5.1.5.Ess scaling

For vehicle simulation on the test bench all its equipment, including energy storages, should be scaled down to test bench size [16].

The traction drive model scaling is made on the basis of Tatra T3M tramcar parameters: P_{tram, nom} = 180 kW – rated power of tramcar all motors; P_{tram, max} = 316 kW – maximal tramcar power; n_{tram, nom} = 1720 rpm – rated speed of motor; k_gear = 7.36 – vehicle gear box ratio; m₀ = 18.5 t – mass of an empty tramcar; m_max = 30.2 t – mass of a full tramcar; D = 0.7 m – wheel diameter.

Depending on the motor rotation speed, linear speed of the tram is

[km/h]. (9)

At nominal motor rotation frequency vehicle speed is v_nom = 30.8 km/h or 8.56 m/s.

Nominal force is

. (10)

Nominal acceleration for an empty vehicle is

. (11)

Accepting that to nominal test bench DC motor rotation frequency there correspond nominal tram motor rotation frequency, equivalent force is

. (12)

To equivalent force there corresponds equivalent mass

. (13)

Thus, the mass scale factor is

, (14)

the power scale factor is

, (15)

the force scale factor is

, (16)

the speed scale factor is

. (17)

According to (9) – (17), the scale factors are: k_m = 48.9; k_P = 85.5; k_F = 48.8; k_n = 1.255.

The size of vehicle ESS may be determined by two parameters: energy capacity E_ESS,vehicle and power capability (at discharged state) P_ESS,vehicle. As the time scale used is 1:1 [17], the relevant bench ESS parameters are calculated as

, (18)

. (19)

On the other hand, these parameters for supercapacitor ESS of capacity C and working voltage range V_SC,min – V_SC,max are determined by equations:

, (20)

, (21)

where I_SC,max is the set reference value of the converter current control loop, restricted rather for converter than supercapacitor protection.

Equations (18) – (21) may be used for both development of a new energy storage or adaptation of existing one for the test bench purposes. In the last case, first, the minimum voltage is calculated at chosen I_SC,max

, (22)

then the maximum voltage is

. (23)

Calculated value V_SC,max should be less than allowed voltage for supercapacitor bank.

If T3M tramcar it equipped with mentioned in [12] storage with C_vehicle = 33.3 F; V_{SC,max,vehicle} = 450 V; V_{SC,min,vehicle} = 300 V; I_{SC,max,vehicle} = 700 A, then: E_ESS,vehicle = 1873 kJ; P_ESS,vehicle = 210 kW.

From (18) and (19) it can be concluded, that E_ESS,bench = 21.9 kJ; P_ESS,bench = 2.46 kW.

Accepting I_C,max = 40 A, working voltage range is: V_SCmin = 61.5 V; V_SCmax = 66.9 V.

In the braking mode the traction drive of the vehicle operates as a generator. Energy E_br which is generated by the motor in this case [18] can be expressed as

, (24)

where K₁ is factor which depends on the internal losses of a vehicle, power auxiliaries etc.; E_Kinetic is the vehicle kinetic energy. The value of K₁ varies in range 0.5-0.6.

In braking mode the braking power will be stored in the supercapacitor until the state of charge (SoC) value won’t reach 1 [3]. SoC can be expressed as

, (25)

where E_SCmax is the maximal possible energy stored by the supercapacitor.

In the cases when supercapacitor is fully charged, the surplus braking power is dissipated in the braking resistor to avoid DC bus overvoltage.

Fig. 8. Supercapacitor working voltage range

The supercapacitor parameters – capacity 63F and maximum operation voltage 125V – equal to rated voltage are oversized in relation to the traction power therefore the energy storage system scaling was executed [19]. Minimum admissible by manufacturer supercapacitor voltage V^*_SC,min is 40% of rated voltage

V. (26)

Fig. 8. presents description of the supercapacitor working voltage range. V_SC,max and V_SC,min are accordingly supercapacitor maximum and minimum voltages, V_SC,max,off is charge permission voltage, V_SC,min,on is discharge permission voltage.

In the Table 1 values of the initial supercapacitor voltage V_SC,0 chosen for experiments according to the current I_SC,max are shown.

TABLE 1. SUPERCAPACITOR INITIAL VOLTAGE V_SC,0 VALUES FOR DIFFERENT SUPERCAPACITOR MAXIMUM CURRENTS I_SC,max

VSC,0	ISC,max = 35 A	ISC,max = 40 A	ISC,max = 45 A
VSC,0<VSCmin, V	65	60	50
VSCmin, V	70.3	61.5	54.7
VSCmin,on, V	71	62.2	55.4
VSC,w1, V	72	62.3	56
VSC,w2, V	73	64	57.7
VSC,w3, V	74	66	59
VSCmax,off, V	74.4	66.2	60
VSCmax, V	75.1	66.9	60.7
VSC,0>VSCmax, V	80	70	65

It is necessary to consider that different V_SC,0 values can differently influence [20] on the ESS discharge power and energy losses on the braking resistor. Fig. 9. presents the ESS discharge power diagrams at various supercapacitor maximum currents (Table 1). According to supercapacitor working voltage range, at voltage less than V_SCmin,on the ESS discharge is forbidden and P_ess = 0. According to Fig. 9. it can be concluded that at increase of supercapacitor maximum current I_SC,max the power of the discharge decreases that can worsen quality of the peak power shaving.

Fig. 10. presents the diagrams of energy losses on the braking resistor R_br.dc.. The minimum losses of energy on a brake resistor are observed, when V_SC,0 initial values are close to V_SCmax,off level. At a supercapacitor current 40 A it is possible to operate with V_SCmax,off, in other cases it is necessary to slightly lower V_SC,0 value.

Fig. 11. presents the diagrams of braking energy losses extended for supercapacitor working voltage range. From Fig. 10. follows that if initial supercapacitor voltage value is between V_SCmin and V_SC,w3 (Table 1.) braking energy losses decrease by increasing of supercapacitor maximum current I_SC,max. The minimum losses of energy on a brake resistor are observed, when initial supercapacitor voltage V_SC,0 values are close to V_SCmax,off level. At a supercapacitor current 40 A which corresponds to a tramcar current, it is possible to operate with value V_SCmax,off, in other cases it is necessary to slightly lower V_SC,0 value.

Small losses appear in a working range of initial supercapacitor voltage, and they decrease as V_SC,0 approach to the value V_SCmax,off.

If initial supercapacitor voltage reaches V_SCmin value, energy losses increase.

At increase of supercapacitor maximum current I_SC,max, losses in a brake resistor decrease.

At increase of I_SC,max the power of a discharge decreases that can worsen quality of the peak power shaving.

Fig. 9. The ESS discharge power diagrams Fig. 10. Braking energy losses

Fig. 11. Braking energy losses in brake resistor at supercapacitor working voltage range

The Matlab/Simulink simulations have been performed to simulate, using TB, a single tram starting and braking processes in the overhead line voltage feeding and autonomous traction modes. During the tram operation modes, 2s long temporary dropouts of the overhead voltage were simulated [18].

The overhead feeding mode is most commonly used for light rail traction. As the autonomous traction mode is provided mainly for emergency operation, to prolong a vehicle running distance without installing a more powerful ESS its speed should be limited. In turn, to prolong the service life of a traction accumulator battery the charging process should run continuously and independent of the operation mode of the tram traction drive simulator.

The comparison of the tram simulated diagrams for overhead feeding mode and autonomous mode is shown on Fig. 12.a In both cases the simulation conditions are provided for full-loaded tram (m=30.2t) at 12s acceleration with maximum current I_a=40A, 10s freewheeling followed by braking. During the freewheeling mode a current of 4.8A for charging the accumulator is received from the substation.

In the autonomous feeding mode (Fig. 12.b), with reduced TB ESS voltage (90V instead of 100V) at the beginning of freewheeling mode the filter capacitor voltage falls to supercapacitor voltage level (85V) thus causing automatic switching of the traction drive model to the generator mode to provide continuous accumulator charging (12s-16s). After 16s the accumulator is charged from ESS supercapacitor. As the accumulator voltage drop is negligible at short-term vehicle starting, the simplified simulation scheme for autonomous start from accumulator does not differ much from that for overhead feeding mode.

Comparison of the traction drive behaviour at a 2s supply voltage dropout without ESS (Fig. 13.a) and with ESS (Fig. 13.b) shows that an energy storage system compensates effectively voltage failures without traction mode switching off (Fig. 12).

However, in the traction mode during voltage dropouts the traction current oscillations can occur. In turn, in the free-wheeling mode during such dropouts the accumulator charging from traction motor takes place due to the high speed when the motor emf is higher than the ESS supercapacitor voltage (Fig. 13).

a b

Fig. 12. Simulated diagrams for TB with ESS in the overhead feeding mode (a) and in the autonomous feeding mode (b)

a b

Fig. 13. Simulated diagrams for TB without ESS (a) and with ESS (b) in the overhead feeding mode with 2s supply voltage dropouts

interruptions are observed (Fig. 13.a). As the ESS supercapacitor is not much discharged before the voltage failure and as the traction motor emf is low, the supercapacitor provides the total energy required for traction motor and accumulator charging, so no switching of the traction drive to the generator mode at voltage failures is observed (Fig. 13.b).