Machine System of Differential Equations and Complete System of Algebraic Equations

An electric machine communicates with the outer world through its electrical and mechanical terminals. Energy received through the terminals is converted into another form or stored as magnetic field or kinetic energy. Electromechanical energy conversion is a time-invariant process, as shown in Chapter 2. Force (torque) does not depend on the time rate of change of state variables but on the state variables themselves. Stored magnetic energy, Li2/2, and kinetic energy, Jω2/2, cannot change instantaneously because it would demand an infinite source of power. The gradual change of energy means that not only the state variables but also their time derivatives, written in the form of ordinary differential equations, define the state in a machine.