DC series machine

2.3 Application of the general theory onto DC machines

2.3.3 DC series machine

Figure 19a–e. They show the time waveforms of variables if= f(t), ui= f(t), iq= f(t), i = f(t), and uq= f(t) from the instant of connecting until the transients are in a steady-state condition in the time of t = 1.5 s.

A waveform of Uq= f(Iq) is shown inFigure 19f. It is terminal voltage U_qvs.

load current Iq. As it was mentioned, it is a basic characteristic for all sources of electrical energy, and in the case of shunt dynamo, it is seen that there is also a stiff characteristic, similar to the case of the separately excited dynamo but only till the rated load. In addition, it is immune to the short circuit condition, because short circuit current can be smaller than its rated current IN. This performance is welcomed in the applications where this feature was required, e.g., in cars, welding set, etc.

Figure 19a–e. They show the time waveforms of variables if= f(t), ui= f(t), iq= f(t), i = f(t), and uq= f(t) from the instant of connecting until the transients are in a steady-state condition in the time of t = 1.5 s.

A waveform of Uq= f(Iq) is shown inFigure 19f. It is terminal voltage U_qvs.

load current Iq. As it was mentioned, it is a basic characteristic for all sources of electrical energy, and in the case of shunt dynamo, it is seen that there is also a stiff characteristic, similar to the case of the separately excited dynamo but only till the rated load. In addition, it is immune to the short circuit condition, because short circuit current can be smaller than its rated current IN. This performance is welcomed in the applications where this feature was required, e.g., in cars, welding set, etc.

2.3.3 DC series machine

A DC series machine has its field winding connected in series with its armature circuit, as it is seen inFigure 20for motoring and generating operation.

Figure 19.

Simulations of the shunt dynamo: time waveforms of (a) field current, (b) induced voltage, (c) armature current, (d) load current, (e) terminal voltage, and (f) terminal voltage vs. load current in steady-state conditions at the constant resistance in the field circuit when the load resistance is changed.

This connection essentially influences properties and shapes of characteristics of the series machine and also equations needed for investigations of its properties.

2.3.3.1 Series DC motor

For a series DC motor, it is typical that the terminal voltage is a sum of the voltages in the field circuit and in the armature circuit:

u¼uqþu_f ¼RqiqþLqdi_q

dt þωL_dfi_fþR_fi_fþL_fd i_f

dt , (114)

but because of only one current flowing in the whole series circuit, the next is valid:

i¼iq¼i_f (115)

and Eq. (114) is simplified:

u¼uqþu_f ¼RqþR_f

iþLqþL_fdi

dtþωL_dfi: (116) Equation (110) for electromagnetic torque is also changed because of only one current:

te¼p ψ_diq�ψ_qid

¼pψ_di¼pLdfi² (117) and angular speed is gained on the basis of the equation:

t_e¼pL_dfi²¼JdΩ

dt þt_L¼J p

dω

dt þt_L: (118)

Figure 20.

Equivalent circuits of the series machine (a) in motoring and (b) in generating operation.

2.3.3.2 Simulations of a DC series motor

The time waveforms of the current, developed electromagnetic torque and angular speed, which can be recalculated to the revolutions per minute, are based on Eqs. (116)–(118). InFigure 20, there are simulated waveforms of the motor; the data of which are shown inTable 2.

Simulated waveforms inFigure 21a–fshow time waveforms of the variables if= iq= f(t), te= f(t), and n = f(t) after the voltage is applied to its terminals. In Figure 21c, one of the basic properties of a series motor is seen, which is that in no load condition (here its load is only torque of its mechanical losses, which is about 10% of the rated torque), the field current is strongly suppressed, which results in enormous increasing of the speed.

For this reason, this motor in praxis cannot be in no-load condition and is not recommended to carry out its connection to the load by means of chain, or band, because in the case of a fault, it could be destroyed. In simulation the motor is after the steady condition at the instant t1= 7 s loaded by its rated torque. In Figure 21d–f, mechanical characteristics n = f(T_e) for steady-state conditions are shown, if speed control is carried out by terminal voltage Uq, resistance in the armature circuit Rq(in this case there is also resistance of field circuit), as well as field current if(there is a resistance parallelly connected to the field winding).

2.3.3.3 Series dynamo

The approach to the simulations is the same as in previous chapters concerning the generating operations: the constant driving speed is supposed, induced voltage is a source for the whole circuit, and this voltage covers not only the voltage drops in the field and armature windings but also the terminal voltage. The current is only one i = if= iq, and the terminal voltage is given also by the load resistance:

u¼R_Li¼ωL_dfi�R_qþR_f

i�L_qþL_fdi

dt: (119)

The magnetizing characteristic, i.e., no load curve Ui= f(If), must be measured by a separate excitation.

2.3.3.4 Simulations of a DC series dynamo

Data and parameters of a machine which was simulated in generating operations are inTable 2. Dynamo is kept at constant speed; at first in the no load condition, it means terminals are opened, and no current flows in its circuit. A small voltage is possible to measure at its terminals at this condition. This voltage is induced by

UqN= 180 V Rq= 1Ω

IqN= 5 A Lq= 0.005 mH

PN= 925 W Rf= 1Ω

nN= 3000 min^�1 Lf= 0.015 H

MN= 3 Nm Lqf= 0.114 H

IfN= 5 A J = 0.003 kg m²

p = 1 Table 2.

Nameplate and parameters of simulated series motor.

means of remanent magnetic flux (Figure 23b, ui= f(t)). For this purpose, it is necessary to measure magnetizing curve at separate excitation Ui= f(If). For the investigated machine, this curve is shown inFigure 22.

After the load is applied to the terminals at the instant t1= 0.2 s, the current starts to flow in the circuit, because of the induced voltage (Figure 23a), if= iq= f(t), which flows also through the field winding and causes higher excitation of the machine, which results in higher induced voltage. Then the current is increased, which results again in the increasing of the induced voltage, etc. The transients are stabilized after the magnetic circuit is saturated. In this condition the voltage is increased with the increasing of the current, very slowly (Figure 22, Ui= f(If)).

Similarly, as induced voltage, also the terminal voltage is increased with the increasing of the current but only till the saturation of the magnetic circuit. Then the terminal voltage can even sink, because the voltage drops on the armature and field resistances can increase quicker than induced voltage. In this simulated case, this did not appear, and the terminal voltage was increased with the increased current (seeFigure 23dand the curve Uq= f(Iq)).

Figure 21.

Simulations of series motor. Time waveforms of (a) armature current and field current, (b) developed electromagnetic torque, and (c) speed and then speed vs. torque in the steady-state conditions for (d) various terminal voltages; (e) various resistances in series with armature circuit, at UqN; and (f) various field currents.

2.3.3.2 Simulations of a DC series motor

The time waveforms of the current, developed electromagnetic torque and angular speed, which can be recalculated to the revolutions per minute, are based on Eqs. (116)–(118). InFigure 20, there are simulated waveforms of the motor; the data of which are shown inTable 2.

Simulated waveforms inFigure 21a–fshow time waveforms of the variables if= iq= f(t), te= f(t), and n = f(t) after the voltage is applied to its terminals. In Figure 21c, one of the basic properties of a series motor is seen, which is that in no load condition (here its load is only torque of its mechanical losses, which is about 10% of the rated torque), the field current is strongly suppressed, which results in enormous increasing of the speed.

For this reason, this motor in praxis cannot be in no-load condition and is not recommended to carry out its connection to the load by means of chain, or band, because in the case of a fault, it could be destroyed. In simulation the motor is after the steady condition at the instant t1= 7 s loaded by its rated torque. In Figure 21d–f, mechanical characteristics n = f(T_e) for steady-state conditions are shown, if speed control is carried out by terminal voltage Uq, resistance in the armature circuit Rq(in this case there is also resistance of field circuit), as well as field current if(there is a resistance parallelly connected to the field winding).

2.3.3.3 Series dynamo

The approach to the simulations is the same as in previous chapters concerning the generating operations: the constant driving speed is supposed, induced voltage is a source for the whole circuit, and this voltage covers not only the voltage drops in the field and armature windings but also the terminal voltage. The current is only one i = if= iq, and the terminal voltage is given also by the load resistance:

u¼R_Li¼ωL_dfi�R_qþR_f

i�L_qþL_fdi

dt: (119)

The magnetizing characteristic, i.e., no load curve Ui= f(If), must be measured by a separate excitation.

2.3.3.4 Simulations of a DC series dynamo

Data and parameters of a machine which was simulated in generating operations are inTable 2. Dynamo is kept at constant speed; at first in the no load condition, it means terminals are opened, and no current flows in its circuit. A small voltage is possible to measure at its terminals at this condition. This voltage is induced by

UqN= 180 V Rq= 1Ω

IqN= 5 A Lq= 0.005 mH

PN= 925 W Rf= 1Ω

nN= 3000 min^�1 Lf= 0.015 H

MN= 3 Nm Lqf= 0.114 H

IfN= 5 A J = 0.003 kg m²

p = 1 Table 2.

Nameplate and parameters of simulated series motor.

means of remanent magnetic flux (Figure 23b, ui= f(t)). For this purpose, it is necessary to measure magnetizing curve at separate excitation Ui= f(If). For the investigated machine, this curve is shown inFigure 22.

After the load is applied to the terminals at the instant t1= 0.2 s, the current starts to flow in the circuit, because of the induced voltage (Figure 23a), if= iq= f(t), which flows also through the field winding and causes higher excitation of the machine, which results in higher induced voltage. Then the current is increased, which results again in the increasing of the induced voltage, etc. The transients are stabilized after the magnetic circuit is saturated. In this condition the voltage is increased with the increasing of the current, very slowly (Figure 22, Ui= f(If)).

Similarly, as induced voltage, also the terminal voltage is increased with the increasing of the current but only till the saturation of the magnetic circuit. Then the terminal voltage can even sink, because the voltage drops on the armature and field resistances can increase quicker than induced voltage. In this simulated case, this did not appear, and the terminal voltage was increased with the increased current (seeFigure 23dand the curve Uq= f(Iq)).

Figure 21.

Simulations of series motor. Time waveforms of (a) armature current and field current, (b) developed electromagnetic torque, and (c) speed and then speed vs. torque in the steady-state conditions for (d) various terminal voltages; (e) various resistances in series with armature circuit, at UqN; and (f) various field currents.