“…The accuracy of the mathematical model and its parameters is one of the main influencing factors in power system operation and power grid security. 1,2 However, issues still must be resolved, for the static characteristic of Francis turbine mechanical power and the characteristic of the guide vane opening are obvious List of symbols and abbreviations: K p , K i , and K d , proportional, integral, and differential gain; f s and f g , system frequency and unit frequency; P GV and y nld , given load opening and no-load vane opening; b p , difference coefficient; V ELopen and V ELclose , rapid opening and closing limits; P max and P min , maximum and minimum guide vane opening; T y , main servomotor time constant; V ELclose1 and V ELclose2 , different rapid opening and closing limits; T 1 , delay link time constant; T 2 , time constant of vane opening feedback loop; y 1 , guide vane section closing point; T w , inertia time constant for water diversion system; T r , pipeline reflection time; A t , proportionality coefficient; q NL , no-load water flow; a 0 , a 1 , …, and a n , fitting coefficients; H 0 , static head; P ref , P e , and P m , given power value, turbine power, and mechanical power; y ref and y, given vane opening and guide vane opening; y PID , output of PID microcomputer regulator; h and q, turbine working head and turbine discharge nonlinear under a certain water head, 3 which has a great influence on the simulation precision. 4 The Hamiltonian modeling was established to describe dynamic behaviors of the hydro-turbine governing system.…”