Quasilinear Control of Wind Farm Active Power Output

Abstract

Quasilinear Control (QLC) is a set of methods for analysis and design of systems with nonlinear actuators and sensors. The approach of QLC is based on the method of stochastic linearization, which replaces each nonlinearity with an equivalent gain and bias. In this chapter, we revisit the wind farm controller from Chap. 4 and apply QLC to the design of the proportional controller gains on its inner feedback loop. QLC is particularly suitable here because each of the wind turbines can be modeled as a linear plant preceded by an asymmetric saturation nonlinearity, which accounts for the limited availability of wind. Through extensive numerical simulation, we show that controller gains designed using QLC perform significantly better in a broad range of wind farm operating regimes, compared to those designed using traditional linear methods, where the asymmetric saturation nonlinearities are ignored. The operating regimes we consider include regimes with low and high wind speed, medium and high power generation, weak and strong wind correlation, and cheap and expensive control.