Keywords

1 Introduction

Over the years, the wind generator sector has become increasingly popular. Conventional power generators did not reach the megawatts system. As a result, the majority of the early models used permanent magnet synchronous generators (PMSGs) or a common asynchronous generator. A gearbox is usually connecting an asynchronous generator to a turbine. If the generator has a large number of poles, a permanent compatible generator (PMSG) can be connected to a turbine with a gearbox or directly outside the gearbox [1, 2]. Because of the increase in power per megawatt system, which is now up to 10 MW, PMSG changes necessitate an increase in converter size and weight. Permanent magnetic generators with synchronous generators having the advantages of being more durable, smaller in size, requiring no additional power supply to stimulate the magnetic field, and requiring less adjustment than conventional generators. Furthermore, when compared to the constant-speed technique, variable-speed wind power has advantages such as magnitude, the ability to track spots, and reduced acoustic noise at low wind speeds [3, 4]. The modeling and control approaches used in two permanent magnet synchronous generator farms for wind applications are described in this paper. A completely integrated rear-turning converter, consisting of two three-phase capacitors, a central DC bus, and an inverter, is used to link generators to the power grid [5, 6]. The entire system is phase connected to the electrical grid. Maximum power point tracking (MPPT) for PMSG speed control, active power control, and DC bus power management are among the proposed control solutions. Some simulation results are shown and examined using the MATLAB/Simulink programming to demonstrate the effectiveness of control schemes [7, 8].

2 Modeling of Wind Turbine

An aerodynamic model of the wind turbines is a basic part of the dynamic models of the electricity producing wind turbines. Theoretical power generated by the turbine is given by,

$${\varvec{P}}_{{\varvec{m}}} = \frac{1}{2}\user2{\rho AV}^{3} {\varvec{C}}_{{\varvec{p}}} \left( {{\varvec{\lambda}},{\varvec{\beta}}} \right)$$
(1)

where

P m :

mechanical power developed in turbine.

ρ :

air density 1.223 kg/m3.

A :

area swept by rotor blades.

C p :

coefficient of power.

λ :

ratio between blade tip speed and wind speed at hub height.

β :

pitch angle,

C p :

(λ, β) can be determined as

$${\varvec{C}}_{{\varvec{p}}} = \frac{1}{2}\left[ {\frac{116}{{\varvec{\lambda}}} - 0.4{\varvec{\beta}} - 5} \right]{\varvec{e}}^{{\left( {\frac{ - 21}{{{\varvec{\lambda}}_{{\varvec{i}}} }}} \right)}}$$
(2)

where λi is defined as,

$$\frac{1}{{{\varvec{\lambda}}_{{\varvec{i}}} }} = \frac{1}{{\varvec{\lambda}}} + 0.08{\varvec{\beta}} - \frac{0.035}{{\left( {1 + {\varvec{\beta}}^{3} } \right)}}$$
(3)

3 Modeling of PMSG

In this research paper, permanent magnet synchronous generator (PMSG) is used as the wind turbine generator due to its property of self-excitation (by permanent magnet) which eliminates the excitation loss, i.e., excitation losses are not increases as number of poles doubled. Two-phase synchronous reference rotating frame (d-q frame) is used to derive the dynamic model of the d-axis with PMSG in which the q-axis is 90° ahead with respect to the direction of rotation [9, 10]. The electrical model of permanent magnet synchronous generator in synchronous reference rotating frame is represented by the differential equations,

$$\frac{{\text{d}}}{{{\text{d}}t}}\left( {i_{d} } \right) = \frac{{ - R_{a} }}{{L_{d} }}i_{d} + \omega_{e} \frac{{L_{q} }}{{L_{d} }}i_{q} + \frac{1}{{L_{d} }}U_{d}$$
(4)
$$\begin{aligned} \frac{{\text{d}}}{{{\text{d}}t}}\left( {i_{q} } \right) & = \frac{{ - R_{a} }}{{L_{q} }}i_{q} - \omega _{e} \left( {\frac{{L_{d} }}{{L_{q} }}i_{d} + \frac{1}{{L_{d} }}\lambda _{o} } \right) + \frac{1}{{L_{q} }}U_{q} \\ \omega _{e} & = P\omega _{g} ,e_{q} = \omega _{e} \lambda _{o} ,T_{e} = 1.5P\left[ {\left( {L_{d} - L_{q} } \right)i_{d} i_{q} + i_{q} \lambda _{o} } \right] \\ \end{aligned}$$
(5)

where Ra is resistance of stator winding, ωe and ωg are electrical and mechanical rotating speed, λ◦ is flux produced by the permanent magnets, P is number of pole pairs, Ud and Uq are d and q-axis voltages, Ld and Lq are d and q-axis inductances, Te is electromagnetic torque, and eq is q-axis counter electrical potential [11–15].

4 Performance Assessment with Balanced and Unbalanced Condition

The various performance characteristics like voltage and current at stator terminal and grid have been plotted for healthy and unbalanced condition are shown from Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. It is observed that THD or harmonics are found to be less with unbalanced condition in comparison to healthy condition. Such comparative analysis is also shown in Table 1.

Fig. 1
A graph of three phase voltage versus time. It plots 3 oscillating waves that have equal magnitudes but different time periods.

Balance three-phase voltage at stator terminal

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Fig. 2
A graph of three phase current versus time. It plots 3 oscillating waves with higher amplitudes for approximately 0.02 on the x axis. The amplitudes decrease and become stable from there on.

Balance three-phase current at stator terminal

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Fig. 3
A graph of current measurement A C-D C versus time. It plots a highly noisy oscillating pattern with higher amplitudes for approximately 0.01 on the x axis. The amplitudes decrease and then become stable.

Current measurement at stator terminal

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Fig. 4
A line graph of voltage measurement versus time. The plot starts at the origin, ascends to a peak at (0.01, 800), and then saturates at 700.

Voltage measurement at DC link

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Fig. 5
A graph of three phase voltage versus time. It plots 3 noisy waves that start from the origin. The amplitudes increase and saturate between negative 750 and 750 volts.

Three-phase voltage at grid

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Fig. 6
A graph of three phase current versus time. It plots 3 waves that start from the origin. They have distortions until 0.01 on the x axis, and then they oscillate.

Three-phase current at grid

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Fig. 7
A line graph of active power versus time. The plot starts at the origin, gradually ascends as an S curve to a peak, descends to a trough, and then saturates.

Active power at stator terminal

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Fig. 8
A graph of three phase current versus time. It plots 3 oscillating waves. The amplitudes of the waves increase and decrease alternatively.

Unbalanced three-phase current (LLL Fault) at stator terminal

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Fig. 9
A graph of three phase voltage at L L L fault versus time. It plots 3 oscillating waves of three phase V I measurement signals 1, 2, and 3. The waves have lower amplitudes between 0.02 and 0.08 on the x axis. The amplitudes then ascend.

Unbalanced three-phase voltage (LLL Fault) at stator terminal

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Fig. 10
A graph of three phase current at L L L fault versus time. It plots 3 oscillating waves that have distortions until 0.02 seconds. The waves have lower amplitudes during the time from 0.02 to 0.08, and the amplitudes then saturate between minus 150 and 150 amperes.

Unbalanced three-phase current (LLL Fault) at grid

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Fig. 11
A graph of three phase voltage L L G fault versus time. It plots 3 oscillating waves of three phase V I measurement signals 1, 2, and 3. Signal 2 has lower amplitudes than 1 and 3, between 0.02 and 0.08 on the x axis.

Unbalanced three-phase voltage (LG Fault) at stator terminal

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Fig. 12
A graph of three phase current L L G fault versus time. It plots 3 oscillating waves. Two of the waves have lower amplitudes than the third during the time from 0.02 to 0.08 on the x axis.

Unbalanced three-phase current (LG Fault) at stator terminal

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Table 1 THD (%) comparison with balanced and unbalanced condition
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Similar kinds of results are also obtained for MSE which is shown in Table 2.

Table 2 MSE comparison with balanced and unbalanced condition
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5 Conclusions

The analysis and modeling of a wind-driven permanent magnet synchronous generator are presented in this study. Controlling the pitch angle and tip to speed ratio of a wind turbine allows it to produce the most power. A permanent magnet synchronous machine's modeling is evaluated. After that, PMSG is analyzed to see if it is healthy or not. Variable loading conditions are used to define the unhealthy situation. Following that, power quality issues such as THD and MSE are investigated for both circumstances. It is observed that MSE and THD are found to be less with healthy condition in comparison with unhealthy condition.