## Wind energy conversion system using perturb & observe-based maximum power point approach interfaced with T-type three-level inverter connected to grid

**Abstract**

Abstract In this paper, the performance of a permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS) supplied to an uncontrolled rectifier-fed boost converter (BC) interfaced with a three-phase T-type three-level inverter (TLI) has been analysed. The proposed WECS involves three converters, namely an uncontrolled rectifier that is used for conversion from AC to DC; a BC supplied by a PMSG-fed rectifier used to enhance the voltage gain; and a grid-connected three-phase T-type TLI is proposed to eliminate power-quality issues with synchronization of grid voltage and current. The main goal of this research is to model and control the grid-connected T-type TLI using a d–q synchronous frame for wind energy for regulating the DC-link voltage and transferring the generated wind power from the BC to the grid. Furthermore, the perturb & observe (P&O)-based maximum power point (MPP) approach is recommended to keep track of the MPP for a BC that is supplied from a PMSG-based WECS under constant and variable wind speeds. The proposed PMSG-based WECS interfaced with grid-connected T-type TLI using d–q control has been computationally modelled, simulated and validated with constant and variable speeds using MATLAB® and Simulink®. It is confirmed that the P&O-based MPP approach ensures maximum power for varying wind speeds, and the total harmonic distortion of the T-type TLI grid current value is 3.18%, which is within IEEE-519 limits. Furthermore, with grid synchronization, the power factor of the T-type TLI is maintained at unity to avoid power-quality issues. Open in new tabDownload slide boost converter, grid synchronization, perturb & observe, T-type three-level inverter, wind turbine Introduction The continuing economic progress as well as the advancement of power electronic technology are driving an increase in worldwide energy demand. Renewable energy sources (RESs) are, on the other hand, believed to be an operative solution to environmental concerns such as carbon dioxide. Inadequate amounts of energy are being used to generate electricity and greenhouse gas emissions, and contribute to the warming of the planet [1–3]. Furthermore, the use of RESs is gaining significant momentum all over the world. Emissions are not caused by sunlight, wind, waterfalls or plant growth [4–6]. Currently, the production of electricity with the assistance of wind power is becoming increasingly popular, i.e. wind energy installations have increased dramatically in recent years. High levels of innovation and interest in wind power systems have been evident all across the world. In 2018, the total amount of installed wind power capacity reached 599 GW and, further, it increased to 645 GW in 2019 with a growth rate of 7% [7]. The Global Wind Energy Council showed different scenarios in which wind energy systems might be able to generate 2110 GW of power by 2030, which would meet 20% of the world’s needs [8]. The wind energy conversion system (WECS) comprises a wind turbine, an electrical generator, power converters and controllers. It is possible to use wind turbines with either a fixed-speed or a variable-speed mode [9, 10]. Due to fixed-speed functioning, all variations in wind speed are conveyed first as variations in mechanical torque and then as variations in electrical power on the grid. Power fluctuations can also contribute to severe voltage variations in weak grids, resulting in significant losses on the transmission lines as well [11, 12]. With an increase in installed wind turbines in recent years, wind turbines with variable speeds have emerged as the dominant form to maximize aerodynamic efficiency and generate electricity at a variable speed. By employing variable-speed turbines, it has been feasible to continually adjust the rotational speed of the turbine in response to changes in the wind speed [13]. It is more complicated to design a variable-speed wind turbine than a fixed-speed one. It is often fitted with a synchronous or induction generator and is connected to the power grid via a suitable power converter to provide electricity [14]. The perturb & observe (P&O)-based MPP approach allows speed control at all times, even in high-wind conditions. The presented model is well suited for smaller wind turbines as well [15, 16]. With the P&O approach, power fluctuation is eliminated by variable wind conditions and the best possible link between them, tracking the PMSG-fed rectifier’s output voltage and current ideal location. However, tracking becomes less effective when using a single optimum constant. In the hill-climb search algorithm, there is a trade-off between speed and efficiency, and incorrect results during rapidly changing wind speeds. For a variable wind speed, the presented P&O approach is more effective for tracking the MPP. This paper proposes a boost converter (BC) supplied by a permanent magnet synchronous generator (PMSG)-based WECS using a P&O-based MPP approach interfaced with a grid-connected T-type three-level inverter (TLI). Typically, three converters are used: the first converter, i.e. the rectifier, is connected to the generator; the second converter, i.e. the BC supplied by the WECS with a PMSG-fed rectifier; and the third converter, i.e. the T-type multilevel inverter (MLI) is associated with the grid [17–19]. The first converter function is to regulate the generator’s rotational speed in the most efficient manner and convert it to DC; the second converter function is to enhance the voltage gain; and the P&O-based MPP approach is advised for monitoring the MPP of BC supplied by the PMSG-based WECS at constant and fluctuating wind speeds [20, 21]. The third converter function, i.e. MLI, is to interface it to the grid using d–q control for maintaining a unity power factor [22, 23]. MLIs have generated considerable interest over RESs, in part because of their broad voltage and current rating ranges. The MLIs are classified as neutral-point-clamped (NPC) or diode-clamped (DC) [24, 25], capacitor-clamped (CC) [26, 27] and cascaded MLIs [28, 29]. Each of these topologies has numerous drawbacks. The NPC MLI requires additional clamping diodes; the CC MLI uses more capacitors and necessitates greater capacitor maintenance; and the cascaded MLIs necessitate the use of several isolated DC sources. To overcome these disadvantages, Madasamy et al. [30] presented a T-type MLI. The T-type MLIs have an advantage over the NPC inverters as they do not need clamping diodes to hold the neutral point to negative or positive DC voltages. Clamping is accomplished in T-type MLIs by connecting an active bidirectional power switch. Furthermore, sine modulation is used in T-type TLI power switches. This paper describes the performance of a T-type TLI interfaced to the grid via d–q control and a PMSG-based WECS. In addition, the paper presents the modelling of wind turbines with their characteristics; modelling of PMSG; BC operation and its control to obtain MPP utilizing P&O to track maximum power. The performance has been evaluated in terms of turbine characteristics for different values of pitch angle, PMSG DC-link voltage, rotor speed, torque, DC power output, BC output, TLI output voltages with harmonic analysis and overall system grid synchronization using phase-locked loop (PLL) control to avoid power-quality issues by maintaining a unity power factor. Furthermore, the performance of T-type TLI has been assessed using the sine-modulation method with variation of the modulation index (MI) from 0.5 to 1. Finally, the proposed PMSG-based WECS results are validated using MATLAB® and Simulink® with uniform and variable wind speeds. 1 WECS using PMSG Fig. 1 depicts the typical functional organization of a WECS using PMSG. It comprises a wind turbine, a PMSG-fed rectifier, a DC–DC BC, P&O-based MPP control, a T-type TLI and grid synchronization using d–q control. An in-depth model of a wind turbine with uniform and non-uniform wind speeds using PMSG has been analysed and it is converted into DC using a three-phase diode rectifier. Further, the output of the diode rectifier is integrated with BC using a P&O-based MPP approach to enhance the voltage gain due to the decrease in voltage gain at low wind speeds. Finally, the output of BC is interfaced with a grid-connected T-type TLI to improve the power quality using d–q control. Fig. 1: Open in new tabDownload slide Block diagram of WECS using PMSG interfaced to T-type TLI. 1.1 Wind-turbine model Fig. 2 depicts the model of WECS, which includes a wind model, an aerodynamic component and a mechanical component. The blades of the wind turbine absorbed wind energy, which was then converted into mechanical energy by the turbine. The results of a horizontal-axis wind-turbine mathematical model are presented in this study along with their characteristics. Fig. 2: Open in new tabDownload slide Model of WECS. The kinetic energy (KE) of the wind is captured by turbine blades and converted into mechanical energy. The KE of mass m moving at a speed of v is calculated using Equation (1): E=12mv2(1) Assuming a constant speed, the moving air power Pw is calculated using Equation (2): Pw=dEdt(2) Using Equations (1) and (2), the Pw is given by Equation (3): Pw=12dmdtv2(3) where the rate of mass flow is: dmdt=ρAv(4) Wind turbines use aerodynamic power [1]. Therefore, the wind turbine’s mechanical power is provided by Equation (5): Pm=12ρAv3Cp(λ,β)(5) where ρ represents the air density = 1.225 kg/m3, A represents the swept area of the blade, v represents the wind speed, λ represents the tip-speed ratio (TSR), β represents the pitch angle and Cp represents the power coefficient with the function of λ and β . The TSR λ of the wind turbine is given by Equation (6): λ=ωRVω(6) The wind-turbine swept area A of each blade is given by Equation (7): A=πR2(7) The power coefficient Cp(λ,β)is given by Equation (8): Cp(λ,β)=K1(K2λi−K3β−K4)e(−K5/λi)+K6(λi1+0.035λi)(8) Where,λi=(1λ+0.08β−0.035β3+1)−1(9) where the coefficients of Equation (8) are estimated as K1 = 0.5176, K2 = 116, K3 = 0.4, K4 = 5, K5 = 21 and K6 = 0.0068. According to Betz’s limit, Cp reaches a maximum value of 59.26% in the ideal scenario, meaning that wind-derived power is rarely greater than this value [2]. In other words, wind power is never >50% efficient due to the poor conversion of power, which causes various sorts of losses because of the generator rotor’s design, which takes into account factors such as weight, rigidity, structure and blade count, and the actual value is lower than the theoretical maximum [3]. When it comes to wind-turbine performance power coefficient Cp and TSR, optimum TSR values yield the highest value of Cp in all operational scenarios. As Fig. 3 shows, the variation in power coefficient Cp relates to the optimal values of TSR for various pitch angles, i.e. β = 0, 2, 4, 6, 8, 10 and 12°C. The output power (Pm) fluctuates with the angular velocity ωm by varying the wind speed. Fig. 4 depicts the per-unit power characteristics of a turbine as a function of β and turbine speed. Fig. 3: Open in new tabDownload slide Characteristics of Cp versus λ for various pitch angles. Fig. 4: Open in new tabDownload slide Turbine power characteristics for β = 0 degree. From Equations (5) and (7), the rotor aerodynamic torque Tw can be calculated using Equation (10): Tω=Pmωm=12ρAv3Cp(λ,β)ωm=12ρπR2v3Cp(λ,β)ωm(10) 2 Mathematical model of PMSG A PMSG has a fixed flux because it has a permanent magnet in it. There are many reasons to prefer PMSG rather than an induction generator. PMSG is preferred as an AC wind generator for WECS due to its high power density, compact size as the gearbox is eliminated, reduced losses and robustness. Therefore, the WECS using PMSG is a good choice for a wind-turbine generator, especially if the wind speed is low enough that the number of poles can be high enough to get a proper frequency. The PMSG is modelled using DC voltages and currents in a d–q reference frame [4]. The rotor currents id and iq are linear functions of the sinusoidal flux distributions ψd and ψq in synchronous machines, which are provided by Equation (11): ψd=Ldsids+ψfandψq=Lqsiqs(11) where Lds represents the d-axis stator inductance, ids represents the d-axis stator current, ψf represents the magnetic flux, Lqs represents the q-axis stator inductance and iqs represents the q-axis stator inductance. In the rotor reference frame, the voltage equations Vds and Vqs of PMSG powered by a wind turbine are represented by Equations (12) and (13), respectively: Vds=−rsids+Ldsddtids+ωrLqsiqs(12) Vqs=−rsiqs+Lqsddtiqs−ωrLdsids+ωrddtψds(13) The electromagnetic torque Tem equation of the rotor is given by Equation (14): Tem=32.P2[idsiqs(Lds−Lqs)+iqsddtψds](14) where rs represents the stator resistance, ψds represents the d-axis stator flux and P represents the number of poles. 2.1 Modelling of PMSG with three-phase rectifier Fig. 5 shows the steady-state model of a non-salient-type PMSG for considering single phase. Fig. 6 shows the uncontrolled diode rectifier configuration with the PMSG three-phase model. It consists of six passive diodes at the generator side in the form of a bridge fashion to convert generator AC power to DC power, and the wind-turbine generator’s output current can only flow towards the grid with this power converter, meaning that there is only one direction in which electricity may flow. Fig. 5: Open in new tabDownload slide Steady-state model of PMSG. Fig. 6: Open in new tabDownload slide PMSG three-phase model fed uncontrolled diode rectifier. From Kiran et al. [5], the rectifier’s average DC output voltage is represented by Equation (15). There are two terms in Equation (15): the first term signifies the DC output voltage of the rectifier without commutation. The second term signifies the voltage drop due to a commutation process triggered by synchronous reactance: Vdc=33πωrΨpm−3πXsio(15) where ψpm represents the flux linkage in the stator, Xs represents the synchronous reactance, io represents the rectifier output current and ωr Ψ pm represents the stator-induced voltage. 3 Modelling of DC–DC BC supplied by WECS-based PMSG-fed rectifier The circuit representation of BC using P&O-based MPP control powered by PMSG-fed rectifier-based WECS is represented in Fig. 7. Fig. 7: Open in new tabDownload slide BC with PMSG-fed rectifier-based WECS using P&O MPP control. In the BC, there is an inductor, a metal-oxide-semiconductor field-effect transistor (MOSFET), a diode and a capacitor that stores the extra energy. It works in two ways due to the presence of a power switch. In the first mode, the switch M is closed when it stores energy and releases it when it is open. In this mode, the power switch turns at the moment t = 0 to t = DT. In the second mode, the power switch is turned off at t = DT. As long as the switch is open, the inductor gives off energy and the capacitor stores energy. The voltage gain of the BC supplied by the PMSG-based WECS can be represented by Equation (16). In this paper, a P&O-based MPP approach has been used to trigger the power switch to extract the MPP from the PMSG-based WECS for the various wind speeds: Vo=(11−D)∗Vdc(16) where D represents the duty ratio. 3.1 P&O-based MPP approach The P&O-based MPP is a simple way to keep track of the MPP for a BC that is supplied from a WECS using a PMSG-fed rectifier. Fig. 7 represents the flowchart of P&O-based MPP control. The P&O-based MPP approach allows speed control at all times, even in high-wind conditions. For variable wind speeds, the presented P&O approach is more efficient for tracking the MPP. The presented model is well suited for smaller wind turbines as well. In this method, a small amount of disturbance is used to make the power of the WECS system fluctuate. Each time the rectifier’s average DC output power is measured, it is compared to the previous output. This method changes the average DC output voltage of the WECS for a given duty ratio. 4 T-type MLIs T-type inverters are a new breed of MLIs that offer higher efficiency than NPC inverters while operating at medium switching frequencies, i.e. 5–30 kHz. The T-type MLIs have an advantage over the NPC inverters because they do not need clamping diodes to hold the neutral point to negative or positive DC voltages. Clamping is accomplished in T-type MLIs by connecting an active bidirectional power switch between the midpoints of each phase leg and the midpoints of series linked DC-link capacitors. Furthermore, T-type MLIs have less total harmonic distortion (THD) than NPC inverters. In this paper, the T-type MLI for the three-phase type has been explored in terms of its configuration, switching states and sine-modulation method. Finally, the presented T-type TLI has been connected to the grid using the d–q control method to maintain good power quality. 4.1 Modelling and operation of T-type TLI Fig. 9 shows the configuration of three-phase T-type TLI. For m-levels, it necessitates (m–1) DC bus capacitors, 6(m–1) power switches and 6(m–1) main diodes connected in anti-parallel to the power switches to generate (2m–1) levels across the load. Consequently, a three-phase T-type MLI requires two DC bus capacitors, 12 power switches and 12 main diodes to produce five levels across any two phases. The operation of the T-type TLI is explicated in the form of three switching states, namely positive state, negative state and zero states, which are represented in Table 1 to generate zero level, +Vdc/2 and –Vdc/2 levels, respectively [13, 14]. Table 1: Switching states of T-type TLI to generate three levels per phase Operating state . Conducting switches . Output voltage . Positive S1AS2A/ S1BS2B/ S1CS2C +Vdc/2 Negative S3AS4A/ S3BS4B/ S3CS4C –Vdc/2 Zero S2AS3A/ S2BS3B/ S2CS3C 0 Operating state . Conducting switches . Output voltage . Positive S1AS2A/ S1BS2B/ S1CS2C +Vdc/2 Negative S3AS4A/ S3BS4B/ S3CS4C –Vdc/2 Zero S2AS3A/ S2BS3B/ S2CS3C 0 Open in new tab Table 1: Switching states of T-type TLI to generate three levels per phase Operating state . Conducting switches . Output voltage . Positive S1AS2A/ S1BS2B/ S1CS2C +Vdc/2 Negative S3AS4A/ S3BS4B/ S3CS4C –Vdc/2 Zero S2AS3A/ S2BS3B/ S2CS3C 0 Operating state . Conducting switches . Output voltage . Positive S1AS2A/ S1BS2B/ S1CS2C +Vdc/2 Negative S3AS4A/ S3BS4B/ S3CS4C –Vdc/2 Zero S2AS3A/ S2BS3B/ S2CS3C 0 Open in new tab 4.2 Modulation of three-phase T-type TLI Three-phase sine-modulation control is explicated to turn on the power switches used in the three-phase T-type TLI. Fig. 10 shows the methodology for generating pulses for the T-type TLI. The control circuit of the T-type TLI uses three sine waves (VrefA, VrefB and VrefC) that are shifted by a 1200 phase shift and two triangular carrier waves (Vtri1 and Vtri2) that are in the same phase. 5 Control of grid-connected T-type TLI A grid-connected three-phase T-type TLI with d–q synchronous frame control is described in Fig. 11. Reduced harmonics in the currents can be achieved by using an LCL filter (where ‘L’ stands for inductance and ‘C’ stands for capacitance) on the T-type TLI. There are two inverter control loops in a T-type TLI interfaced to the grid. The T-type TLI DC-link voltage is controlled by the inner control loop in order to ensure the system’s stability during dynamic conditions. The current injected into the grid-connected T-type TLI is controlled by the outer control loop using a sine-modulation approach with low harmonic distortions. The decoupled current control approach is responsible for power-quality issues and the adjustment of current harmonics. The current control loop also makes use of a PLL device to provide a synchronized reference voltage. The phase angle is utilized for the two-phase transformation, once the frequency and phase have been detected by the PLL from the grid system (abc to dq). The PI controller will be used to manage the voltage and current of these two separate signals. Park’s transformation is used to change the controlled signals into three-phase control signals, i.e. dq to abc. Formulas for expressing three-phase control signals abc to the dq axis and dq–abc are represented in Equations (17) and (18), respectively: [iaibic]=32[230−1333−13−33][iαiβ](17) [VdVq]=23[1−12−12032−32][VaVbVc](18) In order to obtain the d-axis reference current (id*), the T-type TLI output voltage is also taken into consideration. The grid-connected T-type TLI regulates reactive power by feeding the error into a proportional–integral (PI) current controller. The measured T-type TLI output power regulates the controller’s output power. Gains in PI controllers are all based on the difference between the measured voltage and the reference voltage as an input error. The sine-modulation method generates switching signals for the switches used in T-type TLI using current components references ian*, ibn* and icn*, respectively. 6 Results and discussion The simulation of WECS using PMSG supplied to a BC interfaced with a T-type TLI has been analysed using MATLAB® and Simulink® for power-quality improvement. Table 2 exemplifies the parameters and specifications of the proposed WECS system using PMSG. The P&O-based MPP control of the BC supplied by the PMSG has been simulated by taking into account both fixed and variable wind speeds. Table 2: Parameters and specifications of proposed WECS system using PMSG WECS system using PMSG parameters . Value . Wind turbine using PMSG parameters and specifications Round-rotor-type three-phase – Number of pole pairs 15 Rated speed 300 rpm Wind speed Varies from 4 to 12 m/s Air density (ρ) and radius (r) ρ = 1.225 kg/m and r = 40 m BC interfaced with grid-connected T-type TLI parameters L and C of BC L = 80 mH and C = 50 µF Duty cycle (D) 0.5 Switching frequency 25 kHz for BC and 10 kHz for TLI LCL filter for T-type TLI L = 500 mH, C = 100 µF WECS system using PMSG parameters . Value . Wind turbine using PMSG parameters and specifications Round-rotor-type three-phase – Number of pole pairs 15 Rated speed 300 rpm Wind speed Varies from 4 to 12 m/s Air density (ρ) and radius (r) ρ = 1.225 kg/m and r = 40 m BC interfaced with grid-connected T-type TLI parameters L and C of BC L = 80 mH and C = 50 µF Duty cycle (D) 0.5 Switching frequency 25 kHz for BC and 10 kHz for TLI LCL filter for T-type TLI L = 500 mH, C = 100 µF Open in new tab Table 2: Parameters and specifications of proposed WECS system using PMSG WECS system using PMSG parameters . Value . Wind turbine using PMSG parameters and specifications Round-rotor-type three-phase – Number of pole pairs 15 Rated speed 300 rpm Wind speed Varies from 4 to 12 m/s Air density (ρ) and radius (r) ρ = 1.225 kg/m and r = 40 m BC interfaced with grid-connected T-type TLI parameters L and C of BC L = 80 mH and C = 50 µF Duty cycle (D) 0.5 Switching frequency 25 kHz for BC and 10 kHz for TLI LCL filter for T-type TLI L = 500 mH, C = 100 µF WECS system using PMSG parameters . Value . Wind turbine using PMSG parameters and specifications Round-rotor-type three-phase – Number of pole pairs 15 Rated speed 300 rpm Wind speed Varies from 4 to 12 m/s Air density (ρ) and radius (r) ρ = 1.225 kg/m and r = 40 m BC interfaced with grid-connected T-type TLI parameters L and C of BC L = 80 mH and C = 50 µF Duty cycle (D) 0.5 Switching frequency 25 kHz for BC and 10 kHz for TLI LCL filter for T-type TLI L = 500 mH, C = 100 µF Open in new tab 6.1 BC supplied by PMSG-fed rectifier-based WECS at uniform wind speed The PMSG DC-link voltage and rotor speed waveforms with a uniform wind speed of 12 m/s are shown in Figs 12a and b. The corresponding values are 337.6 V and 278.1 rad/sec, respectively. Fig. 13a and b demonstrates the PMSG torque and output power waveforms, respectively, with a uniform wind speed of 12 m/s. The corresponding values are 22.91 N-m and 4791 watts, respectively. Fig. 14a and b demonstrates the voltage and output power waveforms of the BC using the P&O-based MPP approach supplied by the PMSG-based WECS, respectively, with a uniform wind speed of 12 m/s. The corresponding values are 674.5 V and 4550 watts, respectively. The output of the BC is increased from 337.6 to 674.5 V for a 0.5 duty cycle. 6.2 BC supplied by PMSG-fed rectifier-based WECS with a wind speed variation Further, the waveforms of the BC using the P&O-based MPP approach supplied by the PMSG-based WECS are verified by considering the variable wind speed profile as shown in Fig. 15. It depicts the non-uniform wind speeds of 12, 10 and 8 m/s. The uniform wind speed of 10 m/s is considered from 0 to 4 seconds, 12 m/s from 4 to 8 seconds, 8 m/s from 8 to 12 seconds and 10 m/s from 12 to 15 seconds. Fig. 16a and b shows the PMSG DC-link voltage and rotor speed waveforms, respectively, for various wind speeds. It is observed that at 12 m/s, the values of the PMSG DC-link voltage and rotor speed are 337.6 V and 278.1 rad/s, respectively. Similarly, at 10 and 8 m/s, the values of the PMSG DC-link voltages are 279.4 and 219.7 V, respectively, and the corresponding values of rotor speed are 228 and 177.7 rad/s, respectively. From Fig. 16a, it is observed that the output voltage at 12 m/s is higher than those at 10 and 8 m/s. Therefore, wind turbines produce higher voltages as the speed of the wind increases. Similarly, from Fig. 16b, it is observed that the power output at 12 m/s is higher than those at 10 and 8 m/s. Therefore, wind turbines produce more power as the speed of the wind increases. Fig. 8: Open in new tabDownload slide Flowchart of P&O-based MPP control. Fig. 17a and b shows the PMSG torque and output power waveforms, respectively, for various wind speeds. It is observed that at 12 m/s, the values of PMSG torque and output power are 22.91 N-m and 4791 watts, respectively. Similarly, at 10 and 8 m/s, the values of PMSG torque are 18.82 and 14.93 N-m, respectively, and the equivalent values of output power are 3214 and 1998 watts, respectively. Fig. 18a and b shows the BC output voltage and power waveforms using the P&O-based MPP approach supplied by the PMSG-based WECS for various wind speeds. It is observed that at 12 m/s, the values of output voltage and power are 337.6 V and 4550 watts, respectively. Similarly, at 10 and 8 m/s, the values of output voltages are 555 and 434.9 V, respectively, and the equivalent values of output power are 3081 and 1891 watts, respectively. Table 3 shows the results of PMSG DC-link voltage, rotor speed, torque, DC power output, BC output voltage and power for various wind velocities. From Table 3, it is observed that the wind turbines produce more power as the speed of the wind increases, along with an increase in voltage, torque and rotor speed. Table 3: Simulation results of WECS with wind speed variation Wind velocity (m/s) . Rotor speed (rad/s) . Torque (N-m) . PMSG-fed rectifier outputs . . BC outputs . . . . . Voltage(V) . Power (watts) . Voltage (V) . Power (watts) . 12 278.1 22.91 337.6 4791 674.5 4550 11 253 20.85 307.9 3955 614.7 3778 10 228 18.82 279.4 3214 555 3081 9 202.7 16.95 248.7 2580 495 2450 8 177.7 14.93 219.7 1998 434.9 1891 7 152.8 12.93 190.6 1496 374.6 1403 6 128.2 10.8 155.7 1030 314.5 989.2 5 103.4 8.85 130.8 696.2 254.4 647.1 4 79.28 6.75 94.05 387 195.7 382.9 Wind velocity (m/s) . Rotor speed (rad/s) . Torque (N-m) . PMSG-fed rectifier outputs . . BC outputs . . . . . Voltage(V) . Power (watts) . Voltage (V) . Power (watts) . 12 278.1 22.91 337.6 4791 674.5 4550 11 253 20.85 307.9 3955 614.7 3778 10 228 18.82 279.4 3214 555 3081 9 202.7 16.95 248.7 2580 495 2450 8 177.7 14.93 219.7 1998 434.9 1891 7 152.8 12.93 190.6 1496 374.6 1403 6 128.2 10.8 155.7 1030 314.5 989.2 5 103.4 8.85 130.8 696.2 254.4 647.1 4 79.28 6.75 94.05 387 195.7 382.9 Open in new tab Table 3: Simulation results of WECS with wind speed variation Wind velocity (m/s) . Rotor speed (rad/s) . Torque (N-m) . PMSG-fed rectifier outputs . . BC outputs . . . . . Voltage(V) . Power (watts) . Voltage (V) . Power (watts) . 12 278.1 22.91 337.6 4791 674.5 4550 11 253 20.85 307.9 3955 614.7 3778 10 228 18.82 279.4 3214 555 3081 9 202.7 16.95 248.7 2580 495 2450 8 177.7 14.93 219.7 1998 434.9 1891 7 152.8 12.93 190.6 1496 374.6 1403 6 128.2 10.8 155.7 1030 314.5 989.2 5 103.4 8.85 130.8 696.2 254.4 647.1 4 79.28 6.75 94.05 387 195.7 382.9 Wind velocity (m/s) . Rotor speed (rad/s) . Torque (N-m) . PMSG-fed rectifier outputs . . BC outputs . . . . . Voltage(V) . Power (watts) . Voltage (V) . Power (watts) . 12 278.1 22.91 337.6 4791 674.5 4550 11 253 20.85 307.9 3955 614.7 3778 10 228 18.82 279.4 3214 555 3081 9 202.7 16.95 248.7 2580 495 2450 8 177.7 14.93 219.7 1998 434.9 1891 7 152.8 12.93 190.6 1496 374.6 1403 6 128.2 10.8 155.7 1030 314.5 989.2 5 103.4 8.85 130.8 696.2 254.4 647.1 4 79.28 6.75 94.05 387 195.7 382.9 Open in new tab Fig. 9: Open in new tabDownload slide Three-phase T-type TLI configuration. Fig. 10: Open in new tabDownload slide Three-phase T-type TLI using sine modulation. Fig. 11: Open in new tabDownload slide Grid-connected three-phase T-type TLI with d–q synchronous frame control. Fig. 12: Open in new tabDownload slide (a) PMSG DC-link voltage at 12 m/s wind speed. (b) PMSG rotor speed at 12 m/s wind speed. Fig. 13: Open in new tabDownload slide (a) Torque at 12 m/s wind speed. (b) DC power output at 12 m/s wind speed. Fig. 14: Open in new tabDownload slide (a) BC output at 12 m/s wind speed. (b) BC output power at 12 m/s wind speed. Fig. 15: Open in new tabDownload slide Wind speed profile variation. Fig. 16: Open in new tabDownload slide (a) PMSG DC-link voltage with a wind speed variation. (b) PMSG rotor speed with a wind speed variation. Fig. 17: Open in new tabDownload slide (a) PMSG torque with a variable wind speed. (b) PMSG output power with a wind speed variation. Fig. 18: Open in new tabDownload slide (a) BC output powered by PMSG-fed rectifier. (b) Output power of BC with wind speed variation. 6.3 PMSG-based WECS with T-type TLI without grid The performance of the PMSG-based WECS using a T-type TLI has been analysed without grid interfacing. The results of the BC using the P&O-based MPP approach supplied by the PMSG-based WECS interfaced with a grid-connected T-type TLI system are verified by using the MATLAB® and Simulink® platform. Fig. 19a and b represents the stand-alone three-phase line-to-line voltages and %THD of T-type TLI systems using sine modulation. The output voltage of the T-type TLI contains five voltage levels, i.e. –674.5, –337.25, 0, +337.25 and +674.5 V. The corresponding voltage THD is 34.37% by considering the unity MI. Fig. 19: Open in new tabDownload slide (a) Three-phase T-type TLI line voltages. (b) Line voltage THD of T-type TLI for unity MI. Furthermore, Table 4 provides the performance of the T-type TLI using the sine-modulation method, which has been analysed with a variation of MI from 0.5 to 1. Table 4 shows the output voltage and %THD of the T-type TLI using sine modulation for various wind velocities and values of MI. From Table 4, it is observed that the PMSG-based WECS produces more output voltage as the speed of the wind increases along with the increase in MI. In addition, the %THD decreases with an increase in MI. From Table 4, it can be seen that for a wind speed of 12 m/s, the output of the BC is 674.5 V and the output of the T-type TLI generates five levels with a maximum voltage of 584.2 V and a %THD of 34.37 for a unity MI, which is also shown in Fig. 19. Similarly, the output of the T-type TLI generates only three levels, with a maximum voltage of 292.2 V and a THD of 67.02% for a 0.5 MI, which is shown in Table 4. It can be noticed that by increasing the MI, irrespective of wind speeds, the %THD decreases. Further, as the obtained %THD is not acceptable, the T-type TLI is interfaced with grid synchronization using d–q control for power-quality improvement. Table 4: T-type TLI output voltage, THD and number for various wind velocities and MI Wind velocity (m/s) . BC output voltage (V) . MI . T-type TLI . . Levels in the output . . . . Voltage (V) . THD (%) . . 12 674.5 1 584.2 34.37 5 0.9 525.9 38.09 0.8 467 41.10 0.7 408.1 43.21 0.6 349.5 48.02 0.5 292.2 67.02 3 10 555 1 481.7 34.34 5 0.9 432.5 38.13 0.8 385 41.12 0.7 336 43.30 0.6 288.1 47.62 0.5 241.1 67.22 3 8 434.9 1 376.6 34.41 5 0.9 338.7 38.21 0.8 301.6 41.07 0.7 263.7 43.36 0.6 225.7 47.73 0.5 187.4 67.54 3 6 314.5 1 272.4 34.42 5 0.9 245.3 38.18 0.8 317.4 41.01 0.7 190 43.26 0.6 163.3 48.02 0.5 136.1 67.15 3 4 195.7 1 169.1 34.42 5 0.9 152.2 38.31 0.8 135.3 41.11 0.7 118.2 43.35 0.6 101.4 48.01 0.5 84.79 67.02 3 Wind velocity (m/s) . BC output voltage (V) . MI . T-type TLI . . Levels in the output . . . . Voltage (V) . THD (%) . . 12 674.5 1 584.2 34.37 5 0.9 525.9 38.09 0.8 467 41.10 0.7 408.1 43.21 0.6 349.5 48.02 0.5 292.2 67.02 3 10 555 1 481.7 34.34 5 0.9 432.5 38.13 0.8 385 41.12 0.7 336 43.30 0.6 288.1 47.62 0.5 241.1 67.22 3 8 434.9 1 376.6 34.41 5 0.9 338.7 38.21 0.8 301.6 41.07 0.7 263.7 43.36 0.6 225.7 47.73 0.5 187.4 67.54 3 6 314.5 1 272.4 34.42 5 0.9 245.3 38.18 0.8 317.4 41.01 0.7 190 43.26 0.6 163.3 48.02 0.5 136.1 67.15 3 4 195.7 1 169.1 34.42 5 0.9 152.2 38.31 0.8 135.3 41.11 0.7 118.2 43.35 0.6 101.4 48.01 0.5 84.79 67.02 3 Open in new tab Table 4: T-type TLI output voltage, THD and number for various wind velocities and MI Wind velocity (m/s) . BC output voltage (V) . MI . T-type TLI . . Levels in the output . . . . Voltage (V) . THD (%) . . 12 674.5 1 584.2 34.37 5 0.9 525.9 38.09 0.8 467 41.10 0.7 408.1 43.21 0.6 349.5 48.02 0.5 292.2 67.02 3 10 555 1 481.7 34.34 5 0.9 432.5 38.13 0.8 385 41.12 0.7 336 43.30 0.6 288.1 47.62 0.5 241.1 67.22 3 8 434.9 1 376.6 34.41 5 0.9 338.7 38.21 0.8 301.6 41.07 0.7 263.7 43.36 0.6 225.7 47.73 0.5 187.4 67.54 3 6 314.5 1 272.4 34.42 5 0.9 245.3 38.18 0.8 317.4 41.01 0.7 190 43.26 0.6 163.3 48.02 0.5 136.1 67.15 3 4 195.7 1 169.1 34.42 5 0.9 152.2 38.31 0.8 135.3 41.11 0.7 118.2 43.35 0.6 101.4 48.01 0.5 84.79 67.02 3 Wind velocity (m/s) . BC output voltage (V) . MI . T-type TLI . . Levels in the output . . . . Voltage (V) . THD (%) . . 12 674.5 1 584.2 34.37 5 0.9 525.9 38.09 0.8 467 41.10 0.7 408.1 43.21 0.6 349.5 48.02 0.5 292.2 67.02 3 10 555 1 481.7 34.34 5 0.9 432.5 38.13 0.8 385 41.12 0.7 336 43.30 0.6 288.1 47.62 0.5 241.1 67.22 3 8 434.9 1 376.6 34.41 5 0.9 338.7 38.21 0.8 301.6 41.07 0.7 263.7 43.36 0.6 225.7 47.73 0.5 187.4 67.54 3 6 314.5 1 272.4 34.42 5 0.9 245.3 38.18 0.8 317.4 41.01 0.7 190 43.26 0.6 163.3 48.02 0.5 136.1 67.15 3 4 195.7 1 169.1 34.42 5 0.9 152.2 38.31 0.8 135.3 41.11 0.7 118.2 43.35 0.6 101.4 48.01 0.5 84.79 67.02 3 Open in new tab 6.4 PMSG-based WECS with T-type TLI interfaced to grid under constant grid current The performance of the PMSG-based WECS interfaced to the grid has been investigated under constant grid current with a value of 100 A. Fig. 20 represents the simulation outcomes of a three-phase grid-connected T-type TLI system using a d–q synchronous frame operating with constant voltage and constant set current. Fig. 20a and b represents T-type TLI system grid voltages and currents with a peak voltage of 600 V and an injected current peak value of 100 A. Fig. 20c depicts the %THD of T-type TLI grid current and its value is 3.18%, which is within IEEE-519 guidelines, with a fundamental current of 99.99 A. Fig. 20d depicts the angle between the T-type TLI grid voltage and current, which is maintained at unity power factor. Fig. 20: Open in new tabDownload slide (a) T-type TLI system grid voltages. (b) T-type TLI grid currents. (c) %THD of T-type TLI grid current. (d) Angle between T-type TLI grid voltage and current. 6.5 PMSG-based WECS with T-type TLI interfaced to grid under variable grid current The performance of the PMSG-based WECS interfaced to the grid has been investigated under variable grid currents by considering 60, 80 and 100 A. Fig. 21 represents the simulation outcomes of a grid-connected T-type TLI system using a d–q synchronous frame operating with constant voltage and variable grid current. Fig. 21a and b represents T-type TLI system grid voltages with a peak voltage of 600 V and Fig. 20b depicts variable injected current. Initially, the peak value of 80 A is considered to be from 0.1 to 0.14 sec. The injected current of the T-type TLI is reduced to 80 A from 0.14 to 0.18 seconds and the current is increased to 100 A peak at 0.18 seconds. Fig. 21c depicts the %THD of the T-type TLI grid current for 80 A and its value is 3.18% with a fundamental current of 79.92 A. Fig. 21d depicts the %THD of the T-type TLI grid current for 80 A and its value is 3.18% with a fundamental current of 59.98 A. The angle between the T-type TLI grid voltage and current is depicted in Fig. 21e, which maintains a unity power factor even when variable active power is fed to the grid. Fig. 21: Open in new tabDownload slide (a) T-type TLI system grid voltages. (b) T-type TLI grid currents. (c) %THD of T-type TLI grid current for 80 A. (d) %THD of T-type TLI grid current for 60 A. (e) Angle between T-type TLI grid voltage and current. Table 5 compares the proposed BC employing the P&O-based MPP method offered by the PMSG-based WECS to current literature in terms of rising time, settling time and ripple content. It is shown that the proposed system is better because it only takes 0.8 seconds to reach a steady state and 0.72 seconds to rise, which is faster than other systems [31–33]. Table 5: Proposed PMSG-based WECS comparison with the existing literature Configuration . PMSG-fed rectifier . . . . Rise time (seconds) . Settling time (seconds) . Ripple content . Squirrel-cage IG fed to DC through a voltage source converter [31] 3.69 4.1 More Back-to-back converter interfaced with PMSG-based WECS [32] 1.8 2 More PMSG-based WECS interfaced with two voltage source converters [33] 2.4 3 Moderate Proposed system 0.72 0.8 Moderate Configuration . PMSG-fed rectifier . . . . Rise time (seconds) . Settling time (seconds) . Ripple content . Squirrel-cage IG fed to DC through a voltage source converter [31] 3.69 4.1 More Back-to-back converter interfaced with PMSG-based WECS [32] 1.8 2 More PMSG-based WECS interfaced with two voltage source converters [33] 2.4 3 Moderate Proposed system 0.72 0.8 Moderate Open in new tab Table 5: Proposed PMSG-based WECS comparison with the existing literature Configuration . PMSG-fed rectifier . . . . Rise time (seconds) . Settling time (seconds) . Ripple content . Squirrel-cage IG fed to DC through a voltage source converter [31] 3.69 4.1 More Back-to-back converter interfaced with PMSG-based WECS [32] 1.8 2 More PMSG-based WECS interfaced with two voltage source converters [33] 2.4 3 Moderate Proposed system 0.72 0.8 Moderate Configuration . PMSG-fed rectifier . . . . Rise time (seconds) . Settling time (seconds) . Ripple content . Squirrel-cage IG fed to DC through a voltage source converter [31] 3.69 4.1 More Back-to-back converter interfaced with PMSG-based WECS [32] 1.8 2 More PMSG-based WECS interfaced with two voltage source converters [33] 2.4 3 Moderate Proposed system 0.72 0.8 Moderate Open in new tab 7 Conclusion This paper evaluated the performance of a three-phase T-type TLI interfaced to the grid with a PMSG-based WECS in terms of various parameters. The power coefficient Cp reached its maximum value, i.e. 0.48, when the pitch angle β was zero. The proposed WECS analysed the BC supplied by the PMSG using P&O control under constant and variable wind speeds by considering 8, 10 and 12 m/s wind speeds for the pitch angle β = 0. The P&O-based MPP approach was recommended to track the MPP and the developed MPP approach was tested under various wind speeds. From the simulation results, it was observed that the wind turbines produced more voltage as the wind speed increased. Furthermore, by employing the BC, the voltage gain of the wind turbine was enhanced by two. The PMSG-supplied rectifier output voltage at 12 m/s was 337.6 V, which could be enhanced to double, i.e. 674.5 V, by connecting the BC. Finally, the PMSG-based WECS interfaced with three-phase grid-connected T-type TLI using d–q control was verified by maintaining the unity power factor and good power quality with the synchronization of grid voltage and current under constant and variable active power fed to the grid. The %THD of the T-type TLI grid current value was 3.18% with a fundamental current of 99.99 A for a fixed grid current of 100 A, which is within IEEE-519 guidelines. 7.1 Future scope The proposed grid-connected T-type TLI can be implemented with a model predictive controller and extended to higher levels, removing the need for an LCL filter. Also, a high-gain BC can be used instead of a traditional BC in the PMSG-based WECS to make the system work better even when the wind speed is low. Conflict of interest statement None declared. References [1] Ganthia BP , Barik SK, Nayak B. Wind turbines in energy conversion system: types & techniques . In: Singh VK, Bhoi AK, Saxena A, et al. (eds). Renewable Energy and Future Power Systems. Energy Systems in Electrical Engineering. Singapore : Springer , 2021 , 199 – 217 . doi:10.1007/978-981-33-6753-1_9. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC [2] Tawfiq KB , Mansour AS, Ramadan HS, Becherif M, El-Kholy EE. 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