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(B_o - R_s \, B_g) \, G_O +(B_g - R_V \, B_o) \, G_G + (B_w  \, G_W - \phi  )\, (1- R_s \, R_v)  = 0

G_O = V^{-1} \, \delta \, Q_O + \phi_i \, \left[ \frac{s_{oi}}{B_{oi}}  + \frac{R_{vi}\, s_{gi}}{B_{gi}}\right] 

\delta \, Q_O = - Q^{\uparrow}_O

G_G = V^{-1} \, \delta \, Q_G + \phi_i \, \left[ \frac{R_{si}\, s_{oi}}{B_{oi}}  + \frac{ s_{gi}}{B_{gi}}\right] 

\delta \, Q_G = Q^{\downarrow}_G - Q^{\uparrow}_G + Q^{\uparrow}_{GCAP}

G_W = V^{-1} \, \delta \, Q_W +  \frac{ \phi_i \, s_{wi}}{B_{wi}} 

\delta \, Q_W = Q^{\downarrow}_W - Q^{\uparrow}_W + Q^{\uparrow}_{WAQ}