Automatic Control System for Rheostatic-Regenerative Braking of a DC Electric Train

R. K. Gachik, A. P. Zaitsev

(Presented by the scientific seminar of the Electromechanical Faculty).

Under conditions of frequent starts and stops of a DC electric train, the use of electric braking instead of pneumatic braking makes it possible to substantially reduce the wear of brake shoes and wheel tires and to carry out recuperation into the contact network of part of the energy stored by the flywheel masses of the train during acceleration. In the process of regenerative braking it is especially important to make maximum use, in terms of current, of the motors operating in braking mode. This makes it possible to perform braking in the shortest possible time and to increase the average speed of the electric train on runs. The value of the maximum permissible motor current is determined by the conditions of sparking and by the potential conditions at the commutator.

The potential conditions at the commutator are characterized by the value of the maximum interlamellar e.m.f. In order that the interlamellar e.m.f. not exceed the maximum permissible value \(e_{\max}=45\text{ V}\), which determines the region of normal commutation, it is necessary that the excitation current of the traction motors be determined by the expression:

\[ I_{\mathrm{v}}= \frac{ 0.45-\dfrac{2p}{ka}\cdot\dfrac{N}{8ap}\,U_k I }{ W_{\mathrm{v}}\left(45-\dfrac{2p}{ka}-U_k\right) }, \tag{1} \]

where \(I_{\mathrm{v}}\) is the excitation current;
\(I\) is the armature current;
\(U_k\) is the voltage at the commutator;
\(p\) is the number of pole pairs;
\(k\) is the number of commutator segments;
\(\alpha\) is the pole overlap;
\(N\) is the number of active conductors;
\(a\) is the number of parallel paths.

Expression (1) was obtained from A. V. Ioffe’s formula:

\[ e_{\max}= \frac{e_{\mathrm{avg}}}{\alpha} \left( 1+\frac{0.45-\dfrac{IN}{8ap}}{I_{\mathrm{v}}W_{\mathrm{v}}} \right)=45, \]

where

\[ \varepsilon_{\mathrm{av}}=-\frac{2pV}{l}. \]

For rheostatic braking with independent excitation,

\[ U_k=I\left(R_T-r_a\right), \]

where \(R_T\) is the equivalent resistance of the braking circuit per motor.

For regenerative braking,

\[ U_k=\frac{U_c}{n_c}+I\left(r-r_a\right), \]

where \(r\) is the resistance of the braking circuit, referred to one motor;
\(n_c\) is the number of motors connected in series;
\(U_c\) is the contact-line voltage.

After substituting the numerical values of the parameters of the RT-113 motor (RT-113 motors are used on the R-22 electric trains), formula (1) takes the form:

\[ I_{\mathrm{v}}=\frac{0.2096\,U_k I}{1500-U_k}. \tag{2} \]

The expression (2) obtained is the control algorithm of the automatic braking system and determines the structural diagram of the system. It takes into account the influence of the contact-line voltage, which varies over wide limits, on the value of the maximum interlamellar e.m.f. during regenerative braking. In order to brake the electric train in the minimum time, it is necessary to make maximum use, in terms of current, of the traction motors operating in the braking mode. This means that, with the adopted criterion for assessing normal commutation (by the maximum permissible value of the interlamellar e.m.f.), in the region of high speeds the motor must operate at the boundary of the normal-commutation zone until, as the speed decreases, the motor current reaches the maximum permissible value according to adhesion conditions; thereafter this current value must be maintained constant until regenerative braking is exhausted.

The excitation current of the traction motors, \(I_{\mathrm{v}}\), was chosen as the controlled variable in the braking system. The regulating element is the excitation windings, supplied from a controlled thyristor rectifier. An asymmetrical bridge rectifier circuit with a neutral valve is used, since, for the same value of rectified voltage, the reverse and forward voltages in a bridge circuit are half as large as in a neutral circuit. This makes it possible to use, in the bridge circuit, thyristors having lower values of switching voltage and reverse voltage. A disadvantage of the bridge circuit in comparison with the neutral circuit is the need to use twice the number of valves; however, in the asymmetrical bridge circuit only half of the valves need be controlled. Given the high cost of thyristors, this is a significant advantage of the rectifier circuit.

The block diagram of the automatic braking system is presented in Fig. 1, where the following are denoted:

DTYa — armature-current sensor;
DTV — excitation-current sensor;
DNK — commutator-voltage sensor;
DNS — contact-line-voltage sensor;

VU — computing device;
MU — storage device;
UV — controlled thyristor rectifier;
VCS — output comparison circuit;
K — semiconductor switch;
BG — blocking generator controlling the rectifier;
RBN — relay for balancing the line voltage and the voltage at the motor commutators;
RSV — relay for transition to braking with self-excitation. SS “500,” SS “325,” SS “250” are comparison circuits.

Fig. 1

In the process of rheostatic-regenerative braking, the four traction motors, connected in series, are switched to generator mode with independent excitation. The excitation windings of the traction motors are likewise connected in series.

Applied to the inputs of the VU, which solves equation (1), are DC voltages from DTYa and DNK proportional to \(I\) and \(U_k\), respectively. At the output of the VU a voltage is formed proportional to the calculated excitation current \(I_{\mathrm{vr}}\), at which \(e_{\max} = 45\ \mathrm{V}\) for the current values of \(I\) and \(U_k\). From the output of the VU the voltage is fed to the VCS, where it is compared with the output voltage of the DTV, which is proportional to the actual excitation current \(I_{\mathrm{vd}}\). When \(I_{\mathrm{vd}} > I_{\mathrm{vr}}\), the output comparison circuit VCS issues an enabling signal to the BG, which in the initial state generates at high frequency and unlocks the thyristors of the controlled rectifier UV. The thyristors at this moment are fully open. The unlocking voltage \(U_0\), ensuring generation by the BG, is applied through the switch \(K\), which is open under the condition that \(I < I_{\max}\). The excitation current \(I_{\mathrm{v}}\) increases until \(I_{\mathrm{v}}\) becomes greater than \(I_{\mathrm{vd}}\). At this moment a prohibiting signal is formed at the output of the VCS, and the BG ceases generation; the thyristors are locked, and \(I_{\mathrm{v}}\) decreases. As soon as the condition \(I_{\mathrm{vd}} > I_{\mathrm{vr}}\) is again satisfied, the VCS will again issue an enabling signal, and the process will repeat. Thus \(I_{\mathrm{vd}}\) and \(I_{\mathrm{vr}}\) will be maintained equal to each other with a certain degree of accuracy.

When the armature current \(I\) reaches the value \(I_{\max}\), the comparison circuit SS “500,”

to the inputs of which are applied a voltage proportional to the armature current and the reference voltage \(U_{\mathrm{ref}}\), will issue a blocking signal to \(K\). Under the action of this signal, \(K\) closes, which leads to interruption of BG generation, and the thyristors close. This causes \(I\) to decrease. When \(I\) becomes less than \(I_{\max}\), CC “500” opens the switch, which will lead to BG generation. As the speed decreases further, \(I\) will be maintained at the level of the specified value \(I_{\max}\), which is determined by the degree of loading of the car. The signal from the output of VU is continuously applied to the memory device ZU. If it is necessary, for a short time (up to 10 min), to maintain \(I_{\mathrm{v}}\) constant and equal to its current value, the output of ZU is connected to the input of VSS, and VU is disconnected from the latter by means of a pushbutton in the driver’s cab. The same pushbutton disconnects ZU from VU.

The system performs a number of logical operations. During braking from any speed, the relay-contactor circuit of the electric train provides a rheostatic-braking mode with independent excitation, which is preparatory. When the voltages from the outputs of DNS and DNK, proportional to \(U_{\mathrm{s}}\) and \(U_{\mathrm{k}}\), respectively, become equal, RBN issues a contact signal to the relay-contactor control circuit of the electric train for transfer of the system to regenerative braking.

When regenerative braking is exhausted, when the excitation current \(I_{\mathrm{v}}\) reaches its maximum value and the armature current \(I\) decreases to 325 A, the comparison circuits CC “325” and CC “250” issue a signal to RSV. RSV forms the contact signal for transition to rheostatic braking with self-excitation if signals from CC “250” and CC “325” are simultaneously present at its input. The above sequence of braking modes is ensured during braking from any speed.

The output voltage of VU is determined by the expression:

\[ U_{\mathrm{out}}=\frac{kU_3U_4}{U_1-U_2}, \tag{3} \]

where \(k\) is a constant coefficient;

\(U_1\) is the voltage proportional to the constant value 1500 from (2);

\(U_2, U_4\) are voltages proportional to the collector voltage;

\(U_3\) is the voltage proportional to the armature current.

The voltage \(U_{\mathrm{out}}\) during the regulation process is equal to the voltage of the excitation-current sensor. For normal operation of the system, the scales of the quantities entering expression (2) must be chosen quite definitely. Let us denote:

\[ m_{1\mathrm{k}}=\frac{U_{\mathrm{k}}}{U_4} \]
— the first scale of the collector voltage;

\[ m_{2\mathrm{k}}=\frac{U_{\mathrm{k}}}{U_2} \]
— the second scale of the collector voltage;

\[ m_{\mathrm{c}}=\frac{1500}{U_1} \]
— the scale of the constant value \(A=1500\ \mathrm{V}\);

\[ m_{\mathrm{ya}}=\frac{I}{U_3} \]
— the scale of the armature current;

\[ m_{\mathrm{v}}=\frac{I_{\mathrm{v}}}{U_{\mathrm{dv}}}=\frac{I_{\mathrm{v}}}{U_{\mathrm{out}}} \]
— the scale of the excitation current.

Here \(U_{\mathrm{dv}}\) is the voltage of the excitation-current sensor. Dividing expression (3) by expression (2), we obtain:

\[ \frac{kU_3U_4(1500-U_{\mathrm{k}})}{(U_1-U_2)\cdot 0.2096\,U_{\mathrm{k}1}} =\frac{U_{\mathrm{out}}}{I_{\mathrm{v}}^{\prime}}, \tag{4} \]

which can be rewritten, taking the scale factors into account, in the form:

\[ \frac{k(1500-U)} {\left(\dfrac{1500}{m_c}-\dfrac{U_k}{m_{2k}}\right)\cdot 0.2096\, m_{\mathrm{я}}\, m_{1k}} = \frac{1}{m_{\mathrm{в}}}. \tag{5} \]

If we take \(m_c=m_{2k}\), then

\[ m_{\mathrm{в}}= \frac{0.2096\, m_{\mathrm{я}}\, m_{1k}} {m_{2k}\cdot k}. \tag{6} \]

The braking control system of the electric train is implemented entirely with transistors.