The importance of $\phi_v$ is that is can directly control the orientation of the stator voltages with respect to the rotor position. In this animation, we will see how this adjustment can affect machine performance under three different control methods.
Recall that for the three-phase machine, the torque $T_e$ is $$\begin{split}T_e & = \frac{3}{2}\frac{P}{2}\lambda'^r_mi^r_{qs}\\ & = \left(\frac{3}{2}\right)\left(\frac{P}{2}\right)\lambda'^r_m\sqrt{2}I_s\cos\left[\theta_{esi}(0)-\theta_r(0)\right]\end{split}~~~~~~~~~~\text{(7)}$$ where $P$ is the number of poles, $\lambda'^r_m$ is the permanent magnet flux linkage referred to the stator windings, and $i^r_{qs}$ is the q axis current. The number of poles and the permanent magnet flux are fixed; thus, the only way to control the torque is by adjusting the q axis current.
Normal Operation
In Normal operation, the stator voltage is aligned with the q axis and $\phi_v=0$. No attempt is made to control the $q$-axis current directly, and both q and d axis currents are present. This control method mimics how a dc machine operates, which is why the permanent magnet synchronous machine is often called a brushless dc machine.
Maximum-Torque per Volt Operation
In Maximum-Torque per Volt operation, the stator voltage is advanced with respect to the q axis $(\phi_v>0)$ to increase $i^r_{qs}$ compared to its value in Normal operation and achieve more torque. In essence, some q axis voltage is traded for negative d axis voltage in order to cancel out some of the permanent magnet flux. Compared to Normal operation, this reduces back emf and allows an increase in $i^r_{qs}$ (and $T_e$) for a given voltage. As derived in Section 6.9, the control angle needed to achieve maximum torque is given by $$\phi_{vMT/V} = \tan^{-1}\left(\frac{\omega_rL_{ss}}{r_s}\right)~~~~~~~~~~\text{(8)}$$ Notice that $\phi_{vMT/V}$ is not fixed; rather, it varies directly with rotor speed.
Maximum-Torque per Ampere Operation
According to (7) d axis current does not produce torque, to achieve maximum torque per ampere, d axis current should be controlled to be zero. In Maximum-Torque per Ampere operation, the stator voltage is adjusted with respect to the q axis in order to set $i^r_{qs}$. As derived in Section 6.9, the control angle for maximum torque per ampere $\phi_{vMT/A}$ is given by $$\phi_{vMT/A} = \tan^{-1}\left[\omega_r\tau_s\left(\frac{-1\pm\omega_r\tau_v\sqrt{1+\omega_r^2\tau_v^2(1-\omega_r^2\tau_v^2)}}{\omega_r^4\tau_s^2\tau_v^2-1}\right)\right]~~~~~~~~~~\text{(9)}$$ where, for compactness $$\tau_s = \frac{L_{ss}}{r_s}~~~~~~~~~~\text{(10)}$$ $$\tau_v = \frac{\lambda'^r_m}{\sqrt{2}V_s}~~~~~~~~~~\text{(11)}$$ As with Maximum-Torque per Volt control, in Maximum-Torque per Ampere $\phi_{vMT/A}$ varies with rotor speed.