Gyuláné Vincze, Gergely György Balázs

Budapest University of Technology and Economics Department of Electric Power Engineering

As can be seen above, drives with mechanical characteristic fulfilling the requirements indicated in Figure 2.5. can be used for traction without mechanical gear.

The following drives can be used:

serias excited DC motor drive with commutator, extended with field-weakening range;

inverter-fed field-oriented controlled induction motor drive, extended with field-weakening range;

inverter-fed current vector controlled, permanent magnet, sinus-field synchronous motor drive, extended with field-weakening range (PMSM drive);

multi-phase, permanent magnet, rectangle field synchronous motor drive (so-called ECDC or BLDC drive);

switched reluctance motor (SRM) drive (rarely).

Earlier, one-phase commutator motor drives were also used, but not nowadays.

To simulate the behaviour of electric machines, per-unit system is often used. With per-unit system, several behaviours and control modes can be compared easier, and it is also easier to evaluate the simulation results. The quantities in per-unit indicated with superscript comma express relative values related to nominal values indicted with index *n*. Important per-unit quantities for DC machines are: *I’=I/I*
_{n}, *U*
^{’}
*=U/U*
_{n}, *ϕ*
*’=*
*ϕ*
*/*
*ϕ*
_{n}, *M*
^{’}
*=M/M*
_{n}, where *M*
_{n} is nominal torque determined by *ϕ*
_{n} and *I*
_{n}.

This section summarizes the basics of Park-vector method used for three-phase AC electric machines, as it is required for the further parts of this book.

Three-phase electric machines are usually described by voltage, flux and torque equations. Original equations for phases *a, b, c* form an equation system where interactions between phases are also described. This equation system is hardly usable because of inductive couplings. As interactions are cyclic and symmetric in three-phase machines, a transforming method is available where vector based descriptions are available instead of phase quantities. The advantage of this transformation method is that three phase equations are simplified to two equations (without coupling between them): equations for Park-vectors and zero -sequence components. Equation for zero -sequence components can be eliminated if *(i*
_{a}
*+i*
_{b}
*+i*
_{c}
*)=0 *is fulfilled with construction, for example in machines with star connected winding and not-connected star point.

*Vector description* is made with Park-vectors calculated with operators (1, ā, ā^{2}), where and .

Vector description of three-phase electric machines uses the vectors constructed in the way etc., where *u*
_{a}
*, u*
_{b}
*, u*
_{c}
*, i*
_{a}
*, i*
_{b}
*, i*
_{c} etc. are instantaneous values of phase quantities. Using these vectors a Park-vector based equation system can be created.

Park-vector equations describe the system unambiguously if inner or outer zero-sequence component voltage *u*
_{0}=(1/3)(*u*
_{a}
*+u*
_{b}
*+u*
_{c})≠0 cannot create zero -sequence current *i*
_{0}=(1/3)(*i*
_{a}
*+i*
_{b}
*+i*
_{c}), as *(i*
_{a}
*+i*
_{b}
*+i*
_{c}
*)=0* requirement is fulfilled with construction.

Park-vectors calculated as above are complex quantities resulting from the transformation, and their real and imaginary components, magnitude and angle can be calculated in every moment. Advantages of vector description are that vectors can be drawn in plane field, and momentary quantities are easy to calculate. For example, knowing current vector ī phase currents *i*
_{a}
*, i*
_{b}
*, i*
_{c} can be calculated, as shown in Figure 2.6.

Instantaneous three-phase quantities can be calculated from a vector in every moment with a simple projection rule; they can be calculated from the projections to the *a, b, c* axes (1, ā, ā^{2} directions). In the example, *i*
_{a}
* *is positive, while *i*
_{b} and* i*
_{c} are negative and have almost half values, comparing to *i*
_{a}.

Transient processes of three-phase electric machines can be represented easily with Park-vectors, and vector description provides possibility to coordinate transformation, for example to rotating coordinate system.

*Calculating*
* electric power with Park-vectors*

Instantaneous power described with phase voltages and currents is:

2‑3

Park-vector description of the same power, together with zero -sequent components *u*
_{0}=(1/3)(*u*
_{a}
*+u*
_{b}
*+u*
_{c})* *and *i*
_{0}=(1/3)(*i*
_{a}
*+i*
_{b}
*+i*
_{c}), is:

2‑4

In this equation dot means scalar product, i.e. ū·ī=│ū│·│ī│cosφ, where *φ* is the angle between voltage and current vectors. As *i*
_{0}=0, usually, zero -sequent power component, the second part of equation (2.4) is often not indicated.

(References used in this section are: [6]…[9])