Energy consumption and regen on mountain rides?

[Mono]

11 minutes ago, Aneta said:

For 100kg with 10m/s initial speed, that's a total of KE = m*v^2/2 = 5000J, or less than 1.5Wh. With specific heat of copper roughly 400J/kg/C, if there are a couple of kilos of Cu in the motor, that's less than 10C temperature increase.

Thanks for cross-checking, that's about what I had in my lazy mind.

Edited November 22, 2019 by Mono

[mrelwood]

I read somewhere a few years ago that some self-balancing vehicle (don’t remember which) has a threshold speed for regenerative braking set at 10km/h. I have no idea if that is/was standard practice or not. This was obviously not a real data point, but one possibility.

Regarding ”under-leaning”, for example the Lhotz was very easy to under-lean, ie. brake too hard for the wheel to be able to keep up. It felt like it didn’t have any extra braking power compared to acceleration, unlike newer wheels.

[Chriull]

9 hours ago, Aneta said:

You're absolutely right! Motor should be able to swallow this braking energy despite the huge peak power. As long as the MOSFETs don't burn from high peak currents...

With regenerative breaking the phase current is the same as the battery current. So for the mosfets it should be no real challenge.  Edit: that's quite definitely wrog. Should be comparable to "normal" driving conditions...

If they are used "active" and not just their body diodes are misused.

Also the coil resistance should be in about the range of the battery internal resistance - so power dissipation divides between them and some energy is taken from the batteries as charge.

 

11 hours ago, Planemo said:

So you are saying that irrespective of braking force required, regen is always being provided to the batteries and there is no other method of energy dissipation used?

No. Regenerative breaking is the only technique to dissipate the needed powers for longer/repetitive breakings.

The other techniques can be used for the small braking needed for selfbalancing and for some (?smaller?) braking inbetween.

Edited November 23, 2019 by Chriull

[Chriull]

Did some calculations:

Starting from the (very simple first approximation) equivalent diagram of an EUC:

and the following EUC Data (tried to "model" a MSX 84V):

m (rider+wheel)	100,00	kg
Diameter	18,00	inch
Radius	0,23	m
Circumference	1,44	m
v_max_no_load	78,00	km/h	21,67	m/s	15,08	s ^ -1
omega	94,78	rad/s
k_v	0,89	V/rad/s		U = k_v * omega
k_m	1,13	Nm/A		I_motor = k_m * M
P Nom	2000
P Max	6000
P_Max @	As mechanical Output =U_Back_EMF * I_motor
	v=v_max_no_load/2	10,8333333333334	m/s	47,39	rad/s
	U_Back_EMF=U_Batt/2	42	V
	I_motor	142,857142857143	A
	R_coil	0,294	Ohm
	s	p
Battery	20	6	Capacity	1600	Wh
U_cell	4,20	V	U_cell_nom	3,70	V
U_batt	84,00	V	Capacity_cell	3,50	Ah
R_i_cell	0,04	Ohm	Capacity_calc	1554,00	Wh
R_i_batt	0,12	Ohm

 

I assumed as peak mechanical output Power 6000W to get a value for the internal coil resistance. So for maximum dynamic/regen braking once one shorts the motor coil this R_coil determines the maximum Current that the Back EMF from the motor can generate. Neglecting mechanical motor losses and Mosfet resistance this leads to the coil resistance. (Edit: This argument has to be refined - quite some wrong statements gathered here. Max output power is reached at half no load speed - then V Back EMF is half battery voltage andR coil could be estimated by this!? But the internal resistance of the battery should be regarded, so R_coil should be reduced by this 0,12 Ohm... ? But anyhow - the range/magnitude seems/should be about right and these are only rough estimates anyhow...)

This leads to the following chart for possible regenerative braking states at 36 km/h:

with the following results:

v	36,00	km/h	10,00	m/s	43,74	rad/s
U_batt_0	66,00	V
U_Back_EMF	38,77	V		I_batt_max	18,74	A
I_motor_max	131,87	A		Charge rate max	0,89	C
P_mech_max	5112,43	W
M_max	148,79	Nm
a_max	6,51	m/s²

 

I assumed for this example the  minimum battery voltage for maximum battery current. (At 84V the maximum battery current would be 14,9A / 0,71C.)

The right end of this diagram shows in reality dynamic braking (shorting of the motor coils). The more one gets near this dynamic braking the less gets the motor terminal voltage - so the "step up factor" to charge the battery gets higher and higher and the efficiency of the transforming gets worse and worse (which is here neglected).

As efficiency i took mechanical input/braking power vs. Battery charging "power" (U_battery_0 * I_battery - so without the voltage drop on the internal resistance). But imho only the battery current is determining the charging - so the better factor should be Battery current / Braking power? Just tried this and still get the same falling line - it's just the constant battery voltage less in the expression 

As comparison (and as i did this second sheet, too) the possible output power chart while driving at 36 km/h:

v	36,00	km/h	10	m/s	43,74	rad/s
U_batt_0	84,00	V
U_Back_EMF	38,77	V		I_batt_max	105,75	A
I_motor_max	153,85	A		Discharge rate max	5,04	C
P_mech_max	5964,50	W
M_max	173,59	Nm
a_max	7,59	m/s²

 

 

Edited November 24, 2019 by Chriull

[Marty Backe]

5 minutes ago, Chriull said:

Did some calculations:

Starting from the (very simple first approximation) equivalent diagram of an EUC:

and the following EUC Data (tried to "model" a MSX 84V):

m (rider+wheel)	100,00	kg
Diameter	18,00	inch
Radius	0,23	m
Circumference	1,44	m
v_max_no_load	78,00	km/h	21,67	m/s	15,08	s ^ -1
omega	94,78	rad/s
k_v	0,89	V/rad/s		U = k_v * omega
k_m	1,13	Nm/A		I_motor = k_m * M
P Nom	2000
P Max	6000
P_Max @	As mechanical Output =U_Back_EMF * I_motor
	v=v_max_no_load/2	10,8333333333334	m/s	47,39	rad/s
	U_Back_EMF=U_Batt/2	42	V
	I_motor	142,857142857143	A
	R_coil	0,294	Ohm
	s	p
Battery	20	6	Capacity	1600	Wh
U_cell	4,20	V	U_cell_nom	3,70	V
U_batt	84,00	V	Capacity_cell	3,50	Ah
R_i_cell	0,04	Ohm	Capacity_calc	1554,00	Wh
R_i_batt	0,12	Ohm

 

I assumed as peak mechanical output Power 6000W to get a value for the internal coil resistance. So for maximum dynamic/regen braking once one shorts the motor coil this R_coil determines the maximum Current that the Back EMF from the motor can generate. Neglectiong mechanical motor losses and Mosfet resistance this leads to the coil resistance.

This leads to the following chart for possible regenerative braking states at 36 km/h:

with the following results:

v	36,00	km/h	10,00	m/s	43,74	rad/s
U_batt_0	66,00	V
U_Back_EMF	38,77	V		I_batt_max	18,74	A
I_motor_max	131,87	A		Charge rate max	0,89	C
P_mech_max	5112,43	W
M_max	148,79	Nm
a_max	6,51	m/s²

 

I assumed for this example the  minimum battery voltage for maximum battery current. (At 84V the maximum battery current would be 14,9A / 0,71C.)

The right end of this diagram shows in reality dynamic braking (shorting of the motor coils). The more one gets near this dynamic braking the less gets the motor terminal voltage - so the "step up factor" to charge the battery gets higher and higher and the efficiency of the transforming gets worse and worse (which is here neglected).

As efficiency i took mechanical input/braking power vs. Battery charging "power" (U_battery_0 * I_battery - so without the voltage drop on the internal resistance). But imho only the battery current is determining the charging - so the better factor should be Battery current / Braking power? Just tried this and still get the same falling line - it's just the constant battery voltage less in the expression 

As comparison (and as i did this second sheet, too) the possible output power chart while driving at 36 km/h:

v	36,00	km/h	10	m/s	43,74	rad/s
U_batt_0	84,00	V
U_Back_EMF	38,77	V		I_batt_max	105,75	A
I_motor_max	153,85	A		Discharge rate max	5,04	C
P_mech_max	5964,50	W
M_max	173,59	Nm
a_max	7,59	m/s²

 

 

I love what some of you guys do 

[Seba]

12 minutes ago, Marty Backe said:

I love what some of you guys do 

Don't worry. When spring will come, they'll return back to EUC riding and writing scientific dissertations will (hopefully!) end 

[Chriull]

58 minutes ago, Seba said:

Don't worry. When spring will come, they'll return back to EUC riding and writing scientific dissertations will (hopefully!) end 

But for now it goes on 

As it seems best charging efficiency (highest battery current) is reached at exactly half (as with dynamic braking) possible braking power. I just did not disproof this hypothesis by trying some different random speeds in the oo sheet ;).

So drawing this (hopefully) maximum battery current over speed results in the following graph:

... getting to a almost 4C charge at full (no load) speed (which is not really reachable due to air drag/friction without overlean anyways...) With realistic speed of 50 km/h the maximum charge rate would be around 1.6C. Charge rate of 1 is reached about 38 km/h.

---------------------------

Looking on the schematics i'm quite irritated by now in regard to plugging breaking (changing the motors back emf polarity in relation to the battery voltage) and "power braking" (stepping down the battery voltage to a lower value as the back emf) if and how these would be possible with the normal motor driver - so maybe if winter is hard and cold enough some ideas/knowledge by reading will come until spring...;)

Edit: For now i think i'm sticking to my hypthesis by changing the commutation this "power" braking just works like normal acceleration/driving with just the negated torque, since the generated magnetic field runs "behind" the permanent magnets instead of "before"....

 

Edited November 24, 2019 by Chriull

[Aneta]

4 hours ago, Chriull said:

Did some calculations:

Starting from the (very simple first approximation) equivalent diagram of an EUC:

and the following EUC Data (tried to "model" a MSX 84V):

m (rider+wheel)	100,00	kg
Diameter	18,00	inch
Radius	0,23	m
Circumference	1,44	m
v_max_no_load	78,00	km/h	21,67	m/s	15,08	s ^ -1
omega	94,78	rad/s
k_v	0,89	V/rad/s		U = k_v * omega
k_m	1,13	Nm/A		I_motor = k_m * M
P Nom	2000
P Max	6000
P_Max @	As mechanical Output =U_Back_EMF * I_motor
	v=v_max_no_load/2	10,8333333333334	m/s	47,39	rad/s
	U_Back_EMF=U_Batt/2	42	V
	I_motor	142,857142857143	A
	R_coil	0,294	Ohm
	s	p
Battery	20	6	Capacity	1600	Wh
U_cell	4,20	V	U_cell_nom	3,70	V
U_batt	84,00	V	Capacity_cell	3,50	Ah
R_i_cell	0,04	Ohm	Capacity_calc	1554,00	Wh
R_i_batt	0,12	Ohm

 

I assumed as peak mechanical output Power 6000W to get a value for the internal coil resistance. So for maximum dynamic/regen braking once one shorts the motor coil this R_coil determines the maximum Current that the Back EMF from the motor can generate. Neglecting mechanical motor losses and Mosfet resistance this leads to the coil resistance. (Edit: This argument has to be refined - quite some wrong statements gathered here. Max output power is reached at half no load speed - then V Back EMF is half battery voltage andR coil could be estimated by this!? But the internal resistance of the battery should be regarded, so R_coil should be reduced by this 0,12 Ohm... ? But anyhow - the range/magnitude seems/should be about right and these are only rough estimates anyhow...)

This leads to the following chart for possible regenerative braking states at 36 km/h:

with the following results:

v	36,00	km/h	10,00	m/s	43,74	rad/s
U_batt_0	66,00	V
U_Back_EMF	38,77	V		I_batt_max	18,74	A
I_motor_max	131,87	A		Charge rate max	0,89	C
P_mech_max	5112,43	W
M_max	148,79	Nm
a_max	6,51	m/s²

 

I assumed for this example the  minimum battery voltage for maximum battery current. (At 84V the maximum battery current would be 14,9A / 0,71C.)

The right end of this diagram shows in reality dynamic braking (shorting of the motor coils). The more one gets near this dynamic braking the less gets the motor terminal voltage - so the "step up factor" to charge the battery gets higher and higher and the efficiency of the transforming gets worse and worse (which is here neglected).

As efficiency i took mechanical input/braking power vs. Battery charging "power" (U_battery_0 * I_battery - so without the voltage drop on the internal resistance). But imho only the battery current is determining the charging - so the better factor should be Battery current / Braking power? Just tried this and still get the same falling line - it's just the constant battery voltage less in the expression 

As comparison (and as i did this second sheet, too) the possible output power chart while driving at 36 km/h:

v	36,00	km/h	10	m/s	43,74	rad/s
U_batt_0	84,00	V
U_Back_EMF	38,77	V		I_batt_max	105,75	A
I_motor_max	153,85	A		Discharge rate max	5,04	C
P_mech_max	5964,50	W
M_max	173,59	Nm
a_max	7,59	m/s²

 

 

I tried entering the input params into Motor Sumulator (Custom Motor), but only getting 60kph no-load speed, not 78. Thoughts?

https://www.ebikes.ca/tools/simulator.html?batt=cust_84_0.12_21&cont=cust_100_200_0.03_V&wheel=18i&frame=cust_1_0.01&hp=0&blue=Lbs&motor=cust_8.45_0.294_0.2_23_0.77_0.0185_0&cont_b=cust_100_200_0.03_V&batt_b=cust_84_0.2_20&wheel_b=19i&frame_b=cust_1_0.01&hp_b=0

Edited November 24, 2019 by Aneta

[Aneta]

10 minutes ago, Aneta said:

I tried entering the input params into Motor Sumulator (Custom Motor), but only getting 60kph no-load speed, not 78. Thoughts?

https://www.ebikes.ca/tools/simulator.html?batt=cust_84_0.12_21&cont=cust_100_200_0.03_V&wheel=18i&frame=cust_1_0.01&hp=0&blue=Lbs&motor=cust_8.45_0.294_0.2_23_0.77_0.0185_0&cont_b=cust_100_200_0.03_V&batt_b=cust_84_0.2_20&wheel_b=19i&frame_b=cust_1_0.01&hp_b=0

Got it:

https://www.ebikes.ca/tools/simulator.html?batt=cust_84_0.12_21&cont=cust_100_200_0.03_V&wheel=18i&frame=cust_1_0.01&hp=0&blue=Lbs&motor=cust_10.73_0.294_0.2_23_0.77_0.0185_0&cont_b=cust_100_200_0.03_V&batt_b=cust_84_0.2_20&wheel_b=19i&frame_b=cust_1_0.01&hp_b=0

(there's some error in 1.13Nm/A value, if 0.89V/(rad/s) is correct)

[Chriull]

9 hours ago, Aneta said:

I tried entering the input params into Motor Sumulator (Custom Motor), but only getting 60kph no-load speed, not 78. Thoughts?

https://www.ebikes.ca/tools/simulator.html?batt=cust_84_0.12_21&cont=cust_100_200_0.03_V&wheel=18i&frame=cust_1_0.01&hp=0&blue=Lbs&motor=cust_8.45_0.294_0.2_23_0.77_0.0185_0&cont_b=cust_100_200_0.03_V&batt_b=cust_84_0.2_20&wheel_b=19i&frame_b=cust_1_0.01&hp_b=0

 

9 hours ago, Aneta said:

Got it:

https://www.ebikes.ca/tools/simulator.html?batt=cust_84_0.12_21&cont=cust_100_200_0.03_V&wheel=18i&frame=cust_1_0.01&hp=0&blue=Lbs&motor=cust_10.73_0.294_0.2_23_0.77_0.0185_0&cont_b=cust_100_200_0.03_V&batt_b=cust_84_0.2_20&wheel_b=19i&frame_b=cust_1_0.01&hp_b=0

(there's some error in 1.13Nm/A value, if 0.89V/(rad/s) is correct)

Seems i mixed something up since kv should be (rad/s)/V (or rpm/V). 

So it seems for km i have in reality calculated A/Nm...

Will check and update this in the evening.

PS.: But so i've seen the custom motor settings dialogue with the description of a0 and a1 (coefficients of the square omega polynom) - maybe it's possible to find some explanation fir this now!