Analytically derived fixed termination time for stepwise inertial control of wind turbines—Part I: Analytical derivation

Abstract Type-3 (Double fed induction generator, DFIG) and type-4 (full rated power converter connected) wind turbines (WTs) can participate in frequency control of power systems using stepwise inertial control (SIC) by releasing kinetic energy stored in rotors into the grid. During SIC, the rotor speed decreases as a part of a primary frequency drop, when extra active power is injected into the grid, supporting frequency control. Once the available kinetic energy has been released, the SIC has to be terminated and the WT’s output power drops instantaneously to allow rotor to reaccelerate back to the nominal speed. This WT’s output power drop is actually a disturbance, negatively affecting the system frequency, so that a new, secondary frequency drop (SFD) occurs. To minimize the SFD, this paper proposes a new method for determining when the SIC should be terminated. This important information is necessary to be known to optimize the entire SIC and ensure maximal contribution to the frequency control. A new analytical expression, defining the relationship between the SIC termination time and the SFD, is derived. Furthermore, it was concluded that an optimal termination time, minimizing the SFD, can be numerically obtained, but requiring time-consuming calculations. To make the determination of the optimal termination time more practical, a new expression for determining it analytically is derived. This time is referred to as fixed termination time (FTT). If the SIC is terminated at the instance correlating to the FTT, the SFD will be minimal and the contribution of the WT to the frequency control will be the most effective. This paper has its extension, the Part II paper, proposing an application strategy of the FTT.