI voltage regulatorKP155108KI11000100012001118AC PI current regulatorKP20.310.30.2KI2108105DC PI voltage regulatorKP30.00010.0010.090.001KI30.020.010.010.05FFFitness Function, CTComputation Time (sec).The PI gains given in Table10 for PSO, WCA, and WCA-PSO tuning algorithms are compared with gains obtained in [18], where the authors used Ant Colony and Particle Swarm Optimization algorithms. As expected, a slight deviation in tuned parameter results is observed, since metaheuristic optimization algorithms do not guarantee reproducibility. Simulations were conducted on the test system with each STATCOM independently incorporated, and performance analysis was done. In the next section, the dynamic performance of the power system with the proposed STATCOM controller is discussed.


### 4.2.L-G Fault

#### 4.2.1. WPP Active Power Output

The active power output of the WPP forL-G 100% grid voltage sag of 150 ms is given in Figure 10.Figure 10
WPP active power output.Att = 15 s, a fault is simulated in which grid voltage drops to 0p.u. for 150 ms. From Figure 10, without STATCOM, active power output drops from 8.8 MW to −1 MW, due to the low voltage at the connection bus. Once the DFIG protection system detects an undervoltage, the crowbar is activated. The RSC is bypassed and the DFIG acts as a Squirrel Cage Induction Generator (SCIG). As the voltage drops, the active power supply to the grid falls to zero and the WPP draws active power from the grid. When either conventional or tuned STATCOM is incorporated, voltage support is provided at the PCC, and the WPP maintains active power output during the fault period. LVRT capability requirements of German utility state that grid-connected wind power plants should be able to withstand voltage sags of up to 100% for 150 ms, a requirement met for all scenarios. Without a STATCOM, active power fluctuations are larger compared to tuned models.


#### 4.2.2. Voltage Magnitude at WPP Terminals

The voltage profile at WPP terminals is shown in Figure11, for L-G 100% voltage sag of 150 ms on the grid side.Figure 11
Voltage profile at WPP terminals.From Figure11, voltage fluctuations are seen at the WPP terminals. Voltage magnitude drops from 1 p.u. to 0.76 p.u. without STATCOM, whereas for the tuned models, the lowest voltage magnitude is 0.9 p.u. The voltage fluctuations do not exceed ±10%. Bakir and Kulaksiz in [34] used Genetic Algorithm (GA) and Bacterial Foraging Algorithm (BFA) to tune the STATCOM controller and obtained 30% and 20% voltage fluctuations, respectively, for L-G faults. Thus, the WCA and PSO tuned STATCOMs used in this work result in better results. Without a STATCOM, when the fault is cleared, the voltage rises momentarily to 1.12 p.u., due to the excess reactive power injected by the GSC during the fault period. Voltage fluctuations at the WPP terminals settle within 150 ms after fault clearance when a STATCOM is incorporated. Kamel et al. in [18] hybridized Ant Colony and Particle Swarm Optimization techniques and observed a settling time of 350 ms for a similar fault. Thus, WCA-PSO tuning results in a shorter settling time than ACO-PSO.


#### 4.2.3. WPP Reactive Power Output

The reactive power output of the WPP forL-G 100% voltage sag of 150 ms on the grid side is shown in Figure 12.Figure 12
WPP reactive power output.From Figure12, without a STATCOM, when the L-G grid fault occurs, the GSC injects up to 6 MVAr to support voltage at the WPP terminals. With STATCOM incorporation, GSC injects about 2 MVAr. With reactive power support, the PEC is not bypassed; thus, the DFIG generates active power during the grid fault. Reactive power oscillations are higher for conventional STATCOM as opposed to WCA-PSO tuned STATCOM.


#### 4.2.4. DC Capacitor Link Voltage

DC capacitor link voltage of the DFIG WPP forL-G 100% voltage sag of 150 ms on the grid side is given in Figure 13.Figure 13
DC link capacitor voltage.From Figure13, the DC link capacitor voltage fluctuates from a reference value of 1200 V to 1260 V and down to 1140 V (±5%) at the onset of the voltage sag. At the end of the fault period, the voltage rises to about 1280 V, when a STATCOM is not used. The voltage fluctuations are caused by excess reactive power injected by the GSC during the grid fault. When a STATCOM is used, the fluctuations are reduced since the GSC only injects minimum reactive power. The PSO tuned STATCOM results in the least fluctuations.


### 4.3. LLL-G Fault

#### 4.3.1. WPP Active Power Output

The active power output of the WPP for LLL-G 100% grid voltage sag of 150 ms is given in Figure14.Figure 14
WPP active power output.From Figure14, during the LLL-G fault, the active power output at the WPP rapidly drops from about 8.8 MW up to 0 MW for the cases without, with conventional, and with PSO tuned STATCOM, due to the low voltage at the connection bus. The WPP gets disconnected and active power generation does not resume after fault clearance. LVRT capability requirement of German utility is not met for the three scenarios. For the case of WCA and WCA-PSO tuned models, the WPP rides through the LLL-G fault due to the voltage support provided at the PCC. Thus, the WPP stays online, but it does not generate active power. When the fault is cleared, active power generation quickly resumes to its prefault value.


#### 4.3.2. Voltage Magnitude at WPP Terminals

The voltage profile at the WPP terminals is shown in Figure15 for LLL-G 100% grid voltage sag of 150 ms.Figure 15
Voltage profile at WPP terminals.From Figure15, the voltage at the WPP terminal drops to 0 p.u. for cases without, with conventional, and with PSO tuned STATCOM, cases in which the WPP is disconnected. For WCA and WCA-PSO tuned STATCOM, the lowest voltage magnitude is 0.45 p.u. and 0.55 p.u., respectively. When the fault is cleared, there is an overvoltage due to reactive power supplied by the STATCOM during the fault period. The highest overshoot (30%) occurs with the WCA-PSO tuned STATCOM, which injects a maximum amount of reactive power, of 110 MVAr.


#### 4.3.3. WPP Reactive Power Output

Figure16 shows the reactive power output of the WPP for LLL-G 100% grid voltage sags of 150 ms.Figure 16
WPP reactive power output.During the LLL-G grid fault, without STATCOM, the GSC injects up to 3.5 MVAr before WPP disconnection. For the WCA and WCA-PSO tuned STATCOM, the GSC injects 6.5 MVAr, to keep the WPP connected to the grid. The highest overshoots are seen for the WCA model, whereas WCA-PSO has a smoother output. For the WCA and WCA-PSO tuned STATCOMs, due to the excess reactive power after fault clearance, the GSC consumes reactive power up to −6.5 MVAr.


#### 4.3.4. DC Capacitor Link Voltage

The DC link capacitor voltage of the DFIG WPP for LLL-G 100% grid voltage sag of 150 ms is shown in Figure17.Figure 17
DC link capacitor voltage.From Figure17, the DC link capacitor voltage of the DFIG under the LLL-G fault drastically increases from its steady-state value of 1200 V to a maximum of 1980 V when the WPP is disconnected. For the conventional and PSO tuned STATCOM, WPP disconnection is because the DC capacitor voltage limit of 1980 V is violated. The highest values of the DC capacitor link voltage for WCA and WCA-PSO tuned models are 1650 V and 1480 V, respectively, which are safe limits for the operation of the DC link capacitor.


#### 4.3.5. Numerical Summary of Results

A comparison of voltage and current transient points at Bus 1 for the different tuning techniques is reported in Table11.Table 11
Numerical summary of results obtained.
Fault typeMeasured pointsTransient pointsConventional STATCOMPSO tuned STATCOMWCA tuned STATCOMWCA-PSO tuned STATCOML-GVB1 (p.u.)MOS1.101.081.081.07MUS0.900.920.920.90Ts(sec)0.0360.0350.030.028IB1 (p.u.)MOS1.051.041.041.03MUS0.750.800.800.82Ts(sec)0.030.030.030.03Vdc (V)MOS1270126512401230MUS1170116511651160Ts(sec)0.0370.0350.0350.03LLL-GVB1 (p.u.)MOS1.201.251.251.30MUS0.000.000.400.50Ts(sec)0.040.0380.0380.036IB1 (p.u.)MOS1.151.201.381.36MUS0.000.000.200.30Ts(sec)——0.040.04Vdc (V)MOS1980196016201480MUS1200120010001080Ts(sec)——0.350.35MOSmaximum overshoot, MUSmaximum undershoot,Tssettling time.From Table11, PSO, WCA, and PSO-WCA tuned STATCOM utilization results in less voltage and current fluctuations at the point of wind power integration into the grid than the conventional PI method. The settling time is also shorter for tuned models, as compared to the conventional STATCOM. Kamel et al. in [18] made similar deductions on the impact of tuned STATCOM on voltage and current variations at the PCC and the settling time.


### 4.4. Analysis of Total Harmonic Distortion

Although harmonic problems are not as widespread as the RMS voltage fluctuations, harmonic distortion can negatively affect power system components. Harmonic effects include overheating of cables, transformers, and motors and interference in electronic and communication circuits. The Total Harmonic Distortion (THD) for voltage and currents at B1 is summarized in Table 12 for the different algorithms.Table 12
THD as a % of the fundamental value.
ParameterFault typeConventional STATCOM (%)PSO tuned STATCOM (%)WCA tuned STATCOM (%)WCA-PSO tuned STATCOM (%)Vabc (B1)L-G5.664.84.623.92LLL-G8.858.448.337.76Iabc (B1)L-G24.5411.6711.938.84LLL-G2.261.531.721.24From Table12, PSO, WCA, and PSO-WCA tuned STATCOM utilization results in less THD of the voltage and current waveforms at the point of wind power injection into the grid, as compared to incorporating the conventional PI method. Kamel et al. in [18] made similar deductions on the effect of tuned STATCOM on THD.


### 4.5. IEEE 39 Bus Test System

The IEEE 39 bus test system is a simplified model of the high voltage transmission system in the northeast of the USA (New England area), which consists of 10 generators, 19 loads, 34 lines, and 12 transformers. The test system data generator, bus, and transmission line data is given in Tables13–15, respectively. The online diagram of the modified IEEE 39 bus test system is shown in Figure 18 [48].Table 13
Generator data [55].
Generator no.Bus no.Active power generated (MW)Reactive power generated (MVAr)Qmax (MVAr)Qmin (MVAr)Generator voltagePmax (MW)Pmin (MW)130250.00161.764001401.0510400231677.87221.57300−1000.986460332650.00206.973001500.987250433632.00108.2925001.006520534508.00166.6916701.015080635650.00210.66300−1001.056870736560.00100.1724001.065800837540.00−1.3725001.035640938830.0021.73300−1501.03865010391000.0078.47300−1001.0311000Total6297.877367Table 14
Bus data [55].
Bus no.Active power load (MW)Reactive power load (MVAr)197.6044.2020.000.003322.002.404500.00184.0050.000.0060.000.007233.8084.008522.00176.6096.50−66.60100.000.00110.000.00128.5388.00130.000.00140.000.0015320.00153.0016329.0032.30170.000.0018158.0030.00190.000.0020680.00103.0021274.00115.00220.000.0023247.5084.6024308.60-92.2025224.0047.2026139.0017.0027281.0075.5028206.0027.6029283.5026.90300.000.00319.204.60320.000.00330.000.00340.000.00350.000.00360.000.00370.000.00380.000.00391104.00250.00Total6254.231387.10Table 15
Transmission line data [55].
Line no.From busTo busR (p.u.)X (p.u.)B (p.u.)Ratio1120.00350.04110.6987021390.00100.02500.750003230.00130.01510.2572042250.00700.00860.1460052300.00000.01810.00001.0256340.00130.02130.2214073180.00110.01330.213808450.00080.01280.1342094140.00080.01290.1382010560.00020.00260.0434011580.00080.01120.1476012670.00060.00920.11300136110.00070.00820.13890146310.00000.02500.00001.0715780.00040.00460.0780016890.00230.03630.38040179390.00100.02501.200001810110.00040.00430.072901910130.00040.00430.072902010320.00000.02000.00001.072112110.00160.04350.00001.0062212130.00160.04350.00001.0062313140.00090.01010.172302414150.00180.02170.366002515160.00090.00940.171002616170.00070.00890.134202716190.00160.01950.304002816210.00080.01350.254802916240.00030.00590.068003017180.00070.00820.131903117270.00130.01730.321603219200.00070.01380.00001.063319330.00070.01420.00001.073420340.00090.01800.00001.0093521220.00080.01400.256503622230.00060.00960.184603722350.00000.01430.00001.0253823240.00220.03500.361003923360.00050.02720.000014025260.00320.03230.531004125370.00060.02320.00001.0254226270.00140.01470.239604326280.00430.04740.780204426290.00570.06251.029004528290.00140.01510.249004629380.00080.01560.00001.025Figure 18
IEEE 39 bus test system [49].The aggregate capacity of the IEEE 39-bus system is 6140.80 MW while the total connected load is 6097.1 MW. Bus number 39 is taken as the slack bus. All generators in this standard system are modeled as 4th-order synchronous machines equipped with standard IEEE models of automatic voltage regulators, excitation systems, governor systems, and power system stabilizers.Elzemeity et al. in [49] investigate the optimal location of WPPs in the IEEE 39 bus system by sorting the possible locations in ascending order of electromechanical oscillations using Eigenvalue analysis. The best five locations with less electromechanical oscillations are obtained as buses 30, 37, 31, 32, and 36, respectively. These findings agree with Essalah et al. in [50] in which buses 30, 34, 37, and 39 are obtained as the optimal location for WPPs, and Shi et al. in [51] who obtain optimal locations as buses 38 and 37. El-Samanoudy et al. in [52] also assess the impact of large-scale wind generation on the IEEE 39 bus system based on voltage stability and conclude that the integrated wind power generation should not exceed 20% for system stability.In this work, the synchronous generators in bus 30 and bus 37 were replaced with the same amount of active power generation, and reactive power needs were met by installing capacitors. This ensured the same system operating conditions were maintained. The 250 MW, 162 MVAr (bus 30) and 540 MW, −1.4 MVAr (bus 37) synchronous generators were replaced by wind farms equipped with GE 1.5 MW DFIG generators. The penetration level of wind power generation is therefore 12%. Two STATCOMs are also integrated at the point of wind power integration into the grid. Similarly, the STATCOMs are tuned using WCA, PSO, and WCA-PSO optimization algorithms. To investigate the LVRT capability of the WPPs, the LLL-G fault was simulated online 16–17. This fault location has been identified by Arredondo et al. in [53] and Yakout et al. in [54], as the most severe line loss which can lead to transient stability. The IEEE 39 bus test system was thus subjected to LLL-G, online 16–17 for 150 ms, to evaluate the German electric utility LVRT capability requirement. The assumptions for wind speed, simulation time, and crowbar configuration are the same as in the 9 MW test system.


### 4.6. LLL-G Fault

#### 4.6.1. WPP Active Power Output

The active power output of the 250 MW (WPP 1) for the LLL-G grid fault of 150 ms is given in Figure19.Figure 19
WPP 1 active power output.From Figure19, during the LLL-G fault, the active power output of WPP 1 rapidly drops from about 245 MW up to −35 MW for the cases without a STATCOM, with conventional and with PSO tuned STATCOM. For the WCA tuned STATCOM, the lowest output is −20 MW whereas for WCA-PSO tuned STATCOM, the lowest output is 20 MW. For all the scenarios, the WPP stays online, although it only generates active power when WCA-PSO tuned STATCOM is incorporated. The WCA-PSO tuned STATCOM gives the best outcome, in which it injects maximum reactive power of 110 MVAr, and the GSC regulates active power generation. The WPP thus rides through the LLL-G fault due to the voltage support provided at the PCC for all scenarios. When the fault is cleared, active power generation quickly recovers to its prefault value. The active power output of the 540 MW (WPP 2) is given in Figure 20, in which the WPP can ride through the LLL-G fault in all scenarios.Figure 20
WPP 2 active power output.


#### 4.6.2. Voltage Magnitude at WPP 1 Terminals

The voltage profile at WPP 1 terminals is shown in Figure21 for the LLL-G grid fault of 150 ms.Figure 21
Voltage profile at WPP terminals.From Figure21, for WPP 1 at bus 30, some voltage fluctuations are observed. Voltage magnitude drops from 1 p.u. to 0.88 p.u. without STATCOM, whereas for the tuned models, the lowest voltage magnitude is 0.94 p.u. Voltage fluctuations are minimum at the WPP terminals during, and after fault clearance for WCA-PSO tuned STATCOM. The voltage profile at the terminals of WPP 2 at bus 37 is given in Figure 22.Figure 22
Voltage profile at WPP terminals.For the second WPP, voltage fluctuations during the LLL-G fault are minimal, and the WPP rides through the grid fault. The WCA-PSO tuned STATCOM scenario has a better profile.


#### 4.6.3. WPP Reactive Power Output

The reactive power output of WPP 1 for LLL-G grid fault of 150 ms is given in Figure23.Figure 23
WPP 1 reactive power output.The GSC injects reactive power, to aid grid recovery. The highest transients are seen for the WCA model, whereas WCA-PSO has a smoother output.From Figure24, without a STATCOM, when the LLL-G grid fault occurs, the GSC injects up to 350 MVAr to support voltage at the WPP terminals. With STATCOM incorporation, GSC injects less reactive power, with the least amount of reactive injected for WCA-PSO tuned STATCOM, 170 MVAr. The WPP stays online, thus the DFIG generates active power during the grid fault. Reactive power oscillations are higher for conventional STATCOM as opposed to WCA-PSO tuned STATCOM.Figure 24
WPP 2 reactive power output.


#### 4.6.4. DC Capacitor Link Voltage

The DC link capacitor voltage of the DFIG in 250 MW WPP for LLL-G grid fault of 150 ms is shown in Figure25.Figure 25
WPP 1 DC link capacitor voltage.From Figure25, the DC link capacitor voltage fluctuates from a reference value of 1200 V to around 1135 V at the onset of the voltage sag and back to about 1270 V at the end of the fault period, when a STATCOM is not used. The WCA-PSO tuned STATCOM results in the least fluctuations. The DC capacitor voltage for WPP 2 is shown in Figure 26 in which the fluctuations are about ±2%, which is within a safe operating range.Figure 26
WPP 2 DC link capacitor voltage.


## 4.1. 9 MW Test System

LVRT capability investigation is done for a power system integrated with a 9 MW DFIG-based wind power generating plant. The test system was developed by aggregating six, 1.5 MW DFIG wind turbines into a 9 MW WPP. The output of the wind power generating plant is injected into a 25 kV distribution system through a three-phase 12 MVA transformer. The wind turbine and induction generator parameters are presented in Tables6 and 7, as obtained from [18]. A single line diagram of the test system is shown in Figure 9.Table 6
Wind turbine parameters [18].
Wind turbine parametersRated capacity9 MW (6 turbines × 1.5 MW)Cut-in wind speed3.5 ms/Cut-out wind speed25 m/sRated wind speed12 m/sNo. of blades3Rotor diameter82.5Area swept5346m2Rotor speed10.1–18.7 rpmTable 7
Wind generator parameters [18].
DFIG parametersPrated9 MWVrated575 Vrs0.00706rr0.005lls0.171llr0.156Lm2.9pf0.9Figure 9
Single line diagram of test system [35].A medium transmission line of 30 km length connects the WPP to a 120 kV grid through a three-phase 47 MVA transformer at the bus feederB2. The transmission line parameters are found in Table 8. During normal operating conditions, the reactive power output of the DFIGs is regulated at zero MVAr to maintain a unity power factor connection. The wind turbines have a protection system monitoring voltage, current, and machine speed.Table 8
Transmission line parameters [19].
Transmission line parameters (π) modelrl0.1153Ω/kmr00.413Ω/kmll0.00105 H/kml00.00332 H/kmCl11.33e−9F/kmC05.01e−9F/kmThe test system was independently subjected to L-G and LLL-G, 100% voltage sags on the grid side for 150 ms, to investigate the German utility LVRT capability requirement. The German LVRT GCR is investigated since it is very tough to satisfy, as it demands WPP LVRT capability at a voltage level of 0 p.u., at the PCC. LVRT GCRs for other utility grids given in Table1 can also be investigated. A constant wind speed of 12 m/s is assumed since the fault duration is short, for noticeable wind speed variations. Simulation time was taken to be 20 seconds, and faults were introduced at t = 15 seconds and cleared at t = 15.15 seconds. The implementation was conducted in MATLAB 2018b programming software, using the SimScape power system toolbox. Simulations were done on a Lenovo ThinkPad P53s, powered by Intel Core i7-8th gen, 48 GB RAM, 512 GB SSD.A STATCOM was installed at busesB1 and B2 independently, as voltage profile and reactive power injection were monitored, to determine the optimal location and size of the STATCOM. B2 was obtained as the most optimal location, while the optimal size of the STATCOM was obtained as ±100MVA. A conventional 25 kV, 100 MVA STATCOM was adopted, whose classical gains and parameters obtained from [35] were used, presented in Table 9. Utilizing random streams/particles within the search space as initial inputs, and constraints for the search space previously given in Table 2, WCA, PSO, and WCA-PSO algorithms were used to tune the STATCOM, based on the objective function previously given in (6). The PI gains obtained for the three tuning algorithms are presented in Table 10.Table 9
Conventional STATCOM parameters [35].
S.NoSpecificationsQuantity1Nominal voltage andfrequency500 kVL-LRMS, 60 HZ2Converter rating100 MAV3Converter impedanceR1 = 0.00733 puL1=0.22 pu4DC link nominal voltage40 kV5DC link nominal equivalentcapacitanceC = 3000 µF6Reference voltage1 p.u7Droop0.003 p.u8AC voltage regulator gainsKP = 5K1 = 10009DC voltage regulator gainsKP = 0.0001K1 = 0.0210AC current regulator gainsKP = 0.3K1 = 10Table 10
PI controller gains.
STATCOM controllerGainConventional STATCOMPSO tunedWCA tunedWCA-PSO tunedFF = 0.2395CT = 2052FF = 0.2391CT = 2007FF = 0.238CT = 2063AC PI voltage regulatorKP155108KI11000100012001118AC PI current regulatorKP20.310.30.2KI2108105DC PI voltage regulatorKP30.00010.0010.090.001KI30.020.010.010.05FFFitness Function, CTComputation Time (sec).The PI gains given in Table10 for PSO, WCA, and WCA-PSO tuning algorithms are compared with gains obtained in [18], where the authors used Ant Colony and Particle Swarm Optimization algorithms. As expected, a slight deviation in tuned parameter results is observed, since metaheuristic optimization algorithms do not guarantee reproducibility. Simulations were conducted on the test system with each STATCOM independently incorporated, and performance analysis was done. In the next section, the dynamic performance of the power system with the proposed STATCOM controller is discussed.


## 4.2.L-G Fault

### 4.2.1. WPP Active Power Output

The active power output of the WPP forL-G 100% grid voltage sag of 150 ms is given in Figure 10.Figure 10
WPP active power output.Att = 15 s, a fault is simulated in which grid voltage drops to 0p.u. for 150 ms. From Figure 10, without STATCOM, active power output drops from 8.8 MW to −1 MW, due to the low voltage at the connection bus. Once the DFIG protection system detects an undervoltage, the crowbar is activated. The RSC is bypassed and the DFIG acts as a Squirrel Cage Induction Generator (SCIG). As the voltage drops, the active power supply to the grid falls to zero and the WPP draws active power from the grid. When either conventional or tuned STATCOM is incorporated, voltage support is provided at the PCC, and the WPP maintains active power output during the fault period. LVRT capability requirements of German utility state that grid-connected wind power plants should be able to withstand voltage sags of up to 100% for 150 ms, a requirement met for all scenarios. Without a STATCOM, active power fluctuations are larger compared to tuned models.


### 4.2.2. Voltage Magnitude at WPP Terminals

The voltage profile at WPP terminals is shown in Figure11, for L-G 100% voltage sag of 150 ms on the grid side.Figure 11
Voltage profile at WPP terminals.From Figure11, voltage fluctuations are seen at the WPP terminals. Voltage magnitude drops from 1 p.u. to 0.76 p.u. without STATCOM, whereas for the tuned models, the lowest voltage magnitude is 0.9 p.u. The voltage fluctuations do not exceed ±10%. Bakir and Kulaksiz in [34] used Genetic Algorithm (GA) and Bacterial Foraging Algorithm (BFA) to tune the STATCOM controller and obtained 30% and 20% voltage fluctuations, respectively, for L-G faults. Thus, the WCA and PSO tuned STATCOMs used in this work result in better results. Without a STATCOM, when the fault is cleared, the voltage rises momentarily to 1.12 p.u., due to the excess reactive power injected by the GSC during the fault period. Voltage fluctuations at the WPP terminals settle within 150 ms after fault clearance when a STATCOM is incorporated. Kamel et al. in [18] hybridized Ant Colony and Particle Swarm Optimization techniques and observed a settling time of 350 ms for a similar fault. Thus, WCA-PSO tuning results in a shorter settling time than ACO-PSO.


### 4.2.3. WPP Reactive Power Output

The reactive power output of the WPP forL-G 100% voltage sag of 150 ms on the grid side is shown in Figure 12.Figure 12
WPP reactive power output.From Figure12, without a STATCOM, when the L-G grid fault occurs, the GSC injects up to 6 MVAr to support voltage at the WPP terminals. With STATCOM incorporation, GSC injects about 2 MVAr. With reactive power support, the PEC is not bypassed; thus, the DFIG generates active power during the grid fault. Reactive power oscillations are higher for conventional STATCOM as opposed to WCA-PSO tuned STATCOM.


### 4.2.4. DC Capacitor Link Voltage

DC capacitor link voltage of the DFIG WPP forL-G 100% voltage sag of 150 ms on the grid side is given in Figure 13.Figure 13
DC link capacitor voltage.From Figure13, the DC link capacitor voltage fluctuates from a reference value of 1200 V to 1260 V and down to 1140 V (±5%) at the onset of the voltage sag. At the end of the fault period, the voltage rises to about 1280 V, when a STATCOM is not used. The voltage fluctuations are caused by excess reactive power injected by the GSC during the grid fault. When a STATCOM is used, the fluctuations are reduced since the GSC only injects minimum reactive power. The PSO tuned STATCOM results in the least fluctuations.


## 4.2.1. WPP Active Power Output

The active power output of the WPP forL-G 100% grid voltage sag of 150 ms is given in Figure 10.Figure 10
WPP active power output.Att = 15 s, a fault is simulated in which grid voltage drops to 0p.u. for 150 ms. From Figure 10, without STATCOM, active power output drops from 8.8 MW to −1 MW, due to the low voltage at the connection bus. Once the DFIG protection system detects an undervoltage, the crowbar is activated. The RSC is bypassed and the DFIG acts as a Squirrel Cage Induction Generator (SCIG). As the voltage drops, the active power supply to the grid falls to zero and the WPP draws active power from the grid. When either conventional or tuned STATCOM is incorporated, voltage support is provided at the PCC, and the WPP maintains active power output during the fault period. LVRT capability requirements of German utility state that grid-connected wind power plants should be able to withstand voltage sags of up to 100% for 150 ms, a requirement met for all scenarios. Without a STATCOM, active power fluctuations are larger compared to tuned models.


## 4.2.2. Voltage Magnitude at WPP Terminals

The voltage profile at WPP terminals is shown in Figure11, for L-G 100% voltage sag of 150 ms on the grid side.Figure 11
Voltage profile at WPP terminals.From Figure11, voltage fluctuations are seen at the WPP terminals. Voltage magnitude drops from 1 p.u. to 0.76 p.u. without STATCOM, whereas for the tuned models, the lowest voltage magnitude is 0.9 p.u. The voltage fluctuations do not exceed ±10%. Bakir and Kulaksiz in [34] used Genetic Algorithm (GA) and Bacterial Foraging Algorithm (BFA) to tune the STATCOM controller and obtained 30% and 20% voltage fluctuations, respectively, for L-G faults. Thus, the WCA and PSO tuned STATCOMs used in this work result in better results. Without a STATCOM, when the fault is cleared, the voltage rises momentarily to 1.12 p.u., due to the excess reactive power injected by the GSC during the fault period. Voltage fluctuations at the WPP terminals settle within 150 ms after fault clearance when a STATCOM is incorporated. Kamel et al. in [18] hybridized Ant Colony and Particle Swarm Optimization techniques and observed a settling time of 350 ms for a similar fault. Thus, WCA-PSO tuning results in a shorter settling time than ACO-PSO.


## 4.2.3. WPP Reactive Power Output

The reactive power output of the WPP forL-G 100% voltage sag of 150 ms on the grid side is shown in Figure 12.Figure 12
WPP reactive power output.From Figure12, without a STATCOM, when the L-G grid fault occurs, the GSC injects up to 6 MVAr to support voltage at the WPP terminals. With STATCOM incorporation, GSC injects about 2 MVAr. With reactive power support, the PEC is not bypassed; thus, the DFIG generates active power during the grid fault. Reactive power oscillations are higher for conventional STATCOM as opposed to WCA-PSO tuned STATCOM.


## 4.2.4. DC Capacitor Link Voltage

DC capacitor link voltage of the DFIG WPP forL-G 100% voltage sag of 150 ms on the grid side is given in Figure 13.Figure 13
DC link capacitor voltage.From Figure13, the DC link capacitor voltage fluctuates from a reference value of 1200 V to 1260 V and down to 1140 V (±5%) at the onset of the voltage sag. At the end of the fault period, the voltage rises to about 1280 V, when a STATCOM is not used. The voltage fluctuations are caused by excess reactive power injected by the GSC during the grid fault. When a STATCOM is used, the fluctuations are reduced since the GSC only injects minimum reactive power. The PSO tuned STATCOM results in the least fluctuations.


## 4.3. LLL-G Fault

### 4.3.1. WPP Active Power Output

The active power output of the WPP for LLL-G 100% grid voltage sag of 150 ms is given in Figure14.Figure 14
WPP active power output.From Figure14, during the LLL-G fault, the active power output at the WPP rapidly drops from about 8.8 MW up to 0 MW for the cases without, with conventional, and with PSO tuned STATCOM, due to the low voltage at the connection bus. The WPP gets disconnected and active power generation does not resume after fault clearance. LVRT capability requirement of German utility is not met for the three scenarios. For the case of WCA and WCA-PSO tuned models, the WPP rides through the LLL-G fault due to the voltage support provided at the PCC. Thus, the WPP stays online, but it does not generate active power. When the fault is cleared, active power generation quickly resumes to its prefault value.


### 4.3.2. Voltage Magnitude at WPP Terminals

The voltage profile at the WPP terminals is shown in Figure15 for LLL-G 100% grid voltage sag of 150 ms.Figure 15
Voltage profile at WPP terminals.From Figure15, the voltage at the WPP terminal drops to 0 p.u. for cases without, with conventional, and with PSO tuned STATCOM, cases in which the WPP is disconnected. For WCA and WCA-PSO tuned STATCOM, the lowest voltage magnitude is 0.45 p.u. and 0.55 p.u., respectively. When the fault is cleared, there is an overvoltage due to reactive power supplied by the STATCOM during the fault period. The highest overshoot (30%) occurs with the WCA-PSO tuned STATCOM, which injects a maximum amount of reactive power, of 110 MVAr.


### 4.3.3. WPP Reactive Power Output

Figure16 shows the reactive power output of the WPP for LLL-G 100% grid voltage sags of 150 ms.Figure 16
WPP reactive power output.During the LLL-G grid fault, without STATCOM, the GSC injects up to 3.5 MVAr before WPP disconnection. For the WCA and WCA-PSO tuned STATCOM, the GSC injects 6.5 MVAr, to keep the WPP connected to the grid. The highest overshoots are seen for the WCA model, whereas WCA-PSO has a smoother output. For the WCA and WCA-PSO tuned STATCOMs, due to the excess reactive power after fault clearance, the GSC consumes reactive power up to −6.5 MVAr.


### 4.3.4. DC Capacitor Link Voltage

The DC link capacitor voltage of the DFIG WPP for LLL-G 100% grid voltage sag of 150 ms is shown in Figure17.Figure 17
DC link capacitor voltage.From Figure17, the DC link capacitor voltage of the DFIG under the LLL-G fault drastically increases from its steady-state value of 1200 V to a maximum of 1980 V when the WPP is disconnected. For the conventional and PSO tuned STATCOM, WPP disconnection is because the DC capacitor voltage limit of 1980 V is violated. The highest values of the DC capacitor link voltage for WCA and WCA-PSO tuned models are 1650 V and 1480 V, respectively, which are safe limits for the operation of the DC link capacitor.


### 4.3.5. Numerical Summary of Results

A comparison of voltage and current transient points at Bus 1 for the different tuning techniques is reported in Table11.Table 11
Numerical summary of results obtained.
Fault typeMeasured pointsTransient pointsConventional STATCOMPSO tuned STATCOMWCA tuned STATCOMWCA-PSO tuned STATCOML-GVB1 (p.u.)MOS1.101.081.081.07MUS0.900.920.920.90Ts(sec)0.0360.0350.030.028IB1 (p.u.)MOS1.051.041.041.03MUS0.750.800.800.82Ts(sec)0.030.030.030.03Vdc (V)MOS1270126512401230MUS1170116511651160Ts(sec)0.0370.0350.0350.03LLL-GVB1 (p.u.)MOS1.201.251.251.30MUS0.000.000.400.50Ts(sec)0.040.0380.0380.036IB1 (p.u.)MOS1.151.201.381.36MUS0.000.000.200.30Ts(sec)——0.040.04Vdc (V)MOS1980196016201480MUS1200120010001080Ts(sec)——0.350.35MOSmaximum overshoot, MUSmaximum undershoot,Tssettling time.From Table11, PSO, WCA, and PSO-WCA tuned STATCOM utilization results in less voltage and current fluctuations at the point of wind power integration into the grid than the conventional PI method. The settling time is also shorter for tuned models, as compared to the conventional STATCOM. Kamel et al. in [18] made similar deductions on the impact of tuned STATCOM on voltage and current variations at the PCC and the settling time.


## 4.3.1. WPP Active Power Output

The active power output of the WPP for LLL-G 100% grid voltage sag of 150 ms is given in Figure14.Figure 14
WPP active power output.From Figure14, during the LLL-G fault, the active power output at the WPP rapidly drops from about 8.8 MW up to 0 MW for the cases without, with conventional, and with PSO tuned STATCOM, due to the low voltage at the connection bus. The WPP gets disconnected and active power generation does not resume after fault clearance. LVRT capability requirement of German utility is not met for the three scenarios. For the case of WCA and WCA-PSO tuned models, the WPP rides through the LLL-G fault due to the voltage support provided at the PCC. Thus, the WPP stays online, but it does not generate active power. When the fault is cleared, active power generation quickly resumes to its prefault value.


## 4.3.2. Voltage Magnitude at WPP Terminals

The voltage profile at the WPP terminals is shown in Figure15 for LLL-G 100% grid voltage sag of 150 ms.Figure 15
Voltage profile at WPP terminals.From Figure15, the voltage at the WPP terminal drops to 0 p.u. for cases without, with conventional, and with PSO tuned STATCOM, cases in which the WPP is disconnected. For WCA and WCA-PSO tuned STATCOM, the lowest voltage magnitude is 0.45 p.u. and 0.55 p.u., respectively. When the fault is cleared, there is an overvoltage due to reactive power supplied by the STATCOM during the fault period. The highest overshoot (30%) occurs with the WCA-PSO tuned STATCOM, which injects a maximum amount of reactive power, of 110 MVAr.


## 4.3.3. WPP Reactive Power Output

Figure16 shows the reactive power output of the WPP for LLL-G 100% grid voltage sags of 150 ms.Figure 16
WPP reactive power output.During the LLL-G grid fault, without STATCOM, the GSC injects up to 3.5 MVAr before WPP disconnection. For the WCA and WCA-PSO tuned STATCOM, the GSC injects 6.5 MVAr, to keep the WPP connected to the grid. The highest overshoots are seen for the WCA model, whereas WCA-PSO has a smoother output. For the WCA and WCA-PSO tuned STATCOMs, due to the excess reactive power after fault clearance, the GSC consumes reactive power up to −6.5 MVAr.


## 4.3.4. DC Capacitor Link Voltage

The DC link capacitor voltage of the DFIG WPP for LLL-G 100% grid voltage sag of 150 ms is shown in Figure17.Figure 17
DC link capacitor voltage.From Figure17, the DC link capacitor voltage of the DFIG under the LLL-G fault drastically increases from its steady-state value of 1200 V to a maximum of 1980 V when the WPP is disconnected. For the conventional and PSO tuned STATCOM, WPP disconnection is because the DC capacitor voltage limit of 1980 V is violated. The highest values of the DC capacitor link voltage for WCA and WCA-PSO tuned models are 1650 V and 1480 V, respectively, which are safe limits for the operation of the DC link capacitor.


## 4.3.5. Numerical Summary of Results

A comparison of voltage and current transient points at Bus 1 for the different tuning techniques is reported in Table11.Table 11
Numerical summary of results obtained.
Fault typeMeasured pointsTransient pointsConventional STATCOMPSO tuned STATCOMWCA tuned STATCOMWCA-PSO tuned STATCOML-GVB1 (p.u.)MOS1.101.081.081.07MUS0.900.920.920.90Ts(sec)0.0360.0350.030.028IB1 (p.u.)MOS1.051.041.041.03MUS0.750.800.800.82Ts(sec)0.030.030.030.03Vdc (V)MOS1270126512401230MUS1170116511651160Ts(sec)0.0370.0350.0350.03LLL-GVB1 (p.u.)MOS1.201.251.251.30MUS0.000.000.400.50Ts(sec)0.040.0380.0380.036IB1 (p.u.)MOS1.151.201.381.36MUS0.000.000.200.30Ts(sec)——0.040.04Vdc (V)MOS1980196016201480MUS1200120010001080Ts(sec)——0.350.35MOSmaximum overshoot, MUSmaximum undershoot,Tssettling time.From Table11, PSO, WCA, and PSO-WCA tuned STATCOM utilization results in less voltage and current fluctuations at the point of wind power integration into the grid than the conventional PI method. The settling time is also shorter for tuned models, as compared to the conventional STATCOM. Kamel et al. in [18] made similar deductions on the impact of tuned STATCOM on voltage and current variations at the PCC and the settling time.


## 4.4. Analysis of Total Harmonic Distortion

Although harmonic problems are not as widespread as the RMS voltage fluctuations, harmonic distortion can negatively affect power system components. Harmonic effects include overheating of cables, transformers, and motors and interference in electronic and communication circuits. The Total Harmonic Distortion (THD) for voltage and currents at B1 is summarized in Table 12 for the different algorithms.Table 12
THD as a % of the fundamental value.
ParameterFault typeConventional STATCOM (%)PSO tuned STATCOM (%)WCA tuned STATCOM (%)WCA-PSO tuned STATCOM (%)Vabc (B1)L-G5.664.84.623.92LLL-G8.858.448.337.76Iabc (B1)L-G24.5411.6711.938.84LLL-G2.261.531.721.24From Table12, PSO, WCA, and PSO-WCA tuned STATCOM utilization results in less THD of the voltage and current waveforms at the point of wind power injection into the grid, as compared to incorporating the conventional PI method. Kamel et al. in [18] made similar deductions on the effect of tuned STATCOM on THD.


## 4.5. IEEE 39 Bus Test System

The IEEE 39 bus test system is a simplified model of the high voltage transmission system in the northeast of the USA (New England area), which consists of 10 generators, 19 loads, 34 lines, and 12 transformers. The test system data generator, bus, and transmission line data is given in Tables13–15, respectively. The online diagram of the modified IEEE 39 bus test system is shown in Figure 18 [48].Table 13
Generator data [55].
Generator no.Bus no.Active power generated (MW)Reactive power generated (MVAr)Qmax (MVAr)Qmin (MVAr)Generator voltagePmax (MW)Pmin (MW)130250.00161.764001401.0510400231677.87221.57300−1000.986460332650.00206.973001500.987250433632.00108.2925001.006520534508.00166.6916701.015080635650.00210.66300−1001.056870736560.00100.1724001.065800837540.00−1.3725001.035640938830.0021.73300−1501.03865010391000.0078.47300−1001.0311000Total6297.877367Table 14
Bus data [55].
Bus no.Active power load (MW)Reactive power load (MVAr)197.6044.2020.000.003322.002.404500.00184.0050.000.0060.000.007233.8084.008522.00176.6096.50−66.60100.000.00110.000.00128.5388.00130.000.00140.000.0015320.00153.0016329.0032.30170.000.0018158.0030.00190.000.0020680.00103.0021274.00115.00220.000.0023247.5084.6024308.60-92.2025224.0047.2026139.0017.0027281.0075.5028206.0027.6029283.5026.90300.000.00319.204.60320.000.00330.000.00340.000.00350.000.00360.000.00370.000.00380.000.00391104.00250.00Total6254.231387.10Table 15
Transmission line data [55].
Line no.From busTo busR (p.u.)X (p.u.)B (p.u.)Ratio1120.00350.04110.6987021390.00100.02500.750003230.00130.01510.2572042250.00700.00860.1460052300.00000.01810.00001.0256340.00130.02130.2214073180.00110.01330.213808450.00080.01280.1342094140.00080.01290.1382010560.00020.00260.0434011580.00080.01120.1476012670.00060.00920.11300136110.00070.00820.13890146310.00000.02500.00001.0715780.00040.00460.0780016890.00230.03630.38040179390.00100.02501.200001810110.00040.00430.072901910130.00040.00430.072902010320.00000.02000.00001.072112110.00160.04350.00001.0062212130.00160.04350.00001.0062313140.00090.01010.172302414150.00180.02170.366002515160.00090.00940.171002616170.00070.00890.134202716190.00160.01950.304002816210.00080.01350.254802916240.00030.00590.068003017180.00070.00820.131903117270.00130.01730.321603219200.00070.01380.00001.063319330.00070.01420.00001.073420340.00090.01800.00001.0093521220.00080.01400.256503622230.00060.00960.184603722350.00000.01430.00001.0253823240.00220.03500.361003923360.00050.02720.000014025260.00320.03230.531004125370.00060.02320.00001.0254226270.00140.01470.239604326280.00430.04740.780204426290.00570.06251.029004528290.00140.01510.249004629380.00080.01560.00001.025Figure 18
IEEE 39 bus test system [49].The aggregate capacity of the IEEE 39-bus system is 6140.80 MW while the total connected load is 6097.1 MW. Bus number 39 is taken as the slack bus. All generators in this standard system are modeled as 4th-order synchronous machines equipped with standard IEEE models of automatic voltage regulators, excitation systems, governor systems, and power system stabilizers.Elzemeity et al. in [49] investigate the optimal location of WPPs in the IEEE 39 bus system by sorting the possible locations in ascending order of electromechanical oscillations using Eigenvalue analysis. The best five locations with less electromechanical oscillations are obtained as buses 30, 37, 31, 32, and 36, respectively. These findings agree with Essalah et al. in [50] in which buses 30, 34, 37, and 39 are obtained as the optimal location for WPPs, and Shi et al. in [51] who obtain optimal locations as buses 38 and 37. El-Samanoudy et al. in [52] also assess the impact of large-scale wind generation on the IEEE 39 bus system based on voltage stability and conclude that the integrated wind power generation should not exceed 20% for system stability.In this work, the synchronous generators in bus 30 and bus 37 were replaced with the same amount of active power generation, and reactive power needs were met by installing capacitors. This ensured the same system operating conditions were maintained. The 250 MW, 162 MVAr (bus 30) and 540 MW, −1.4 MVAr (bus 37) synchronous generators were replaced by wind farms equipped with GE 1.5 MW DFIG generators. The penetration level of wind power generation is therefore 12%. Two STATCOMs are also integrated at the point of wind power integration into the grid. Similarly, the STATCOMs are tuned using WCA, PSO, and WCA-PSO optimization algorithms. To investigate the LVRT capability of the WPPs, the LLL-G fault was simulated online 16–17. This fault location has been identified by Arredondo et al. in [53] and Yakout et al. in [54], as the most severe line loss which can lead to transient stability. The IEEE 39 bus test system was thus subjected to LLL-G, online 16–17 for 150 ms, to evaluate the German electric utility LVRT capability requirement. The assumptions for wind speed, simulation time, and crowbar configuration are the same as in the 9 MW test system.


## 4.6. LLL-G Fault

### 4.6.1. WPP Active Power Output

The active power output of the 250 MW (WPP 1) for the LLL-G grid fault of 150 ms is given in Figure19.Figure 19
WPP 1 active power output.From Figure19, during the LLL-G fault, the active power output of WPP 1 rapidly drops from about 245 MW up to −35 MW for the cases without a STATCOM, with conventional and with PSO tuned STATCOM. For the WCA tuned STATCOM, the lowest output is −20 MW whereas for WCA-PSO tuned STATCOM, the lowest output is 20 MW. For all the scenarios, the WPP stays online, although it only generates active power when WCA-PSO tuned STATCOM is incorporated. The WCA-PSO tuned STATCOM gives the best outcome, in which it injects maximum reactive power of 110 MVAr, and the GSC regulates active power generation. The WPP thus rides through the LLL-G fault due to the voltage support provided at the PCC for all scenarios. When the fault is cleared, active power generation quickly recovers to its prefault value. The active power output of the 540 MW (WPP 2) is given in Figure 20, in which the WPP can ride through the LLL-G fault in all scenarios.Figure 20
WPP 2 active power output.


### 4.6.2. Voltage Magnitude at WPP 1 Terminals

The voltage profile at WPP 1 terminals is shown in Figure21 for the LLL-G grid fault of 150 ms.Figure 21
Voltage profile at WPP terminals.From Figure21, for WPP 1 at bus 30, some voltage fluctuations are observed. Voltage magnitude drops from 1 p.u. to 0.88 p.u. without STATCOM, whereas for the tuned models, the lowest voltage magnitude is 0.94 p.u. Voltage fluctuations are minimum at the WPP terminals during, and after fault clearance for WCA-PSO tuned STATCOM. The voltage profile at the terminals of WPP 2 at bus 37 is given in Figure 22.Figure 22
Voltage profile at WPP terminals.For the second WPP, voltage fluctuations during the LLL-G fault are minimal, and the WPP rides through the grid fault. The WCA-PSO tuned STATCOM scenario has a better profile.


### 4.6.3. WPP Reactive Power Output

The reactive power output of WPP 1 for LLL-G grid fault of 150 ms is given in Figure23.Figure 23
WPP 1 reactive power output.The GSC injects reactive power, to aid grid recovery. The highest transients are seen for the WCA model, whereas WCA-PSO has a smoother output.From Figure24, without a STATCOM, when the LLL-G grid fault occurs, the GSC injects up to 350 MVAr to support voltage at the WPP terminals. With STATCOM incorporation, GSC injects less reactive power, with the least amount of reactive injected for WCA-PSO tuned STATCOM, 170 MVAr. The WPP stays online, thus the DFIG generates active power during the grid fault. Reactive power oscillations are higher for conventional STATCOM as opposed to WCA-PSO tuned STATCOM.Figure 24
WPP 2 reactive power output.


### 4.6.4. DC Capacitor Link Voltage

The DC link capacitor voltage of the DFIG in 250 MW WPP for LLL-G grid fault of 150 ms is shown in Figure25.Figure 25
WPP 1 DC link capacitor voltage.From Figure25, the DC link capacitor voltage fluctuates from a reference value of 1200 V to around 1135 V at the onset of the voltage sag and back to about 1270 V at the end of the fault period, when a STATCOM is not used. The WCA-PSO tuned STATCOM results in the least fluctuations. The DC capacitor voltage for WPP 2 is shown in Figure 26 in which the fluctuations are about ±2%, which is within a safe operating range.Figure 26
WPP 2 DC link capacitor voltage.


## 4.6.1. WPP Active Power Output

The active power output of the 250 MW (WPP 1) for the LLL-G grid fault of 150 ms is given in Figure19.Figure 19
WPP 1 active power output.From Figure19, during the LLL-G fault, the active power output of WPP 1 rapidly drops from about 245 MW up to −35 MW for the cases without a STATCOM, with conventional and with PSO tuned STATCOM. For the WCA tuned STATCOM, the lowest output is −20 MW whereas for WCA-PSO tuned STATCOM, the lowest output is 20 MW. For all the scenarios, the WPP stays online, although it only generates active power when WCA-PSO tuned STATCOM is incorporated. The WCA-PSO tuned STATCOM gives the best outcome, in which it injects maximum reactive power of 110 MVAr, and the GSC regulates active power generation. The WPP thus rides through the LLL-G fault due to the voltage support provided at the PCC for all scenarios. When the fault is cleared, active power generation quickly recovers to its prefault value. The active power output of the 540 MW (WPP 2) is given in Figure 20, in which the WPP can ride through the LLL-G fault in all scenarios.Figure 20
WPP 2 active power output.


## 4.6.2. Voltage Magnitude at WPP 1 Terminals

The voltage profile at WPP 1 terminals is shown in Figure21 for the LLL-G grid fault of 150 ms.Figure 21
Voltage profile at WPP terminals.From Figure21, for WPP 1 at bus 30, some voltage fluctuations are observed. Voltage magnitude drops from 1 p.u. to 0.88 p.u. without STATCOM, whereas for the tuned models, the lowest voltage magnitude is 0.94 p.u. Voltage fluctuations are minimum at the WPP terminals during, and after fault clearance for WCA-PSO tuned STATCOM. The voltage profile at the terminals of WPP 2 at bus 37 is given in Figure 22.Figure 22
Voltage profile at WPP terminals.For the second WPP, voltage fluctuations during the LLL-G fault are minimal, and the WPP rides through the grid fault. The WCA-PSO tuned STATCOM scenario has a better profile.


## 4.6.3. WPP Reactive Power Output

The reactive power output of WPP 1 for LLL-G grid fault of 150 ms is given in Figure23.Figure 23
WPP 1 reactive power output.The GSC injects reactive power, to aid grid recovery. The highest transients are seen for the WCA model, whereas WCA-PSO has a smoother output.From Figure24, without a STATCOM, when the LLL-G grid fault occurs, the GSC injects up to 350 MVAr to support voltage at the WPP terminals. With STATCOM incorporation, GSC injects less reactive power, with the least amount of reactive injected for WCA-PSO tuned STATCOM, 170 MVAr. The WPP stays online, thus the DFIG generates active power during the grid fault. Reactive power oscillations are higher for conventional STATCOM as opposed to WCA-PSO tuned STATCOM.Figure 24
WPP 2 reactive power output.


## 4.6.4. DC Capacitor Link Voltage

The DC link capacitor voltage of the DFIG in 250 MW WPP for LLL-G grid fault of 150 ms is shown in Figure25.Figure 25
WPP 1 DC link capacitor voltage.From Figure25, the DC link capacitor voltage fluctuates from a reference value of 1200 V to around 1135 V at the onset of the voltage sag and back to about 1270 V at the end of the fault period, when a STATCOM is not used. The WCA-PSO tuned STATCOM results in the least fluctuations. The DC capacitor voltage for WPP 2 is shown in Figure 26 in which the fluctuations are about ±2%, which is within a safe operating range.Figure 26
WPP 2 DC link capacitor voltage.


## 5. Conclusion

In this paper, the LVRT capability of grid-connected DFIG-based WPPs is investigated against requirements for the German utility grid. The STATCOM has been used for reactive power compensation to enhance LVRT capability and improve the dynamic performance of grid-connected WPPs. STATCOM controller tuning has been done using WCA, PSO, and WCA-PSO hybrid algorithms. The WCA is a recent optimizer which has not been previously employed in power system applications such as controller tuning. The validity of the proposed STATCOM controller tuning approach was verified duringL-G and LLL-G grid faults for 150 ms. Simulations were conducted in MATLAB programming language using the SimScape toolbox, for the 9 MW WPP test system and the IEEE 39 bus test system. Performance comparison was done for conventional, WCA, PSO, and WCA-PSO tuned STATCOM, in terms of voltage profiles, active and reactive power, under L-G and LLL-G faults independently. For the 9 MW test system, the LVRT capability of the German power system was met for L-G faults. During the L-G fault, voltage magnitude drops from 1 p.u. to 0.76 p.u. without STATCOM, whereas for the tuned models, the lowest voltage magnitude is 0.9 p.u. During LLL-G faults, without, with conventional, and with PSO tuned STATCOMs, the WPP could not ride through the fault. When WCA and WCA-PSO tuned STATCOM was incorporated, the German LVRT capability requirement for the 9 MW test system was met. During the LLL-G fault, the voltage at the WPP terminal drops to 0 p.u. for cases without, with conventional, and with PSO tuned STATCOM, whereas WCA and WCA-PSO tuned STATCOM have the lowest voltage magnitude of 0.45 p.u. and 0.55 p.u., respectively. The two WPPs installed in the IEEE 39 bus test system were able to ride through the LLL-G grid fault. Voltage magnitude drops from 1 p.u. to 0.88 p.u. without STATCOM, while for the tuned models, the lowest voltage magnitude is 0.94 p.u. In all test scenarios, WCA-PSO tuned STATCOM utilization resulted in less voltage and active and reactive power overshoots. However, transients were observed at the beginning and end of the fault period. Since the STATCOM provides reactive power support, an additional technique of limiting the fault current can be incorporated, such as the FCL, SDBR, or a DC chopper, thus ensuring that the WPP meets LVRT capability requirements during LLL-G faults. The proposed tuned STATCOM can also be investigated in the enhancement of LVRT GCRs for other utility grids such as Denmark, the USA, or any other country, as given in Table 1. WCA-PSO algorithm can further be applied in various power system optimization problems. STATCOM controller tuning using other metaheuristic optimization algorithms should be explored further and evaluated on larger practical power systems, under different grid faults.



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*Source: 2873053-2022-06-25.xml*