Regenerative Braking System of an Electric Train

A. P. Zaitsev, R. K. Gachik, V. M. Shadt

(Presented by the scientific and technical seminar of the Research Institute of AEM at TPI)

The use of electric braking in various mechanisms with direct-current motors makes it possible to improve the technical and economic performance of the mechanisms. This is especially characteristic of electric drives associated with large masses and operating with frequent starts and stops, for example, electrified transport. The most economical type of electric braking is regenerative braking, especially for electrified transport.

On electric trains, regenerative braking is service braking and, owing to frequent stops, yields a considerable economic effect.

The main factors hindering the use of regenerative braking systems on electric trains are the instability of the voltage of the contact network and the need, at high speeds of motion, to limit the braking current according to the potential conditions on the commutators of uncompensated traction motors.

This article describes a control system for regenerative braking of the ER-22 direct-current electric train, supplied from a contact network and equipped with uncompensated traction motors.

The commutation condition and the possibility of flashover on the motor commutator are associated with the magnitude of the maximum interlamellar emf \(e_{\mathrm{m}}\). Commutation will be normal, and the danger of flashover on the commutator will be minimal, if the value of \(e_{\mathrm{m}}\) does not exceed a value determined for each type of motor. The value \(e_{\mathrm{m}}\) is determined by the formula proposed by A. V. Ioffe.

\[ e_{\mathrm{m}} = \frac{2pU_{\mathrm{k}}}{K\alpha} \left( 1 + \frac{0.45\,\dfrac{I_{\mathrm{я}}N}{8a'p}}{I_{\mathrm{в}}W_{\mathrm{в}}} \right) = aU_{\mathrm{k}} + \frac{B_{\mathrm{в}}U_{\mathrm{k}}I_{\mathrm{я}}}{I_{\mathrm{в}}}, \tag{1} \]

where \(p\) is the number of pairs of motor poles;
\(k\) 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;
\(W_{\mathrm{в}}\) is the number of turns of the field winding;
\(U_{\mathrm{k}}\) is the voltage at the motor commutator;
\(I_{\mathrm{я}}\) is the armature current;
\(I_{\mathrm{в}}\) is the field current.

A regenerative-braking control system is proposed with the constraints \(e_{\mathrm{m}}=\mathrm{const}\) and \(I_{\mathrm{я}}=\mathrm{const}\), whose control algorithm ...

... in the limiting zone \(e_{\mathrm{m}}\) is equation (1), solved with respect to the armature current:

\[ I_{\mathrm{ya}}=-\frac{(e_{\mathrm{m}}-aU_{\mathrm{k}})I_{\mathrm{v}}}{bU_{\mathrm{k}}}. \tag{2} \]

From (2) it is evident that, in order to maintain \(e_{\mathrm{m}}=\mathrm{const}\) at constant \(U_{\mathrm{k}}\), the armature current must be proportional to the excitation current, i.e., \(I_{\mathrm{ya}}=mI_{\mathrm{v}}\). The value of \(m\) is determined by the value of \(U_{\mathrm{k}}\):

\[ m=\frac{e_{\mathrm{m}}-aU_{\mathrm{k}}}{bU_{\mathrm{k}}}. \tag{3} \]

If the control system is constructed so that, during the regulation process, the output quantities of the sensors \(I_{\mathrm{ya}}\) and \(I_{\mathrm{v}}\) are maintained equal, and the transmission coefficient of one of the sensors is made dependent on \(U_{\mathrm{k}}\), then \(e_{\mathrm{m}}\) will be maintained constant for any combination of train speed and voltage at the motor collectors.

The block diagram of the system is shown in Fig. 1, where

Fig. 1

\(Ya_{1}\)--\(Ya_{4}\) — armature windings of the traction motors;
\(LK\) — contact of the line contactor;
\(T\) — contact of the braking contactor;
\(R_{\mathrm{t}}\) — braking resistance;
\(DNK\) — sensor of voltage at the motor collectors;
\(DTYa\) — armature-current sensor;
\(DTV\) — excitation-current sensor;
\(RBN\) — voltage-balance relay;
\(SS\) — comparison device;
\(TV\) — thyristor exciter;
\(U_{\mathrm{e2}}\) — reference voltage proportional to the specified value of the armature current \(I_{\mathrm{ya}}\);
\(U_{1}; U_{3}\) — output voltages of \(DTYa\) and \(DTV\), respectively;
\(SP_{1}\) — contact signal for transition to regenerative braking;
\(SP_{2}\) — contact signal for transition to rheostatic braking with self-excitation.

Figure 3 presents a voltage diagram explaining the operation of the control system. The BTG and BTC are constructed so that their output voltages decrease as the input currents increase. If \(U_1>U_3\), a sequence of short rectangular pulses is formed at the output of the SS, which open \(TB\). A process of increase of \(I_{\mathrm{v}}\) and \(I_{\mathrm{a}}\) takes place. If \(U_1\) becomes less than \(U_3\), the pulses at the output of the SS disappear and \(TB\) closes; \(I_{\mathrm{a}}\) and \(I_{\mathrm{v}}\) will decrease. When the condition \(U_1>U_3\) is fulfilled, the process repeats. Thus the braking current will be regulated, with \(e_{\mathrm{m}}=\mathrm{const}\). As the speed decreases, when at \(e_{\mathrm{m}}=\mathrm{const}\) \(I_{\mathrm{a}}\) reaches the greatest permissible value, \(U_3\) becomes equal to \(U_{\mathrm{e}2}\). Now \(U_1\) and \(U_{\mathrm{e}2}\) are compared at the SS. Since \(U_{\mathrm{e}2}\) does not change, \(I_{\mathrm{a}}\) will also be maintained constant.

Fig. 2

All the sensors of the system are made on the basis of symmetrical transistor multivibrators with transformer feedback and a saturable transformer. The schematic circuit of the BTC is shown in Fig. 2. The multivibrator is made with transistors \(T_1\) and \(T_2\) and transformer \(T_{\mathrm{p}}\), which is biased by the measured current. The frequency of the multivibrator output voltage is determined by

\[ f_{\mathrm{v}} = k_{\mathrm{v}} I_{\mathrm{v}}, \tag{4} \]

where

\[ k_{\mathrm{v}} \]

is the slope coefficient of the multivibrator characteristic

\[ f_{\mathrm{v}} = F(I_{\mathrm{v}}). \]

Transistor \(T_3\) operates in the current-stabilizer mode, the value of the stabilization current being determined by the value of \(U_2\):

\[ I_{\mathrm{c}}=\frac{U_2\alpha'}{R_4}. \tag{5} \]

When the positive half-period of the voltage is taken from the multivibrator, \(T_4\) is closed and a linearly increasing voltage \(U_{\mathrm{c}}\) is formed on \(C_1\). During the negative half-period, \(T_4\) is open and \(C_1\) discharges. The amplitude value \(U^{*}_{\mathrm{c}1}\) is determined by:

\[ U^{*}_{\mathrm{c}1} = \frac{1}{C_1}\int_{0}^{T/2} I_{\mathrm{c}}\,dt = \frac{T U_2\alpha'}{2C_1R_4}, \tag{6} \]

Having determined \(T\) from (4) and substituted it into (6), we obtain

\[ U^*_{c1}=\frac{U_2 a}{2C_1R_4k_{\mathrm{B}}I_{\mathrm{B}}} =\frac{U_{\mathrm{k}}m_{\mathrm{k}}a}{2C_1R_4k_{\mathrm{B}}I_{\mathrm{B}}}, \tag{7} \]

An amplitude detector is implemented on \(T_5\), i.e., the voltage on \(C_2\) will be equal to \(U^*_{c1}\).

The output voltage \(U_3\) is taken through an “OR” circuit implemented on \(D_1\) and \(D_2\), which ensures the transition from the mode of maintaining \(e_{\mathrm{m}}=\mathrm{const}\) to the mode of maintaining \(I_{\mathrm{a}}=\mathrm{const}\).

The DTYa is implemented according to the same circuit, only without an amplitude detector, and instead of \(U_2\), \(U_0=\mathrm{const}\) is applied; therefore, by analogy with (7), one may write:

\[ U_1=\frac{U_0a}{2C'_1R'_4k_{\mathrm{a}}I_{\mathrm{a}}}, \tag{8} \]

Since, in the regulation process, the equality of \(U_3\) and \(U_1\) is maintained, then

\[ \frac{U_0}{C'_1R'_1k_{\mathrm{a}}I_{\mathrm{a}}} = \frac{U_{\mathrm{k}}m_{\mathrm{k}}}{C_1R_4k_{\mathrm{B}}I_{\mathrm{B}}}. \tag{9} \]

Multiplying (2) term by term by (9), we obtain

\[ U_0 b C_1 R_4 k_{\mathrm{B}} = \left(e_{\mathrm{m}}-aU_{\mathrm{k}}\right)m_{\mathrm{k}}C'_1R'_4k_{\mathrm{a}}. \tag{10} \]

Expression (10) makes it possible to relate to one another, in the proper ratio, the transmission coefficients of the DNK, DTV, and DTYa. The DNK is likewise implemented on a multivibrator, but a magnetic demodulator and a filter are connected at the output, which makes it possible to obtain a dc output voltage proportional to \(U_{\mathrm{k}}\). The SS is implemented on a balanced diode-regenerative comparator. A two-half-period three-phase unsymmetrical rectifier is used as the exciter.

Fig. 3

According to the circuits described above, a braking system was manufactured; it was tested on the stand of the NII AEM at TPI and in the traction labora-

Fig. 4

…ry of the Special Design Bureau for Traction of the Riga Electric Machine-Building Plant. The tests showed that the system is fully operational. Figure 4 shows an oscillogram of a quasi-steady-state process during regenerative braking, recorded on the stand of the Research Institute of Automatic Electrical Machines under a traction power supply. Analysis of the oscillogram shows that the ripple of the armature current does not exceed 5%.