Nonlinear modelling and multi-stability characteristics of asymmetric hydro turbine governing system

Abstract

The asymmetric hydro turbine governing system (AHTGS) has been widely applied in engineering practice, yet the stability characteristics and nonlinear behaviours of AHTGS are seldom studied. Therefore, the authors are motivated to study the stability characteristics and nonlinear behaviours of AHTGS by using Hopf bifurcation theory. Firstly, the refined nonlinear mathematical model of AHTGS is constructed, which takes account of the nonlinear head loss in asymmetric penstocks. Subsequently, the multi-stability characteristics of AHTGS is revealed based on the refined nonlinear mathematical model by using stable domain. Then, the multi-timescale oscillation phenomenon is revealed, i.e. system dynamic response consists of two subwaves with different frequencies. Moreover, the relationship of the two subwaves and the system multi-stability is investigated. The result indicates that the two supercritical bifurcation lines are emerged and a two-timescale oscillation is generated. The stability of the two-timescale oscillation is determined by the two emerged stable domains. In addition, the cause of high-frequency and low-frequency subwaves has been verified as the natural hydraulic oscillation and hydraulic interference between the hydro turbine generating units, respectively. The overall stability of AHTGS is determined by the intersection area of the two stable domains, therefore the reasonable tuning of control parameters within the comprehensive stable domain is critical to maintain the stability of AHTGS.