LVRT capability enhancement in the grid-connected DFIG-driven WECS using adaptive hysteresis current controller

Abstract

With high access of wind energy conversion system (WECS) into the grid, it is essential that the wind energy producing companies have to conform the grid code standards laid down by the country. The low voltage-ride through (LVRT) capability is one among the obligations of all grid code standards. The LVRT capability can be enhanced by controlling the power electronic converters without any additional cost. This work proposes a novel adaptive hysteresis controller (AHC) for the LVRT capability enhancement of grid connected double-feed induction generator (DFIG)-driven WEC system. The active and reactive power flow at the DFIG is managed by modified PQ controller, and the results are compared with PQ controller. The DC link voltage (V_dc) under normal and fault conditions is controlled by fuzzy logic control (FLC). The proposed AHC controller is tested with 9 MW grid connected WEC system on Matlab/Simulink platform, and a detailed simulation was carried out under normal and fault conditions. The test results disclose the efficiency of the proposed approach.

Appendices

Appendix 1

1.1 A. Mathematical model of WT

The power harvested by the WT is provided by the relation

$$P = \frac{1}{2}\rho A\mathop V\nolimits^{3} \mathop C\nolimits_{p} \left( {\lambda ,\beta } \right)$$

where the density of air is ρin $\left( {kg/m3} \right)$;

the rotor blade swept area is A in $\left( {m2} \right)$;

the speed of the wind is V in $\left( {m/s} \right)$;

the coefficient of power is C_p;

C_p relies on ƛ the tip speed ratio (TSR) and β the pitch angle

$$\mathop C\nolimits_{p} = \frac{1}{2}\left( {\gamma - 0.022\mathop \beta \nolimits^{2} - 5.6} \right)\mathop e\nolimits^{ - 0.17\gamma }$$

(21)

$$\lambda = \frac{Tip\,Speed}{{Wind\,Speed}}$$

(22)

$$\gamma = 2.237\frac{{\mathop V\nolimits_{{}} }}{{\mathop \omega \nolimits_{\beta } }}$$

ω_β is the angular velocity of the blade in (rad/sec).

1.2 B. Model of drive train

A drive train with high-power-density and compact in size is needed by the DFIG-driven WEC system to transmit the varying input in a very demanding environment. Two masses model drive train is used in this model. The major application of the drive train is to transmit the shaft speed of WT from low to high. The WT inertia and the generator inertia are connected by a single spring shaft.

The mechanical torque of the drive train is given as

$$\mathop T\nolimits_{m} = K\frac{\theta }{n} + D\left( \frac{1}{n} \right)\left( {\frac{d\theta }{{dt}}} \right)$$

(23)

$$\frac{d\theta }{{dt}} = \mathop \omega \nolimits_{g} - \mathop \omega \nolimits_{n}$$

(24)

Motion of WT is

$$\mathop H\nolimits_{m} \frac{{\mathop {d\omega }\nolimits_{m} }}{dt} = \mathop T\nolimits_{\omega } - \mathop T\nolimits_{m}$$

(25)

Motion of generator is

$$\mathop H\nolimits_{g} \frac{{\mathop {d\omega }\nolimits_{g} }}{dt} = \mathop T\nolimits_{e} + \frac{{\mathop T\nolimits_{m} }}{n}$$

(26)

where the torque of WT is $\mathop T\nolimits_{\omega }$; $\mathop T\nolimits_{e}$ is the electromagnetic torque; the speed of the rotor of WT is $\mathop \omega \nolimits_{m}$; the rotor speed of generator is $\mathop \omega \nolimits_{g}$; the constant of inertia of the WT is $\mathop H\nolimits_{m}$; the constant of inertia of the generator is $\mathop H\nolimits_{g}$; the stiffness constant is K; the damping constant is D; the gear ratio is n; θ is the angle among WT rotor and generator rotor

1.3 C. Model of DFIG

The DFIG’s dynamic modeling of a synchronous rotating dq reference frame has been given as:

$$Stator\;voltage\;\mathop V\nolimits_{s} = \mathop R\nolimits_{s} \mathop I\nolimits_{s} + \frac{{d\mathop \varphi \nolimits_{s} }}{dt}$$

(27)

$${\text{ }}V_{{ds}} = {\text{ }}R_{s} {\text{ }}I_{{ds}} - \omega _{s} \phi _{{qs}} + \frac{{d\phi _{{ds}} }}{{dt}}$$

(28)

$${\text{ }}V_{{qs}} = {\text{ }}R_{s} {\text{ }}I_{{qs}} + \omega _{s} \phi _{{ds}} + \frac{{d\phi _{{qs}} }}{{dt}}$$

(29)

$$\phi _{{ds}} = {\text{ }}L_{s} {\text{ }}I_{{ds}} + {\text{ }}L_{m} {\text{ }}I_{{dr}}$$

(30)

$$\phi _{{qs}} = {\text{ }}L_{s} {\text{ }}I_{{qs}} + {\text{ }}L_{m} {\text{ }}I_{{qr}}$$

(31)

$$\phi _{s} = {\text{ }}L_{s} {\text{ }}I_{s} + {\text{ }}L_{m} {\text{ }}I_{r}$$

(32)

where ${R}_{s}$ is the stator resistance, ${I}_{s}$ is the stator current, ɸ_s is the stator flux, ω_s is the stator angular speed; ${L}_{m}$ denotes the mutual inductance,${ L}_{s}$ denotes the stator inductance,${ V}_{ds}$ denotes the direct axis voltage of the stator, ${V}_{qs}$ is the quadrature axis voltage of the stator, I_ds is the direct axis current of the stator,${I}_{qs}$ is the quadrature axis current of the stator,${ I}_{dr}$ is the direct axis rotor current,${ I}_{qr}$ is the quadrature axis rotor current, and ${I}_{r}$ is the rotor current.

$$Rotor{\mkern 1mu} \;voltage\;{\text{ }}V_{r} = {\text{ }}R_{r} {\text{ }}I_{r} + \frac{{d\phi _{r} }}{{dt}} - j\omega _{m} \phi _{r}$$

(33)

$${\text{ }}V_{{dr}} = {\text{ }}R_{r} {\text{ }}I_{{dr}} - s\omega _{s} \phi _{{qr}} + \frac{{d\phi _{{dr}} }}{{dt}}$$

(34)

$$\mathop V\nolimits_{qr} = \mathop R\nolimits_{r} \mathop I\nolimits_{qr} + s\mathop \omega \nolimits_{s} \mathop \varphi \nolimits_{dr} + \frac{{d\mathop \varphi \nolimits_{qr} }}{dt}$$

(35)

$$\phi _{{dr}} = {\text{ }}L_{r} {\text{ }}I_{{dr}} + {\text{ }}L_{m} {\text{ }}I_{{ds}}$$

(36)

$$\phi _{{qr}} = L_{r} I_{{qr}} + L_{m} I_{{qs}}$$

(37)

$$\phi _{r} = L_{r} I_{r} + L_{m} I_{s}$$

(38)

$$slip\;\mathop \omega \nolimits_{slip} = \frac{{\mathop \omega \nolimits_{s} - \mathop \omega \nolimits_{r} }}{{\mathop \omega \nolimits_{s} }}$$

(39)

where R_r is the rotor resistance; ɸ_r is the rotor flux; ω_r is the rotor angular speed; ω_m is the generator angular speed; L_r is the rotor inductance; V_dr is the direct axis voltage of the rotor; V_qr is the quadrature axis voltage of the rotor; I_dr is the direct axis current of the rotor; I_qr is the quadrature axis current of the rotor; s is slip.

1.4 D. Modelling of converter

The power electronic apparatus used in the WEC system are bi-directional power converters. It has two voltage source converters (VSC) with three-phase switched PWM and a DC bus that connects the back-to-back converters (B2B) through a DC-link capacitor.

The average model of the B2B in the WEC system is explained as follows:

After Park’s transformation of variables,

$$\frac{d}{dt}\left[ {\begin{array}{*{20}c} {\mathop I\nolimits_{d1} } \\ {\mathop I\nolimits_{q1} } \\ \end{array} } \right] = \frac{1}{{\mathop L\nolimits_{1} }}\left[ {\begin{array}{*{20}c} {\mathop D\nolimits_{d1} } \\ {\mathop D\nolimits_{q1} } \\ \end{array} } \right]\mathop V\nolimits_{dc1} - \frac{1}{{\mathop L\nolimits_{1} }}\left[ {\begin{array}{*{20}c} {\mathop V\nolimits_{d} } \\ {\mathop V\nolimits_{q} } \\ \end{array} } \right] - \left[ {\begin{array}{*{20}c} 0 & { - \omega } \\ \omega & 0 \\ \end{array} } \right].\left[ {\begin{array}{*{20}c} {\mathop I\nolimits_{d1} } \\ {\mathop I\nolimits_{q1} } \\ \end{array} } \right]$$

(40)

$$\frac{d}{dt}\left[ {\begin{array}{*{20}c} {\mathop I\nolimits_{d2} } \\ {\mathop I\nolimits_{q2} } \\ \end{array} } \right] = \frac{1}{{\mathop L\nolimits_{2} }}\left[ {\begin{array}{*{20}c} {\mathop D\nolimits_{d2} } \\ {\mathop D\nolimits_{q2} } \\ \end{array} } \right]\mathop V\nolimits_{dc2} - \frac{1}{{\mathop L\nolimits_{2} }}\left[ {\begin{array}{*{20}c} {\mathop V\nolimits_{d} } \\ {\mathop V\nolimits_{q} } \\ \end{array} } \right] - \left[ {\begin{array}{*{20}c} 0 & { - \omega } \\ \omega & 0 \\ \end{array} } \right].\left[ {\begin{array}{*{20}c} {\mathop I\nolimits_{d2} } \\ {\mathop I\nolimits_{q2} } \\ \end{array} } \right]$$

(41)

$$\frac{d}{dt}\left[ {\begin{array}{*{20}c} {\mathop V\nolimits_{d} } \\ {\mathop V\nolimits_{q} } \\ \end{array} } \right] = \frac{1}{2C}\left[ {\begin{array}{*{20}c} {\mathop I\nolimits_{d1} } \\ {\mathop I\nolimits_{q1} } \\ \end{array} } \right] + \frac{1}{2C}\left[ {\begin{array}{*{20}c} {\mathop I\nolimits_{d2} } \\ {\mathop I\nolimits_{q2} } \\ \end{array} } \right] - \frac{1}{RC}\left[ {\begin{array}{*{20}c} {\mathop V\nolimits_{d} } \\ {\mathop V\nolimits_{q} } \\ \end{array} } \right] - \left[ {\begin{array}{*{20}c} 0 & { - \omega } \\ \omega & 0 \\ \end{array} } \right].\left[ {\begin{array}{*{20}c} {\mathop V\nolimits_{d} } \\ {\mathop V\nolimits_{q} } \\ \end{array} } \right]$$

(42)

If the input DC sources are assumed to be ideal, then

$$\frac{d}{dt}\left[ {\begin{array}{*{20}c} {\mathop {\mathop I\nolimits_{d1} }\limits^{ - } } \\ {\mathop {\mathop I\nolimits_{q1} }\limits^{ - } } \\ \end{array} } \right] = \frac{1}{{\mathop L\nolimits_{1} }}\left[ {\begin{array}{*{20}c} {\mathop {\mathop D\nolimits_{d1} }\limits^{ - } } \\ {\mathop {\mathop D\nolimits_{q1} }\limits^{ - } } \\ \end{array} } \right]\mathop V\nolimits_{dc1} - \frac{1}{{\mathop L\nolimits_{1} }}\left[ {\begin{array}{*{20}c} {\mathop {\mathop V\nolimits_{d} }\limits^{ - } } \\ {\mathop {\mathop V\nolimits_{q} }\limits^{ - } } \\ \end{array} } \right] - \left[ {\begin{array}{*{20}c} 0 & { - \omega } \\ \omega & 0 \\ \end{array} } \right].\left[ {\begin{array}{*{20}c} {\mathop {\mathop I\nolimits_{d1} }\limits^{ - } } \\ {\mathop {\mathop I\nolimits_{q1} }\limits^{ - } } \\ \end{array} } \right]$$

(43)

$$\frac{d}{dt}\left[ {\begin{array}{*{20}c} {\mathop {\mathop I\nolimits_{d2} }\limits^{ - } } \\ {\mathop {\mathop I\nolimits_{q2} }\limits^{ - } } \\ \end{array} } \right] = \frac{1}{{\mathop L\nolimits_{2} }}\left[ {\begin{array}{*{20}c} {\mathop {\mathop D\nolimits_{d2} }\limits^{ - } } \\ {\mathop {\mathop D\nolimits_{q2} }\limits^{ - } } \\ \end{array} } \right]\mathop V\nolimits_{dc1} - \frac{1}{{\mathop L\nolimits_{2} }}\left[ {\begin{array}{*{20}c} {\mathop {\mathop V\nolimits_{d} }\limits^{ - } } \\ {\mathop {\mathop V\nolimits_{q} }\limits^{ - } } \\ \end{array} } \right] - \left[ {\begin{array}{*{20}c} 0 & { - \omega } \\ \omega & 0 \\ \end{array} } \right].\left[ {\begin{array}{*{20}c} {\mathop {\mathop I\nolimits_{d2} }\limits^{ - } } \\ {\mathop {\mathop I\nolimits_{q2} }\limits^{ - } } \\ \end{array} } \right]$$

(44)

$$\frac{d}{dt}\left[ {\begin{array}{*{20}c} {\mathop {\mathop V\nolimits_{d} }\limits^{ - } } \\ {\mathop {\mathop V\nolimits_{q} }\limits^{ - } } \\ \end{array} } \right] = \frac{1}{2C}\left( {\left[ {\begin{array}{*{20}c} {\mathop {\mathop I\nolimits_{d1} }\limits^{ - } } \\ {\mathop {\mathop I\nolimits_{q1} }\limits^{ - } } \\ \end{array} } \right] + \left[ {\begin{array}{*{20}c} {\mathop {\mathop I\nolimits_{d2} }\limits^{ - } } \\ {\mathop {\mathop I\nolimits_{q2} }\limits^{ - } } \\ \end{array} } \right]} \right) - \left[ {\begin{array}{*{20}c} \frac{1}{RC} & { - \omega } \\ \omega & \frac{1}{RC} \\ \end{array} } \right].\left[ {\begin{array}{*{20}c} {\mathop {\mathop V\nolimits_{d} }\limits^{ - } } \\ {\mathop {\mathop V\nolimits_{q} }\limits^{ - } } \\ \end{array} } \right]$$

(45)

Equations (43) to (45) could be written in general matrix structure as:

X = AX + BU.

Y = CX.where $X$ is the state vector and $U$ is the control vector

$$X = \mathop {\left[ {\begin{array}{*{20}c} {\mathop {\mathop V\nolimits_{d} }\limits^{ - } } & {\mathop {\mathop V\nolimits_{q} }\limits^{ - } } & {\mathop {\mathop I\nolimits_{d1} }\limits^{ - } } & {\mathop {\mathop I\nolimits_{q1} }\limits^{ - } } & {\mathop {\mathop I\nolimits_{d2} }\limits^{ - } } & {\mathop {\mathop I\nolimits_{q2} }\limits^{ - } } \\ \end{array} } \right]}\nolimits^{T}$$

(46)

$$U = \mathop {\left[ {\begin{array}{*{20}c} {\mathop {\mathop D\nolimits_{d1} }\limits^{ - } } & {\mathop {\mathop D\nolimits_{q1} }\limits^{ - } } & {\mathop {\mathop D\nolimits_{d2} }\limits^{ - } } & {\mathop {\mathop D\nolimits_{q2} }\limits^{ - } } \\ \end{array} } \right]}\nolimits^{T}$$

(47)

$$C = I$$

(48)

$$A = \left[ {\begin{array}{*{20}c} { - 1/RC} & \omega & {1/2C} & 0 & {1/2C} & 0 \\ { - \omega } & { - 1/RC} & 0 & {1/2C} & 0 & {1/2C} \\ { - 1/\mathop L\nolimits_{1} } & 0 & 0 & \omega & 0 & 0 \\ 0 & { - 1/\mathop L\nolimits_{1} } & { - \omega } & 0 & 0 & 0 \\ { - 1/\mathop L\nolimits_{2} } & 0 & 0 & 0 & 0 & \omega \\ 0 & { - 1/\mathop L\nolimits_{2} } & 0 & 0 & { - \omega } & 0 \\ \end{array} } \right]$$

(49)

$$B = \mathop {\left[ {\begin{array}{*{20}c} 0 & 0 & {\mathop V\nolimits_{dc1} /\mathop L\nolimits_{1} } & 0 & 0 & 0 \\ 0 & 0 & 0 & {\mathop V\nolimits_{dc1} /\mathop L\nolimits_{1} } & 0 & 0 \\ 0 & 0 & 0 & 0 & {\mathop V\nolimits_{dc1} /\mathop L\nolimits_{1} } & 0 \\ 0 & 0 & 0 & 0 & 0 & {\mathop V\nolimits_{dc1} /\mathop L\nolimits_{1} } \\ \end{array} } \right]}\nolimits^{T}$$

(50)

1.5 E. Derivation for AHC bandwidth

$$\begin{gathered} \mathop {dI}\nolimits_{ag}^{ + } = \frac{1}{L}\left( {0.5\mathop V\nolimits_{dc} - \mathop V\nolimits_{ag} } \right) \hfill \\ \hfill \\ \end{gathered}$$

(51)

$$\begin{gathered} \mathop {dI}\nolimits_{ag}^{ - } = - \frac{1}{L}\left( {0.5\mathop V\nolimits_{dc} + \mathop V\nolimits_{ag} } \right) \hfill \\ \hfill \\ \end{gathered}$$

(52)

where V_ag is the per phase grid voltage, I_ag is the grid current per phase, and L is the inductance of the line. T₁ and T₂ are the switching periods.

$$\mathop T\nolimits_{1} + \mathop T\nolimits_{2} = T = \frac{1}{f}$$

(53)

Here, the modulation frequency is denoted as f.

$$\frac{{d\mathop I\nolimits_{ag}^{ + } }}{dt}\mathop T\nolimits_{1} - \frac{{d\mathop I\nolimits_{agref} }}{dt}\mathop T\nolimits_{1} = 2\mathop {HB}\nolimits_{a}$$

(54)

$$\frac{{d\mathop I\nolimits_{ag}^{ - } }}{dt}\mathop T\nolimits_{2} - \frac{{d\mathop I\nolimits_{agref} }}{dt}\mathop T\nolimits_{1} = - 2\mathop {HB}\nolimits_{a}$$

(55)

Appendix 2

DFIG-driven WECS parameters.

Rated power of DFIG:$1.5 MW$	Stator_ Resistance: $0.023 p.u$
Stator voltage:$575 V$	Rotor_ Resistance: $0.016 p.u$
Rotor voltage:$1975 V$	Stator_Leakage Inductance: $0.18 p.u$
DC link capacitor voltage:$1150 V$	Rotor_Leakage Inductance: $0.16 p.u$
Capacitance of DC link capacitor:$0.1 F$	Mutual_Inductance: $2.9 p.u$