Phase-Lag Compensator based Approach for Realizing MPPT through PMSG based Wind Turbine Generator

Proportional-Integral (PI) controllers are widely accepted industrial controllers. These controllers also find their applications in wind energy conversion systems (WECSs). Although such controllers are well researched and developed too, their linear nature and sensitivity of their gains towards variations in plant’s parameter are some noticeable disadvantages associated with them. Moreover, tuning of their gains involves certain approximations, which leads to demean their accuracy. On contrary, the designing of lag-compensators is procedural and discussed well in literature. Although such compensators could not have drawn the attention of wind turbine manufacturers but may a potential candidate for future developments. The focus of this paper is to design phase-lag compensators and use them to extract maximum available power in the wind, at every wind speed upto its rated value. Ability of the compensators is assessed through detailed simulation of a PMSG based WECS in MATLAB/Simulink environment. Observed responses are motivating and demonstrates the effectiveness of the designed compensators. KeywordsController Design, Lag Compensator, Rotor-Field-Oriented-Control (R-FOC), Tip-Speed-Ratio (TSR), Maximum Power Point Tracking (MPPT).


Introduction
Amongst various wind turbine generators (WTGs), the permanent magnet synchronous generator (PMSG) based WTGs are most popular in variable speed wind turbines (VSWTs). VSWTs also uses doubly fed inducton generator (DFIG), however, PMSG based WTGs are more advantageous over DFIG based WTGs. Most of the modern WTGs are PMSG based owing to its several advantages such as gearless design, self-excitation capability, higher efficiency, improved reliability, and less maintenance (Sharma and Singh, 2012;Yaramasu et al., 2017). The most lucrative feature of PMSG based WTGs is its wide operating speed range and fully utilization of the converter's capacity (Chinchilla et al., 2006;Polinder et al., 2006). In general, the major challenge associated with wind energy generation is WTG's integration with the grid (Dahbi et al., 2014;Mohseni and Islam, 2012). Due to intermittency in the wind the power generated from such sources are inconsistent, and affects the system's stability and power quality. In order to address these, power electronic interfaces are required for bridging such sources with the grid, which needs to be properly controlled, so as to obtain optimum generation along with fulfilling the grid code requirements in terms of voltage, frequency, active and reactive power injection (Freire et al., 2012;Jain et al., 2015;Tripathi et al., 2015).
Various power electronic interfaces proposed for bridging the PMSG based WTGs with the grid are reviewed in past, and back-to-back connected pulse-width-modulated voltage-sourceconverters (BTB-PWM-VSCs) are unanimously accepted, and hence are most preffered interfaceing option (Baroudi et al., 2007;Yaramasu et al., 2015). In BTB-PWM-VSCs, the VSCs are usually termed as mashine-side-converter (MSC) and grid-side-converter (GSC) based on their location. Field-Oriented-Control (FOC) and direct-torque-control (DTC) are used to control the MSC, whereas, voltage-oriented-control (VOC) and direct-power-control (DPC) are used to control GSC. Amoung these, FOC and VOC are vector based conrol approaches, whereas, DTC and DPC are direct control approaches. A comparative analysis of PMSG drives with direct and vector based control is presented in (Freire et al., 2012). The vector based control approaches are highly researched and established in view of their better performance in terms of current distortions, power factor, and efficiency (Jain et al., 2015;Tiwari and Babu, 2016). FOC and VOC are of cascaded structure, and consists of a faster inner-current-control loop and a slower outer-speed/voltage-control loop (Dahbi et al., 2014;Jain et al., 2015). Propper control of MSC and GSC is imperative for achieving desired performance and system's stability, which needs the involve controllers to meet certain design specifications, such as; percentage overshoot; rise time; settling time; phase margin; and specified bandwidth (Basilio and Matos, 2002;Kristiansson and Lennartson, 2006;Li, 2012). Simple structure, cost-effectiveness and simple designing procedure makes the PI controllers as most preffered controller option for industrial drives. In view of aforementioned attributes such controllers also has dragged WT manufacturer's attension. PI controller design/tuning requires computation of proportional and integral gains and number of tuning procedures are proposed in literature (Krohling and Rey, 2001;Neath et al., 2014;Zigmund et al., 2011).
As the idea of compensation seems lucrative as compared to control. In view of this, the focus of present study is on designing of lag compensators to control the speed of PMSG based WTGs. Besides noticeable benifits of lag-compensators over PI controllers very few studies are found on its use in WECS control. One such work is reported in Wang et al. (2009) , in which autors have used phase-lag compensator to enhance the low-voltage-ride-through (LVRT) capability of a doubly-fed-induction-generator (DFIG) based wind energy conversion system. In another work reported in Hamatwi et al. (2017), authors have presented a detailed lag-compensator design procedure for MSC control of a PMSG based WECS, in which they have directly controlled the generated power to achieve MPPT. As large current involves in power control, it should be avoided for megawatt capacity WTGs. This paper focuses on designing of phase-lag compensators for both inner and outer control loops of the MSC control to achive MPPT. The inner and outer control loops are used to control the current and speed, respectively.

PMSG based WTG
PMSG's stator voltage equations in rotating reference frame, electromagnetic torque relation, and rotor dynamics are expressed as (Wu et al.,

Machine Side Converter Control
Usually, MSC control, controls the generator's speed in order to maintain the tip-speed-ratio (TSR) at it's optimum value. It enables the WT to operate in constant Cp mode and hence to achieve the MPPT. The control philosophy of MSC control has already discussed in various publications in the past (Freire et al., 2012;Jain et al., 2015). Field-oriented-control (FOC) techniques are highly researched and accepted control technique for MSC control. Amongst various FOC techneques, such as, stator-field-oriented-control (SFOC); rotor-field-orientedcontrol (RFOC) and Airgap-field-oriented-control (AGFOC), the RFOC is most popular control scheme for controlling the MSC of PMSG based WECSs. In present work RFOC scheme is used. The scheme is well discussed in Wu et al. (2011).

Compensator Design Specifications
The ripple content in the converter's output may badly affect the compensator's performance. In order to avoid this, the compensator's bandwidth must be chosen high. The converter switching frequency has considered 10 kHz in present study. Compensator bandwidths for inner and outer control loops are considered 2 kHz and 0.5 kHz, respectively. In addition, the maximum overshoot allowed is considered 20% for inner and 5% for outer control loop in view of their faster and slower response. Other compensator design parameters are computed and are presented in Table 1 (Ogata and Yang, 2002).

Open Loop Transfer Function: ICC loop of MSC
Block diagram of the ICC loop of MSC control is shown in Figure 1.
Now, the converter transfer function Gconv (s) is represented as first-order transfer function with a delay d T (Tripathi et al., 2016). The transfer function of the converter block is expressed as, The phase-margin (PM) and bandwidth (BW) from the frequency response of the uncompensated system has found as 88.2 0 and 635 rad/s, respectively. Obtained value of PM is high enough and indicates high robustness, whereas, obtained BW is far below to the desired and indicates slower response of uncompensated system. In order to obtain the required BW, the magnitude plot needs upward shifting, so that it may cross the 0 dB axis at the desired BW or gain crossover frequency. This has achieved by including a gain 'K'.
The PM and BW obtained from the frequency response of the gain-compensated system are as 57.9 0 and 1.26*10 4 rad/s, respectively. With this, BW requirement is met but the PM is more than the desired. Figure 2 presents the magnitude and phase plots for both uncompensated and gaincompensated systems. Magnitude curve shifting and BW adjustment is clearly demonstrated in Figure 2, itself. Futher, in order to achive the desired PM, the gain compensated system is augmented with a phase-lag compensator. Designing of lag-compensator is presented in subsection to be followed.

Phase-Lag Compensator Design
Phase-lag cpmensator designing requires computation of the amount of phase to be compensated/attenuated, edge frequencies corresponding to location of compensator's pole and zero, compensator's gain and lag time-constant. Numarical values of aforementioned quantities has computed and are presented in Table 2. For the relations used to compute these parameters readers are suggested to refer Ogata and Yang (2002).  The PM and BW obtained from the bode diagram of gain-lag compensated system are as 48.1 0 and 1.26*10 4 rad/s, respectively. Therefore, both PM and BW requirement are met. Actually, the phase-lag compensator shifts the phase curve down corresponding to the desired attenuation (around the desired BW). Bode diagram of both gain-compensated and gain-lag compensated systems are shown in Figure 3.  In order to observe the time-response of the system, step-responses of uncompensated, gain compensated and gain-lag compensated systems are obtained and system's performance parameters such as; maximum overshoot, rise time and settling time are noted. Figure 4, shows these responses along with different performance indices.

Open Loop Transfer Function: OSC loop of MSC
Block diagram of the OSC loop of MSC control is shown in Figure 5.
The PM and BW from the frequency response of the uncompensated system has found as 90 0 and 0.835 rad/s, respectively. Obtained value of PM is very high indicating high robustness, whereas, obtained BW is far below to the desired and indicates slower response of uncompensated system. In order to obtain the required BW, the magnitude plot needs upward shifting, so that it may cross the 0 dB axis at the desired BW or gain crossover frequency. This has achieved by including a gain 'K'. The desired gain 'K' has obtained as 3660, and the OLTF of gain-compensated system   The PM and BW obtained from the frequency response of the gain-compensated system are as 79.4 0 and 3.14*10 3 rad/s, respectively. With this, BW requirement is met but the PM is more than the desired. Figure 6, presents the magnitude and phase plots for both uncompensated and gaincompensated systems. Futher, in order to achive the desired PM, the gain compensated system is augmented with a phase-lag compensator. Designing of lag-compensator is presented in subsection to be followed.

Phase-Lag Compensator Design
Numarical values of various design parameters for phase-lag compensator has computed and are presented in Table 3.
The PM and BW obtained from the bode diagram of gain-lag compensated are are 64.6 0 and 3.14x10 3 rad/s, respectively. Therefore, both PM and BW requirement are met. Actually, the phase-lag compensator shifts the phase curve down corresponding to the desired attenuation (around the desired BW). Bode diagram of both gain-compensated and gain-lag compensated systems are shown in Figure 7.  In order to observe the time-response of the system, step-responses of uncompensated, gain compensated and gain-lag compensated systems are obtained and system's performance parameters such as; maximum overshoot, rise time and settling time are noted. Figure 8, shows these responses along with different performance indices. Compensator's design specification, outcomes of frequency and time responces of uncompensated, gain-compensated and gain-lag compensated systems for both ICC and OSC loop are made available in Table 4.

Simulation Outcomes and Discussion
Having designed the involved compensators for the system concern, a detailed simulation model of the PMSG based WECS is developed in MATLAB/Simulink environment, for evaluation of effectiveness of the design compensators. The WECS performance with such designed compensators has observed under different wind speed conditions. The test wind profiles used to evaluate the effectiveness of the designed compensators for different control loops and simulation outcomes are presented in Figure 9. WECS parameters are given in Appendix. Initial wind speed is considered 9.6 m/s which drives the wind turbine at 18 r.p.m.. Turbine/generator torque, and average active power generatd are observed about 5.43 kNm and 1.02 MW, respectively. After 3s, the wind speed gradually increases and settelled at 12 m/s, rotor speed is also found increasing accordingly and smmothly tracking the reference rotor speed corresponding to the MPPT. The rotor speed, turbine/generator torque, generated power corresponding to the wind speed of 12 m/s are observed as 22.5 r.p.m., 8.48 kNm and 2 MW, repectivelly. At 6s, the wind speed starts gradually decreasing to a value of 8.4 m/s, and the rotor speed is also found decreasing accordingly and smmothly tracking the reference rotor speed recursively calculated by MPPT algorithm. The rotor speed, turbine/generator torque, generated power corresponding to the wind speed of 8.4 m/s are observed as 15.75 r.p.m., 4.15 kNm and 0.68 MW, repectivelly. At 9s, the wind speed starts gradually increasing g and setteled to a value of 10.8 m/s, the rotor speed is also found increasing accordingly and smmothly tracking the reference rotor speed. The rotor speed, turbine/generator torque, generated power corresponding to the wind speed of 10.8 m/s are observed as 20.25 r.p.m., 6.86 kNm and 1.46 MW, repectivelly. At 12s, the wind speed starts gradually decreasing and setteled to a value of 7.2 m/s, the rotor speed is also found decreasing accordingly and smmothly tracking the reference rotor speed. The rotor speed, turbine/generator torque, generated power corresponding to the wind speed of 7.2 m/s are observed as 13.5 r.p.m., 3.05 kNm and 0.43 MW, repectivelly. Dependency of the torque on q-axis current can also be seen. From the curve of the power coefficient which is maintained at its reference i.e. at 0.48 demonstrates that MPPT operation has achived successfully, hense good compensator performance. The steady-state evaluation of different performance parameters of the turbine considered for the present study has carried out in our prior work (Srivastava et al., 2018).
The considered system is also subjected to a stochastically varying wind and the responses obtained are presented. Obtained responses demonstrates the effectiveness of the designed compensators aand achievement of MPPT successfully.

Conclusions
The research investigation presented in this paper is dedicated to present an alternative control solutions to renewable energy generation systems. In this study, phase-lag compensators has developed for both inner and outer loop of the machine-side-converter of a BTB-PWM-VSCs as an interface between PMSG based WTG and the grid. The designed compensators for inner and outer control loops of the R-FOC has used to control the generator current and rotor speed (to achieve MPPT). Compensators performance has evaluated through a detailed simulation of a PMSG base WECS in MATLAB/Simulink environment and promising responces has observed. The observed responses motivates for an extended work presenting the designing such compensators for grid-side-converter control of the aforementioned power electronic interface. Although, the compensator designing presented in this paper is for PMSG based system, the procdure discuused in the paper may attract the researchers in this field.