**Appendix B**

1. Coefficients of rotor current in Equation (19):

$$
\Delta i\_{r1} = k\_0 \frac{2\omega\_{cl}k\_4 + k\_2}{k\_1k\_4 - k\_2k\_3} (\frac{1}{\tau\_s} + j\omega\_1)
$$

$$
\Delta i\_{r2} = -k\_0 \frac{k\_1 + 2\omega\_{cl}k\_3}{k\_1k\_4 - k\_2k\_3} \frac{1}{\tau\_l}
$$

*Energies* **2018**, *11*, 2471

$$
\Delta d\_{r3} = k\_0 [2\omega\_{cl}(\frac{k\_1 + 2\omega\_{cl}k\_3}{k\_1k\_4 - k\_2k\_3} - \frac{2\omega\_{cl}k\_4 + k\_2}{k\_1k\_4 - k\_2k\_3}) - k\_5],
$$

$$
\Delta d\_{r4} = k\_0k\_5
$$

where

$$k\_0 = -j(\frac{1}{\omega\_1 \tau\_s} + j)\frac{L\_{un}}{sL\_s}\frac{\Delta l\_l}{3\tau\_s K\_{p\_l} K\_{pwo}}$$

$$k\_1 = \frac{1}{\tau\_l}[(\omega\_{cl} - \frac{1}{\tau\_s} - j\omega\_1)^2 + \omega\_{cl}^2]$$

$$k\_2 = (\frac{1}{\tau\_s} + j\omega\_1)[(\frac{1}{\tau\_l} - \omega\_{cl})^2 + \omega\_{cl}^2]$$

$$k\_3 = -\omega\_{cl}^2 - [\omega\_{cl} - (\frac{1}{\tau\_s} + j\omega\_1)]^2$$

$$k\_4 = -\omega\_{cl}^2 - (\omega\_{cl} - \frac{1}{\tau\_l})^2$$

$$k\_5 = \frac{(2\omega\_{cl} - \frac{1}{\tau\_l})(k\_1 + 2\omega\_{cl}k\_3) - [2\omega\_{cl} - (\frac{1}{\tau\_s} + j\omega\_1)](k\_2 + 2\omega\_{cl}k\_4)}{k\_1k\_4 - k\_2k\_3}$$

2. Coefficients of DC bus voltage in Equation (21):

*Udc*1 = <sup>−</sup>0.75*m*|<sup>Δ</sup>*ir*<sup>1</sup>| *ω*1*a Cn Udc*2 = 0.75*m ω*1*C* |<sup>Δ</sup>*ir*<sup>2</sup>| cos(*<sup>α</sup>*2 + *δ*) 1/*<sup>τ</sup>i* (*R* + 1/*<sup>τ</sup>i*)<sup>2</sup> − *M*<sup>2</sup> *Udc*3 = −0.75*<sup>m</sup> ω*1*C* |Δ**i***r*<sup>3</sup>| cos(*<sup>α</sup>*3 + *δ*) √<sup>2</sup>*ωci x Udc*4 = −0.75*<sup>m</sup> ω*1*C* |Δ**i***r*<sup>4</sup>| cos(*<sup>α</sup>*4 + *δ*) √<sup>2</sup>*ωci x Udc*5 = −0.75*<sup>m</sup> ω*1*C* |Δ**i**<sup>∗</sup>*r* | cos(*<sup>α</sup>*5 + *δ*)[ *ωci* (*R* + *<sup>ω</sup>ci*)<sup>2</sup> − *M*<sup>2</sup> ] *Udc*6 = 12*M* [*Udc*1 *na λ*1 cos(*<sup>α</sup>*1+*δ*−*θ*4) (*<sup>λ</sup>*1+1/*<sup>τ</sup>s*)<sup>2</sup>+*ω*<sup>2</sup> + *Udc*2 (*<sup>R</sup>*+1/*<sup>τ</sup>i*)<sup>2</sup>−*M*<sup>2</sup> 1/*<sup>τ</sup>i λ*1 *λ*1+1/*<sup>τ</sup>i* +*Udc*3 √ *x*2*ωci λ*1+*ωci* (*<sup>λ</sup>*1+*ωci*)<sup>2</sup>+(*<sup>ω</sup>ci*)<sup>2</sup> + *Udc*4 √*x*2 *λ*1 (*<sup>λ</sup>*1+*ωci*)<sup>2</sup>+(*<sup>ω</sup>ci*)<sup>2</sup> + *Udc*5 (*<sup>R</sup>*+*ωci*)<sup>2</sup>−*M*<sup>2</sup> *λ*1+*ωci* ] *Udc*7 = − 12*M* [*Udc*1 *na λ*2 cos(*<sup>α</sup>*1+*δ*−*θ*5) (*<sup>λ</sup>*2+1/*<sup>τ</sup>s*)<sup>2</sup>+*ω*<sup>2</sup> + *Udc*2 (*<sup>R</sup>*+1/*<sup>τ</sup>i*)<sup>2</sup>−*M*<sup>2</sup> 1/*<sup>τ</sup>i λ*2 *λ*2+1/*<sup>τ</sup>i* +*Udc*3 √ *x*2*ωci λ*2+*ωci* (*<sup>λ</sup>*2+*ωci*)<sup>2</sup>+(*<sup>ω</sup>ci*)<sup>2</sup> + *Udc*4 √*x*2 *λ*2 (*<sup>λ</sup>*2+*ωci*)<sup>2</sup>+(*<sup>ω</sup>ci*)<sup>2</sup> + *Udc*5 (*<sup>R</sup>*+*ωci*)<sup>2</sup>−*M*<sup>2</sup> *λ*2+*ωci* ]

where *λ*1,2 = *R* ± *M*,

$$\alpha\_1 = a \tan \frac{\text{Re}[\Delta t\_1]}{\text{Im}[\Delta t\_1]}, \ a\_2 = a \tan \frac{\text{Re}[\Delta t\_2]}{\text{Im}[\Delta t\_2]}, \ a\_3 = a \tan \frac{\text{Re}[\Delta t\_3]}{\text{Im}[\Delta t\_3]}, \ a\_4 = a \tan \frac{\text{Re}[\Delta t\_4]}{\text{Im}[\Delta t\_4]}, \ a\_5 = a \tan \frac{\text{Re}[\Delta t\_5^\mu]}{\text{Im}[\Delta t\_5^\mu]}$$

$$a e^{\theta\_1} = 1 / \tau\_s + j\omega$$

$$n e^{\theta\_2} = (R + 1/\tau\_s)^2 - \omega^2 + M^2 + 2j\omega (R + 1/\tau\_s)$$

$$x e^{\theta\_3} = (R + 1/3T\_s + j/3T\_s)^2 + M^2$$

$$\theta\_4 = a \tan \frac{\omega\_1}{\lambda\_1 + 1/\tau\_s}$$

$$\theta\_5 = a \tan \frac{\omega\_1}{\lambda\_2 + 1/\tau\_s}$$

$$\beta\_1 = a\_1 + \delta + \theta\_1 - \theta\_2$$

$$
\theta\_2 = \theta\_3 - \frac{\pi}{4}
$$

#### 3. Coefficient of GSC current in Equation (22):

$$I\_{\mathcal{S}1} = (\omega\_{\mathcal{C}0} - \frac{1}{a^2 \tau\_0 \tau\_5}) \cos \beta\_1 - \frac{\omega}{a^2 \tau\_0} \sin \beta\_1$$

$$I\_{\mathcal{S}2} = (\omega\_{\mathcal{C}0} - \frac{1}{a^2 \tau\_0 \tau\_5}) \sin \beta\_1 + \frac{\omega}{a^2 \tau\_0} \cos \beta\_1$$

$$I\_{\mathcal{S}3} = \mathcal{U}\_{\mathcal{L}\mathcal{C}3} (\cos \beta\_2 - \frac{\cos \beta\_2 - \sin \beta\_2}{2 \omega\_{\mathcal{C}1} \tau\_5}) - \mathcal{U}\_{\mathcal{L}\mathcal{C}4} (\sin \beta\_2 - \frac{\sin \beta\_2 - \cos \beta\_2}{2 \omega\_{\mathcal{C}1} \tau\_5})$$

$$I\_{\mathcal{S}4} = \mathcal{U}\_{\mathcal{L}\mathcal{C}3} (\sin \beta\_2 - \frac{\sin \beta\_2 + \cos \beta\_2}{2 \omega\_{\mathcal{C}2} \tau\_5}) - \mathcal{U}\_{\mathcal{L}\mathcal{C}4} (\cos \beta\_2 - \frac{\cos \beta\_2 + \sin \beta\_2}{2 \omega\_{\mathcal{C}1} \tau\_5})$$

$$I\_{\mathcal{S}5} = -\frac{\mathcal{U}\_{\mathcal{S}0}}{\tau\_0} \frac{\cos \beta\_1 (1/\tau\_0 - 1/\tau\_1) - \omega \sin \beta\_1}{(1/\tau\_0 - 1/\tau\_1)^2 + \omega^2} + \frac{\mathcal{U}\_{\mathcal{S}0} \tau\_5}{\tau\_0} - \frac{\mathcal{U}\_{\mathcal{S}0} \tau\_1}{\tau\_0} \frac{(1/\tau\_0 - \omega\_{\mathcal{C}1}) \cos \beta\_2 + \omega\_{\mathcal{C}1} \sin \beta\_1}{(1/\tau\_0 - \omega\_{\mathcal{C}1})^1 + \omega^2}$$
