Assessment of proposed maximum power point tracking–unity power factor algorithms for optimum operation permanent magnet synchronous generator

Abstract

It is very important to select proper maximum power point tracking algorithm in order to achieve best performance and low cost for wind turbine–generator combination. A permanent magnet synchronous generator steady-state unity power factor analytical model based on a current source—equivalent circuit is provided. Validation of the identified load angle effect in current source as compared with that of the commonly used voltage source permanent magnet synchronous generator is presented. Then three new maximum power point tracking–load angle control algorithms based on current source model are presented. They all apply magnitude and frequency control techniques for Digital Signal Processor control systems. The first one presents maximum power point tracking–unity power factor applying constrained load angle control algorithm. The merits of the next two developed schemes are quickly and precisely tracking the maximum power output of the wind turbine; thus, the second and third algorithms are then characterized with linear control systems. The linearity of the second scenario is between load angle and reference speed while the third one has a load angle–torque linear relationship which shows its optimality. Finally, the controlled characteristics and implementation for the optimum case are presented for both stationary and synchronous reference frames (for vector control purposes). Simulation modeling for optimum case is provided and its results match well with the proposed predictive control algorithm.

Keywords

Permanent magnet synchronous generator maximum power point tracking unity power factor current control schemes

Introduction

Wind energy has grown rapidly and becomes the most competitive form of renewable energy (Errami et al., 2013). By the end of 2018, the overall worldwide capacity of all wind turbines (WTs) installed reached 600 GW. 53.9 GW were added in 2018 and 52.55 GW were added in 2017 when 52’552 Megawatt were installed; 600 GW can cover close to 6% of the global electric power demand (WWEA, 2019). In the global market, there are many configuration of the wind energy conversion system (WECS). Due to its enhanced energy capture, variable speed WECSs are the most used configuration (Hossain and Ali, 2015; Kumar and Chatterjee, 2016). There are several types of generators used in variable-speed WECSs. In recent years, permanent magnet synchronous generators (PMSGs) have extended usage by researchers due to their advantages such as high power density, higher efficiency and reliability, self-excitation and higher speed range of operation (Bonfiglio et al., 2017; Xie et al., 2017; Shengquan et al., 2016; Yang et al., 2018). The selection of the material and the conventional orientation in the rotor of the permanent magnet are very important factors in designing a high-performance PMSG for wind energy conversion system. There are many types of PMSG; one of them is surface-mounted permanent magnet synchronous generator (SPMSG) which is used in WECS. SPMSG does not add the reluctance power of PMSG, and the SPMSG becomes popular in WECS as it is designed for low speed operation (Saleh et al., 2011). Another type of PMSG is the interior permanent magnet synchronous generator (IPMSG); it is a salient pole synchronous generator with a cylindrical rotor which has permanent magnet embedded inside the rotor body. These embedded permanent magnet generator cause saliency in terms of direct axis and quadrature axis reactance (Caruso et al., 2017).

In general, WECS consists of a generator, an AC/DC converter, a DC filter, a DC/AC inverter, and an AC output filter (Oğuz et al., 2013). PMSG can be controlled by a number of methods. The knowledge of machine model accurate mandatory to analysis the performance and to design efficient and fast controller for the variable speed WT, then accurate measurements of these parameter is essential for designing control system and predicting performance such as torque response (Bunjongjit and Kumsuwan, 2013; Chowdhury et al., 2015; Rajalakshmi, 2018; Shen et al., 2011; Singh and Agrawa, 2013; Wenshan et al., 2019).

Increasing the power transfer capability and regulating active and reactive powers of the PMSG are the targets of researchers (Delfino et al., 2012). To achieve these targets, many control methods are developed such as zero d-axis current (ZDC), maximum torque per ampere (MTPA) control, and unity power factor (UPF) control (Purushotham et al., 2017). These control methods are voltage source (VS)-based equivalent circuit parameter. None of researches (up to authors’ knowledge) deal with maximum power point tracking (MPPT) up to rated PMSG speed at UPF operation. In PMSG, the stator current reaches its rated value at a stator current vector angle δ varies in non-linear form with the speed. It approaches its maximum value of π/4 at a rotor speed much less than the rated speed. Thus, PMSG with UPF control may be limited. It is noted that a PMSG can be specially designed to operate with UPF in the full-speed range, if required (Rajalakshmi, 2018). This article approves this problem and presents an alternative optimal solution. It introduces an equivalent circuit as a replacement of the voltage based equivalent circuit which called current source (CS)-based equivalent circuit which will be described later. The proposed equivalent circuit with three proposed MPPT-UPF for PMSG-WT operation are introduced to solve this problem. The article is organized as follows. The following section presents a PMSG CS-based model for wind conversion applications. The next section shows the MPPT-UPF constrained load angle algorithm in XY frame. UPF constrained load angle based on CS model, UPF constrained load angle based on VS model, and MPPT-UPF constrained load angle model are also analyzed in this section. The subsequent section describes the proposed load angle effect in CS model, which is followed by the “Model of MPPT-UPF optimum algorithm in reference frame” section. Simulation modeling and results discussions are described and comparison with steady-state characteristics are presented then, showing the response of the proposed control scheme to wind MPPT at unity PF. In the final section, conclusions are outlined about the performance achieved by the proposed optimum algorithm with regard to the conventional VS one.

CS-based model of PMSG-WT

In terms of control purpose, the two commonly reference frames used are stationary reference frame (XY) and synchronously rotating reference frames, d-q. The per-phase equivalent circuit of a CS-based PMSG (CSPMSG) in XY is shown in Figure 1. The current $I_{F}$ (FC) denotes a constant magnitude of the equivalent AC current established by the permanent magnet as viewed from the stator phase windings, such that if it were to flow in the stator windings, it would have the same effects as the rotor current, i_f.

Figure 1.

Per-phase current source (CS)-based equivalent circuit.

The angle of this CS is determined by the rotor position angle $β$ and the stator electromagnetic force (EMF) such that it becomes zero at open circuit operation. This CS produces the permanent magnet’s share of the air gap flux linkage. It can be determined by running the synchronous generator (SG) at its rated speed with no load, that is, $I_{F}$ = $I_{m}$ at no load. The total EMF induced in the stator winding is $E_{a}$ .

Figure 2 illustrates a proposed equivalent circuit for the CSPMSG in d-q frames and the corresponding space vector diagram is depicts in Figure 3.

Figure 2.

CSPMSG d-q equivalent circuit.

Figure 3.

Space vector diagram in stationary and Synchronously rotating reference frames.

MPPT-UPF constrained load angle algorithm in XY frame

In this section, the load angle which achieves unity power factor is deduced based on CS model and VS model of PMSG as shown below.

UPF constrained load angle based on CS model

From the phasor diagram, steady-state equations can be written as follows:

{\overset{⇀}{I}}_{F} = {\overset{⇀}{I}}_{m} + {\overset{⇀}{I}}_{a}

(1)

Figure 4 represents the generator phasor diagram at UPF in XY coordinates. At steady-state operation the XY frame is the same as d_s q_s frame, respectively.

Figure 4.

Phasor diagram at UPF in XY frame.

From Figure 4, steady-state equations at UPF can be written as follows

{I_{F}}^{2} = {I_{m}}^{2} + {I_{a}}^{2}

(2)

Where

I_{a} = - I_{F} \sin β

(3)

I_{m} = I_{F} \cos β

(4)

E_{a} = J ω_{s} L_{S} I_{m}

(5)

L_{S} = L_{mS} + L_{ls}

(6)

The PMSG mechanical (developed) power $P_{m}$ at UPF takes alternative forms as follows

P_{m} = 3 E_{a} I_{a} = - 3 E_{a} I_{F} \sin β = - 3 X_{S} I_{m} I_{F} \sin β

(7)

Equation (3) confirms UPF operation can be achieved by stator current control at any load angle within its permissible range. Another important formula by which the PMSG developed power may be controlled by the load angle $β$ only at each speed as shown below

P_{m} = - (3 / 2) X_{S} {I_{F}}^{2} \sin 2 β

(8)

The maximum mechanical (developed) power $P_{mmax}$ can be calculated as follows

P_{mmax} = - (3 / 2) X_{S} {I_{F}}^{2}

(9)

At condition

β = 45^{o}

(10)

The load angle $β$ shown in equation (8) for UPF control can be rewrite as follows

β = - 0.5 \tan^{- 1} [\frac{2 P_{m}}{\sqrt{{(3 X_{S} {I_{F}}^{2})}^{2} - {(2 P_{m})}^{2}}}]

(11)

UPF constrained load angle based on VS model

The equivalent circuit for phase (a) in stator coordinates is shown in Figure 5, where E denotes the amplitude of the induced EMF due to PM flux. Figure 6 represents the generator load increase effect with maintaining constant UPF.

Figure 5.

Per-phase voltage source (VS)-based equivalent circuit.

Figure 6.

Load increase effect with maintaining constant UPF.

UPF operation can be realized when the stator voltage $V_{a}$ is linked with E by the following relationship

V_{a} \sin θ = - E \sin (δ - θ)

(12)

The mechanical power using VS-based equivalent circuit can be deduced to be

P_{m} = (3 / Z_{s}) [E^{2} \cos θ - E V_{a} \cos (δ + θ)]

(13)

Substituting equation (12) into equation (13) and after mathematical manipulation, the following important mechanical power formula is deduced

P_{m} = - (3 / 2) (E^{2} / X_{S}) \sin 2 δ

(14)

The maximum mechanical (developed) power $P_{mmax}$ can be calculated as follows

P_{mmax} = - (3 / 2) (E^{2} / X_{S})

(15)

At condition

δ = 45^{o}

(16)

The load angle $δ$ shown in equation (14) for UPF control can be rewrite as follows

δ = - 0.5 \tan^{- 1} [\frac{2 X_{S} P_{m}}{\sqrt{{(3 E^{2})}^{2} - {(2 X_{S} P_{m})}^{2}}}]

(17)

The similarity between the power formulas given by equations (8, 11) and (14, 17) for CS and VS equivalent circuit, respectively, is remarkable.

MPPT-UPF constrained load angle

Algorithms based on knowledge of optimum WT extracted power $P_{mo} (ω)$ characteristics are well known and widely used (Kumar and Chatterjee, 2016; Sahu et al., 2018; Wei et al., 2016; Wu et al., 2011). The generator can be forced to track maximum power by optimally loading the turbine. Peak power curve for desired power range is stored in a microcontroller memory as a cubic speed/power function as follows

P_{mo} = K_{o} ω^{3}

(18)

Based on the measurement and stored data, the reference value (power or rotational speed) is determined. Main advantage of this method is its simplicity and fast response. Assuming precise data, algorithm immediately finds optimum operation point. At rated power and speed, $K_{o}$ is determined, thus $P_{mo}$ varies only by speed variation.

The PMSG can be forced to track the turbine MPP by controlling one of the generator power dependent variable such as constrained load angle $β$ for CS model ( friction and windage losses are neglected), as shown below

β = - 0.5 \tan^{- 1} [\frac{2 P_{mo}}{\sqrt{{(3 X_{S} {I_{F}}^{2})}^{2} - {(2 P_{mo})}^{2}}}]

(19)

For CS model, the MPPT-UPF operation is constrained by

{(3 X_{S} {I_{F}}^{2})}^{2} > {(2 P_{mo})}^{2}

(20)

Similarly for VS model

δ = - 0.5 \tan^{- 1} [\frac{2 X_{S} P_{mo}}{\sqrt{{(3 E^{2})}^{2} - {(2 X_{S} P_{mo})}^{2}}}]

(21)

For VS model, the MPPT-UPF operation is constrained by

{(3 E^{2})}^{2} > {(2 X_{S} P_{mo})}^{2}

(22)

Equation (22) clearly shows that for tracking maximum wind power $P_{mo}, an$ over design either by increasing PM pieces or decreasing the armature reactance $X_{S}$ is necessary.

Figure 7 illustrates the required optimum power to be tracked by the PMSG at which parameters are given in appendix 2.

Figure 7.

Variation of the optimum turbine power with PMSG speed for CS & VS models.

It is interesting to note that the load angles $β and δ$ are completely matching with each other as shown in Figures 7 –13.

Figure 8.

Variation of the stator current with PMSG speed for CS & VS models.

Figure 9.

Variation of the load angle ( $β, δ$ ) with PMSG speed for CS & VS models.

Figure 10.

Variation of the stator voltage with PMSG speed for CS & VS models.

Figure 11.

Variation of the stator induced EMF with PMSG speed for CS & VS models.

Figure 12.

Variation of the torque /ampere with PMSG speed for CS & VS models.

Figure 13.

Variation of the resultant flux with PMSG speed for CS & VS models.

To extend the operating range up to rated power at rated speed at UPF, the current I_F must be increased by 1.09% (5.5485 instead of 5.1) which means more required PM in PMSG. In wound rotor SG, field current control is possible. In VS control technique, the synchronous reactance $X_{S}$ may be decreased by 20% by reducing the armature reaction.

Load angle effect in CS model

Unlike the VS model, the presented CS model can extend the UPF operating range up to full rated at any given $< 45^{o}$ load angle. This can be explained by referring back to the equivalent circuit and the phasor diagram given by Figures 3 and 4. It can be noticed that this system, in addition to UPF operation, offers SVO as well as ZDC. E_a and I_m may represent x-axis and y-axis (real and imaginary axis), respectively, in stator reference frame as will be given in a very near future article.

Linear load angle-speed control for MPPT-UPF up to rated power

For wind energy MPPT, the control can be achieved by speed and or by torque control. In this technique, the load angle variation is linked to the generator speed variation by a linear relationship (linear load angle algorithm) given by

β = C ω

(23)

Where the slop C can be calculated as follows

C = β_{\Pr} / ω_{r}

(24)

A computing algorithm is built using equation (23) and the equations given in the third section except $β$ laws (11 & 19).

As expected, MPPT is achieved at rated power and speed with no need for redesign of the PMSG for either increasing PM pieces or decreasing the armature reaction. Unfortunately, the obtained efficiency is less than MPPT-UPF constrained load angle algorithm.

Non-linear load angle-speed control for MPPT-UPF up to rated power

This control can be achieved with nonlinear load angle-speed square methodology. In this technique (optimum load angle algorithm), the load angle variation is given by

β = C ω^{2}

(25)

Where the slop C can be calculated as follows

C = β_{\Pr} / {ω_{r}}^{2}

(26)

Figure 14 illustrate a comparison between load angle-speed characteristics for all algorithms. Figures 15 –17 show clearly how the stator voltage and PMSG torque varies also as a function of the load angle $β$ of all algorithms.

Figure 14.

Variation of the load angle with PMSG speed for all algorithms.

Figure 15.

Torque and stator voltage as function of the load angle at MPPT-UPF constrained load angle algorithms.

Figure 16.

Torque and stator voltage as function of the load angle at MPPT-UPF linear load angle algorithms.

Figure 17.

Torque and stator voltage as function of the load angle at MPPT-UPF optimum algorithms.

Figures 18 –21 illustrate a comparison between the PMSG characteristics of the three at all proposed algorithms.

Figure 18.

Variation of the stator voltage & EMF with PMSG speed for all algorithms.

Figure 19.

Variation of the stator current with PMSG speed for all algorithms.

Figure 20.

Variation of the flux with PMSG speed for all algorithms.

Figure 21.

Variation of the efficiency with PMSG speed for all algorithms.

From previous figures, it is clear that the output voltage with MPPT-UPF constrained algorithm is much less than rated voltage; an excess voltage resulted from MPPT-UPF linear algorithm but with lower efficiency, while rated voltage at rated power is obtained with MPPT-UPF optimum algorithm with higher efficiency.

Model of MPPT-UPF optimum algorithm in reference frame

Referring back to MPPT-UPF optimum algorithm, CSPMSG d-q equivalent circuit shown in Figure 2, and phasor diagram shown in Figure 3, the stator induced EMF can be deduced as shown below

E_{a} = P_{mo} / (- 3 I_{F} \sin β)

(27)

d and q stator induced EMFs can be written as follows

E_{aq} = \sqrt{2} E_{a} \cos β

(28)

E_{ad} = \sqrt{2} E_{a} \sin β

(29)

d and q stator current can be written as follows

I_{aq} = \sqrt{2} I_{a} \cos β

(30)

I_{ad} = \sqrt{2} I_{a} \sin β

(31)

Similarly d and q stator voltage can be deduced as

V_{aq} = E_{aq} - I_{aq} R_{a}

(32)

V_{ad} = E_{ad} - I_{ad} R_{a}

(33)

So the stator voltage will be

V_{a} = (\sqrt{{V_{aq}}^{2} + {V_{ad}}^{2}}) / \sqrt{2}

(34)

Figure 22 shows the construction of d-q control diagram. The three phase abc first are to be controlled in stationary reference frame as given in previous section, then converted to d-q rotor reference frame.

Figure 22.

Proposed CSPMSG control system in rotor reference frame.

Figures 23 –27 illustrate the accuracy between the two applied system of stator and rotor reference frames characteristics.

Figure 23.

Variation of stator current with speed at d-q rotor reference frame & XY stator reference frame.

Figure 24.

Variation of stator voltage & EMF with speed at d-q rotor reference frame & XY stator reference frame.

Figure 25.

Variation of mechanical power with speed at d-q rotor reference frame & XY stator reference frame.

Figure 26.

Variation of input & output power with speed at d-q rotor reference frame & XY stator reference frame.

Figure 27.

Variation of efficiency with speed at d-q rotor reference frame & XY stator reference frame.

Simulation modeling and results discussions

In order to evaluate the performance of the proposed control schemes, several sets of simulations are conducted using Matlab / Sim-Power Systems toolbox. The simulation model is shown in Figure 28(a) and (b). Pi controller is used to compare the reference d-q current using equations (29)–(34) and the measured d-q current from the d-q model of the synchronous machine; pi controller output is the stator reference d-q variables. Where the d-q voltage equations for dynamic model are

v_{ad} = R_{a} i_{ad} + l_{d} \frac{d i_{ad}}{dt} - ω_{e} l_{q} i_{aq}

v_{aq} = R_{a} i_{aq} + l_{q} \frac{d i_{aq}}{dt} - ω_{e} (l_{d} i_{ad} + ψ_{pms})

The generated active power is calculated as

p_{g} = \frac{3}{2} (v_{ad} i_{ad} + v_{aq} i_{aq})

Figure 28.

(a) Id-Iq model and (b) PMSG model.

Figure 29.

Simulation results: Figure a to h depicts comparison between dynamic and steady-state characteristics versus speed using the proposed optimum algorithm. Figure a, b represent voltage and current d-q components. Figure c, d illustrate stator phase voltage, and phase current respectively, Figure e and f show mechanical tracked MPP and the generator output power, respectively. Variable speed dynamic results in terms of time are illustrated in Figure g to l).

Match of the steady-state calculations in respect with simulated results can be easily verified as shown in figure 29. Further alternative mathematical formulas that directly link the PMSG variables with speed are deduced as follows to enrich the proposed algorithm.

The stator induced EMF, $E_{a} = \frac{Ko ω_{s}^{3}}{(- 3 I_{F} \sin β)}$ ,

The stator current, $I_{a} = ko ω_{2}^{3} / Ea,$

The stator voltage, $V_{a} = \frac{K_{o} ω_{s}^{3}}{(- 3 I_{F} \sin β)} - (- I_{F} R_{a} \cos β),$

The torque per ampere T/A = $\frac{{Ko ω}_{s}^{2}}{(- I_{F} \cos β)}$ ,

The resultant flux = $\frac{E_{a}}{ω_{s}} = \frac{K_{o} ω_{s}^{2}}{(- 3 I_{F} \sin β)}$

Where $ω_{s}$ is the angular speed in rad/s.

Conclusion

VS-based equivalent performance characteristics are carried out; the resulted matching between CS and VS based system performance characteristics validates the proposed algorithm. Unlike other researches, the proposed PMSG-WT CS-based equivalent has the following advantages:

It explicitly validates MPPT while UPF operation without over design either by increasing PM pieces or decreasing the armature reactance $X_{S}$ .

This system analysis is much simpler and efficient than that of the commonly used voltage source-based equivalent circuit.

No decoupling control is needed as both torque and flux dependent parameters are naturally separated which greatly simplifies the required control.

Three strategies of magnitude and frequency control type of CS-PMSG load angle control algorithm are presented for Digital Signal Processor control applications. The constraint load angle MPPT-UPF method resulted in less than rated power; however, it has high efficiency over its limited speed range. The other two methods of linear load angle MPPT-UPF and optimum load angle MPPT-UPF methods extend the MPPT range up to rated power and speed. Although linear load angle MPPT-UPF strategy enable up to rated MPPT, its efficiency is low at low speeds. Optimum load angle MPPT-UPF method has proven to be an efficient control method. It enables MPPT up to rated power while UPF operation at the highest efficiency.

Footnotes

Appendix 1

Appendix 2

The machine under study is 2.4 KVA, 220 V, 6.3 A, 50 Hz, 4-pole 3-phase synchronous generator with below parameters (Mohamed et al., 2012):

Stator per-phase resistance R_a=3.602 $Ω$

Stator per-phase synchronous reactance $X_{S}$ = 51.304 $Ω$

Stator per-phase leakage reactance $X_{ls}$ = 11.2 $Ω$ .

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Elymany Mahmoud

References

Bonfiglio

Delfino

Gonzalez-Longatt

, et al. (2017) Steady-state assessments of PMSGs in wind generating units. International Journal of Electrical Power and Energy Systems 90: 87–93.

Bunjongjit

Kumsuwan

(2013) Performance enhancement of PMSG systems with control of generator-side converter using d-axis stator current controller. In: 2013 10th international conference on electrical engineering/electronics, computer, telecommunications and information technology, Krabi, 15–17 May.

Caruso

Di Tommaso

Miceli

, et al. (2017) Characterization of the parameters of interior permanent magnet synchronous motors for a loss model algorithm. Measurement 106: 196–202.

Chowdhury

Haque

Das

, et al. (2015) Modeling, parameter measurement and sensorless speed estimation of IPM synchronous generator for direct drive variable speed wind turbine application. International Transactions on Electrical Energy Systems 25: 1814–1830.

Delfino

Pampararo

Procopio

, et al. (2012) A feedback linearization control scheme for the integration of wind energy conversion systems into distribution grids. IEEE Sys. J 6(1): 85–93.

Errami

Ouassaid

Maaroufi

(2013) Control of a PMSG based wind energy generation system for power maximization and grid fault conditions. Energy Procedia 42: 220–229.

Hossain

Ali

(2015) Future research directions for the wind turbine generator system. Renewable and Sustainable Energy Reviews 49: 481–489.

Kumar

Chatterjee

(2016) A review of conventional and advanced MPPT algorithms for wind energy systems. Renewable and Sustainable Energy Reviews 55: 957–970.

Mohamed

Elshewy

Abdel-kader

(2012) Dynamic Operation of Synchronous Motor Using DTC Technique Instead of Damper Winding. In: 15th International Middle East Power Systems conference, MEPCON, Alexandria University, Egypt, 23–25 December, 2012.

10.

Oğuz

Güney

Çalık

(2013) Power quality control and design of power converter for variable-speed wind energy conversion system with permanent-magnet synchronous generator. The Scientific World Journal 2013: 783010.

11.

Purushotham

Girish

Kiran

(2017) An improved SMC control strategies for PMSG based WECS. International Journal of Advanced Engineering Research and Science (IJAERS) Special Issue 5: 63–72.

12.

Rajalakshmi

(2018) A novel PMSG based WECS for grid integration using direct matrix converter. International Journal of Engineering and Advanced Technology (IJEAT) 8(2S): 7–11.

13.

Rezvani

Esmaeily

Etaati

, et al. (2019) Intelligent hybrid power generation system using new hybrid fuzzy-neural for photovoltaic system and RBFNSM for wind turbine in the grid connected mode. Frontiers in Energy 13: 131–148.

14.

Sahu

Gupta

Singh

, et al. (2018) Design of permanent magnet synchronous generator for wind energy conversion system. In: SenGupta

Zobaa

Sonam Sherpa

, et al. (eds) Advances in Smart Grid and Renewable Energy. Singapore: Springer, pp. 23–32.

15.

Saleh

Khan

Rahman

(2011) Steady-state performance analysis and modelling of directly driven interior permanent magnet wind generators. IET Renewable Power Generation 5: 137–147.

16.

Shen

Wang

Gang

(2011) A novel UPF control strategy of PMSG based on stator flux orientation. In: 2011 Asia-Pacific power and energy engineering conference, Wuhan, China, 25–28 March.

17.

Shengquan

Kezhao

Juan

, et al. (2016) On the rejection of internal and external disturbances in a wind energy conversion system with direct-driven PMSG. ISA Transaction 61: 95–106.

18.

Singh

Agrawa

(2013) A survey on power quality improvement converter of PMSG. In: IET Chennai fourth international conference on sustainable energy and intelligent systems (SEISCON 2013), Chennai, India, 12–14 December.

19.

Wei

Zhang

Qiao

, et al. (2016) An adaptive network-based reinforcement learning method for MPPT control of PMSG wind energy conversion systems. IEEE Transactions on Power Electronics 31: 7837–7848.

20.

Wenshan

Zhang

Xuhui

, et al. (2019) Unity power factor control for surface mounted permanent magnet synchronous generator (PMSG) based on polar coordinate current locus. Journal of Physics: Conference Series1303: 012129.

21.

Lang

Zargari

, et al. (2011) Power Conversion and Control of Wind Energy Systems (Vol. 76). John Wiley & Sons.

22.

WWEA (2019) WWEA Statistics. Available at: https://wwindea.org/information-2/information/

23.

Xie

Sun

, et al. (2017) Small signal stability analysis for different types of PMSGs connected to the grid. Renewable Energy 106: 149–167.

24.

Yang

Shu

, et al. (2018) Democratic joint operations algorithm for optimal power extraction of PMSG based wind energy conversion system. Energy Conversion Management 159: 312–329.

Assessment of proposed maximum power point tracking–unity power factor algorithms for optimum operation permanent magnet synchronous generator–based wind turbine