Electrical Drives

A drawback of this method is that it is not resilient in the presence of disturbances. Moreover it cannot ensure high dynamic performance when the operating point of the drive system changes because, e.g. of an abrupt load torque step.

However, the instantaneous value of the stator voltage may differ from the reference voltage because of switching harmonics, non-idealities of the commanding power inverter, phase delay, and non-idealities and presence of passive components elements in the electrical connection path between inverter and machine.

uk(t) = (+,–,0).

A voltage source inverter converts dc voltage to single-phase or multi-phase switched ac voltage of given amplitude and frequency to feed a load such as an electrical machine. Depending on the number L of discrete voltage levels of the switched voltage waveform(s), the power inverter can be two-level (L = 2) or multi-level (L > 2).

In optimal PWM, the switching angles of the pulse sequence are calculated over a fundamental period in such way that an objective function is observed; an example of such objective function is the minimization of the THD of the stator currents that are produced in an electrical machine which is fed by the pulsewidth-modulated voltage waveform.

In synchronous PWM, the switched voltage sequence is in synchronism with the reference voltage waveform; subharmonic and interharmonic content of the pulse sequence is zero as a result.

An induction machine is fed by three-phase pulsewidth-modulated (PWM) voltage waveforms that are optimized for minimum THD (total harmonic distortion) of the currents generated in the stator winding. The voltages exhibit half-wave symmetry. Will the optimization procedure result, by necessity, in voltage waveforms that also exhibit quarter-wave symmetry?

The differential-mode voltage harmonics of a balanced, three-phase system that exhibits half-wave symmetry are of odd, non-triplen order, i.e. 5, 7, 11, 13, 17, 19, ...

A set of five differential equations of scalar state variables describes the synchronous machine model: two equations for the armature winding, two for the damper winding, and one for the field winding.

The mechanical subsystem of the induction machine is described by the motion equation of the rotor shaft: the difference between the electromagnetic torque of the machine and the load torque is proportial to the derivative of the angular velocity of the rotor with the proportionality factor being the mechanical time constant of the machine. The electromagnetic torque is proportional to the amplitude of the cross product of two state variables of the machine model, e.g. the stator current and the rotor flux.

The electrical subsystem of the induction machine is described by two space vector differential equations. The stator voltage space vector is the input. Two state variables are required: they are chosen among the stator current, rotor current, stator flux, and rotor flux space vectors. A common selection is to choose the stator current and rotor flux as state variables. The stator current can be considered as the output of the model.

The field coordinate system is displaced by the rotor field angle with respect to the stationary coordinate system.

The field coordinate system is in synchronism with the rotor flux space vector.

The voltage space vector describes the sinusoidal stator voltage distribution inside an induction machine.

The current space vector describes the sinusoidal current density distribution inside an induction machine.

The rated dc-link voltage of a three-phase power inverter should be greater than the line-to-line rated peak voltage.

-Douglas Adams, "Life, the Universe and Everything"