*4.3. The Flywheel Variables*

The direct *isd* and quadrature *isq* stator currents of the ASM, relative to the 360 A ASM base current and the flywheel shaft speed, relative to the 3000 r.p.m ASM base speed are shown for the FESS test in Figure 11. The direct current creates the ASM magnetic flux, and its sign is always positive. The quadrature current sets the ASM torque and its sign is positive/negative for motor/brake torque (sign criteria usually employed with servos), increasing/decreasing the flywheel speed, and with the FESS consuming/supplying power from/to the isolated grid. There is no PWM current ripple in quadrature and direct currents, since the FESS power converters use average models for faster simulation. The ASM (flywheel) speed indicates how the FESS changes its stored energy, as FESS SOC

is proportional to the square of the flywheel speed. Figure 11 left scale is for currents pu and right scale is for speed pu.

Following the ASM-FOC, the direct current value is +0.1923 pu, which is the optimum magnetizing current for maximum power factor at rated power. As explained in Section 2.4, the FESS exchanged power is controlled by adjusting the ASM quadrature current as the ASM-flywheel speed can be considered fairly constant, due to the flywheel high inertia and the short length of the simulations. The initial FESS power and quadrature current are null. After the wind speed step, the 87 kW FESS consumed power is the sum of the WTG power excess (143–75 kW) and the minimum loading of the DG (19 kW), the quadrature current maximum is 0.3951 pu at *t* = 0.5354 s, and its steady state value is 0.3724 pu. During the +100 kW load step transient, the quadrature current has small negative peaks, which corresponds to the FESS supplying power. After the transient, the FESS power is null, and so the quadrature current returns to null value.

Initially, the FESS speed is 0.5898 pu. After the wind speed step, the FESS speed increases almost linearly as the FESS absorbed power is constant after the transient. After the load step transient, the FESS power is null and the FESS speed remains constant in 0.6061 pu, as FESS losses are not considered.
