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Appendix

A. Parameters of the Simulation Models

Table 9.A.1

Parameters of the Simplified Model (Turbine and Generator)

Parameter	Value
Density area, ρ (kg/m)	1.225
Nominal mechanical power, P_m,n (MW)	5
Radius of the turbine, R (m)	63
Nominal wind speed, v_n (m/s)	12
Gain of the multiplier, G	97
Inertia of the turbine, J_t (kg/m)	35.44 × 10⁶
Inertia of the generator, J_g (kg/m)	534.116
Shaft spring constant, K (N/m/rad)	867.64 × 10⁶
Shaft mutual damping, D (N/m/s/rad)	6.217 × 10⁶
Hydraulic time constant, τ_H (s)	0.05

Table 9.A.2

Parameters of the Detailed Model

Parameters	SCIG 2 kW	SCIG 149.2 kW	DFIG 1.5 MW
Grid
Effective voltage, V_s (V)	380	460	610
Frequency, f_s (Hz)	50	50	50
Transformer
Leakage resistance, R_f (Ω)	3.4	0.1	3
The leakage inductance, L_f (mH)	3.3	2	2.5
Turbine
Density area, ρ (kg/m²)	1.225	1.225	1.225
Nominal mechanical power, P_m,n (kW)	2.68	149.2	1.5
Radius of the turbine, R (m)	1.4	10.5	35
Nominal wind speed, v_n (m/s)	12	12	11
Gain of the multiplier, G	2.445312	17.1806	75
SCIG and DFIG
Nominal frequency, f_g,n (Hz)	50	50	50
Stator resistance, R_s (mΩ)	4850	14.85	12
Stator leakage inductance, L_ls (mH)	16	0.3027	13.7
Rotor resistance, R_r (mΩ)	3805	9.295	21
Rotor leakage inductance, L_lr (mH)	16	0.3027	13.7
Cyclic mutual inductance, L_m (mH)	258	10.46	13.5
Inertia, J (kg/m²)	0.031	3.1	1000
Viscous friction coefficient , f (Nm s/rad)	0.00114	0.08	0.0024
Number of pole pairs, p	2	2	2
Table Continued

Parameters	SCIG 2 kW	SCIG 149.2 kW	DFIG 1.5 MW
DTC-SVM
Flux hysteresis band, $Δ φ$ $Δ φ$	±0.01 Wb
Torque hysteresis band, $Δ T_{e m}$ $Δ T_{e m}$	±0.5 Nm
SVM switching frequency (Hz)	2000	2000

Table 9.A.3

Parameters of the PI Controllers

Parameters	SCIG 2 kW	SCIG 149.2 kW
DTC-SVPWM Control Block
Proportional gain of speed controller, K_p	1	30
Integral gain of the speed controller, K_i	15.872	200
Proportional gain of torque controller, K_pt	2	1.5
Integral gain of torque controller, K_it	150	100
Proportional gain of flux controller, K_pf	200	250
Integral gain of flux controller, K_if	1200	4000
DC-Side Control Block
Proportional gain of DC voltage controller, K_pdc	2	2
Integral gain of DC voltage controller, K_pdc	25	33.33
Source-Side Control Block
Proportional gain of current controller, K_pc	6	6
Integral gain of current controller, K_ic	4500	4.50

Table 9.A.4

Parameters of the PI Controllers of the IFOC Blocks

IFOC Control Block
Regulator Parameters	SCIG 2 kW
Proportional gain of current controller, K_pc	1
Integral gain of current controller, K_ic	15.872

B. Influence of Order 3 Harmonic on the Behavior of the SVPWM

In three phase, harmonics can be reduced without reducing the amplitude of the output voltage because the harmonic of order 3 or a multiple of 3 are eliminated from output voltages. A harmonic of order 3 can be added to a sinusoid of frequency f to form the reference waveform. This harmonic appears in the three fictitious voltages V_ao, V_b0, and V_c0with respect to the fictitious midpoint 0, but does not appear in the phase output voltages V_an, V_bn, and V_cn and line-to-line output voltages V_ab, V_bc, and V_ca.

The addition of harmonic of order 3 increases the maximum amplitude of the fundamental in the output voltages.

With reference to Fig. 9.B.1, the reference voltage is composed of two sinusoids: one for the fundamental and the other for the harmonic of order 3.

The new reference signal for the PWM is:

${(V_{a} - V_{o})}_{w} = \frac{U}{2} (M I \sin (ω t) + k \sin (3 ω t))$ ${(V_{a} - V_{o})}_{w} = \frac{U}{2} (M I \sin (ω t) + k \sin (3 ω t))$

(9.B.1)

This is called suboptimal control.

The maximum value of MI occurs for

k = 1 / 3 \sqrt{3}

$k = 1 / 3 \sqrt{3}$

and is found as:

$M I_{\max} = \frac{2}{\sqrt{3}}$ $M I_{\max} = \frac{2}{\sqrt{3}}$

(9.B.2)

Figure 9.B.1 Suboptimal SVPWM. (A) Triangular carrier V_t(t) and reference (V_a − V_o)_w. (B) Control pulse for phase i(where i = a, b, c).

Therefore, with suboptimal control, the maximum amplitude of the fundamental output voltage V₁ corresponding to MI_max is:

$V_{1, M I_{m a x}} = 2 / \sqrt{3} V_{d c}$ $V_{1, M I_{m a x}} = 2 / \sqrt{3} V_{d c}$

(9.B.3)

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Appendix

A. Parameters of the Simulation Models

B. Influence of Order 3 Harmonic on the Behavior of the SVPWM

Table of Contents for
Appendix