Week-11 Challenge: Braking

1. Energy required for braking.

WLTP drive cycle is used for braking energy calculation. Drive Cycle is shown below.

Excel data of the WLTC Class-3 drive cycle is shown below.

Time (Sec)	Speed (km/h)	Speed (m/s)	Acceleration	Braking Energy (J)
1	0.00	0.00	0.00	0.00
2	0.00	0.00	0.00	0.00
3	0.00	0.00	0.00	0.00
4	0.00	0.00	0.00	0.00
5	0.00	0.00	0.00	0.00
6	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00
11	0.00	0.00	0.14	0.00
12	1.00	0.28	0.29	0.00
13	2.10	0.58	0.53	0.00
14	4.80	1.33	0.97	0.00
15	9.10	2.53	1.31	0.00
16	14.20	3.94	1.49	0.00
17	19.80	5.50	1.57	0.00
18	25.50	7.08	1.49	0.00
19	30.50	8.47	1.29	0.00
20	34.80	9.67	1.15	0.00
21	38.80	10.78	1.13	0.00
22	42.90	11.92	1.06	0.00
23	46.40	12.89	0.75	0.00
24	48.30	13.42	0.32	0.00
25	48.70	13.53	0.03	0.00
26	48.50	13.47	-0.04	1.54
27	48.40	13.44	-0.04	0.39
28	48.20	13.39	-0.08	1.54
29	47.80	13.28	-0.17	6.17
30	47.00	13.06	-0.26	24.69
31	45.90	12.75	-0.29	46.68
32	44.90	12.47	-0.21	38.58
33	44.40	12.33	-0.08	9.65
34	44.30	12.31	0.01	0.39
35	44.50	12.36	0.11	0.00
36	45.10	12.53	0.17	0.00
37	45.70	12.69	0.13	0.00
38	46.00	12.78	0.04	0.00
39	46.00	12.78	0.00	0.00
40	46.00	12.78	0.01	0.00
41	46.10	12.81	0.10	0.00
42	46.70	12.97	0.22	0.00
43	47.70	13.25	0.31	0.00
44	48.90	13.58	0.36	0.00
45	50.30	13.97	0.38	0.00
46	51.60	14.33	0.32	0.00
47	52.60	14.61	0.19	0.00
48	53.00	14.72	0.06	0.00
49	53.00	14.72	-0.01	0.00
50	52.90	14.69	-0.04	0.39
51	52.70	14.64	-0.04	1.54
52	52.60	14.61	0.06	0.39
53	53.10	14.75	0.24	0.00
54	54.30	15.08	0.29	0.00
55	55.20	15.33	0.17	0.00
56	55.50	15.42	0.10	0.00
57	55.90	15.53	0.11	0.00
58	56.30	15.64	0.11	0.00
59	56.70	15.75	0.08	0.00
60	56.90	15.81	0.01	0.00
61	56.80	15.78	-0.13	0.39
62	56.00	15.56	-0.36	24.69
63	54.20	15.06	-0.54	125.00
64	52.10	14.47	-0.57	170.14
65	50.10	13.92	-0.68	154.32
66	47.20	13.11	-0.96	324.46
67	43.20	12.00	-1.11	617.28
68	39.20	10.89	-0.93	617.28
69	36.50	10.14	-0.68	281.25
70	34.30	9.53	-0.76	186.73
71	31.00	8.61	-1.15	420.14
72	26.00	7.22	-1.43	964.51
73	20.70	5.75	-1.47	1083.72
74	15.40	4.28	-1.06	1083.72
75	13.10	3.64	-0.47	204.09
76	12.00	3.33	-0.08	46.68
77	12.50	3.47	0.28	0.00
78	14.00	3.89	0.90	0.00
79	19.00	5.28	1.28	0.00
80	23.20	6.44	1.25	0.00
81	28.00	7.78	1.22	0.00
82	32.00	8.89	0.83	0.00
83	34.00	9.44	0.56	0.00
84	36.00	10.00	0.56	0.00
85	38.00	10.56	0.56	0.00
86	40.00	11.11	0.32	0.00
87	40.30	11.19	0.07	0.00
88	40.50	11.25	-0.18	0.00
89	39.00	10.83	-0.67	86.81
90	35.70	9.92	-1.00	420.14
91	31.80	8.83	-1.19	586.81
92	27.10	7.53	-1.25	852.24
93	22.80	6.33	-0.83	713.35
94	21.10	5.86	-0.54	111.50
95	18.90	5.25	-0.31	186.73
96	18.90	5.25	0.33	0.00
97	21.30	5.92	0.69	0.00
98	23.90	6.64	0.64	0.00
99	25.90	7.19	0.63	0.00
100	28.40	7.89	0.61	0.00
101	30.30	8.42	0.35	0.00
102	30.90	8.58	0.11	0.00
103	31.10	8.64	0.13	0.00
104	31.80	8.83	0.22	0.00
105	32.70	9.08	0.19	0.00
106	33.20	9.22	-0.04	0.00
107	32.40	9.00	-0.68	24.69
108	28.30	7.86	-0.92	648.53
109	25.80	7.17	-0.72	241.13
110	23.10	6.42	-0.56	281.25
111	21.80	6.06	-0.26	65.20
112	21.20	5.89	-0.11	13.89
113	21.00	5.83	-0.03	1.54
114	21.00	5.83	-0.01	0.00
115	20.90	5.81	-0.15	0.39
116	19.90	5.53	-0.42	38.58
117	17.90	4.97	-0.67	154.32
118	15.10	4.19	-0.71	302.47
119	12.80	3.56	-0.43	204.09
120	12.00	3.33	0.06	24.69
121	13.20	3.67	0.71	0.00
122	17.10	4.75	1.10	0.00
123	21.10	5.86	0.65	0.00
124	21.80	6.06	0.01	0.00
125	21.20	5.89	-0.46	13.89
126	18.50	5.14	-1.01	281.25
127	13.90	3.86	-0.90	816.36
128	12.00	3.33	-0.26	139.27
129	12.00	3.33	0.14	0.00
130	13.00	3.61	0.56	0.00
131	16.00	4.44	0.76	0.00
132	18.50	5.14	0.64	0.00
133	20.60	5.72	0.56	0.00
134	22.50	6.25	0.47	0.00
135	24.00	6.67	0.57	0.00
136	26.60	7.39	0.82	0.00
137	29.90	8.31	1.14	0.00
138	34.80	9.67	1.10	0.00
139	37.80	10.50	0.75	0.00
140	40.20	11.17	0.53	0.00
141	41.60	11.56	0.24	0.00
142	41.90	11.64	0.06	0.00
143	42.00	11.67	0.04	0.00
144	42.20	11.72	0.06	0.00
145	42.40	11.78	0.07	0.00
146	42.70	11.86	0.10	0.00
147	43.10	11.97	0.14	0.00
148	43.70	12.14	0.13	0.00
149	44.00	12.22	0.06	0.00
150	44.10	12.25	0.18	0.00
151	45.30	12.58	0.32	0.00
152	46.40	12.89	0.26	0.00
153	47.20	13.11	0.13	0.00
154	47.30	13.14	0.03	0.00
155	47.40	13.17	0.01	0.00
156	47.40	13.17	0.01	0.00
157	47.50	13.19	0.07	0.00
158	47.90	13.31	0.15	0.00
159	48.60	13.50	0.21	0.00
160	49.40	13.72	0.17	0.00
161	49.80	13.83	0.06	0.00
162	49.80	13.83	-0.01	0.00
163	49.70	13.81	-0.07	0.39
164	49.30	13.69	-0.17	6.17
165	48.50	13.47	-0.24	24.69
166	47.60	13.22	-0.31	31.25
167	46.30	12.86	-0.54	65.20
168	43.70	12.14	-0.97	260.80
169	39.30	10.92	-1.33	746.91
170	34.10	9.47	-1.43	1043.21
171	29.00	8.06	-1.44	1003.47
172	23.70	6.58	-1.47	1083.72
173	18.40	5.11	-1.31	1083.72
174	14.30	3.97	-0.89	648.53
175	12.00	3.33	-0.21	204.09
176	12.80	3.56	0.56	0.00
177	16.00	4.44	0.88	0.00
178	19.10	5.31	0.89	0.00
179	22.40	6.22	0.90	0.00
180	25.60	7.11	1.07	0.00
181	30.10	8.36	1.35	0.00
182	35.30	9.81	1.36	0.00
183	39.90	11.08	1.28	0.00
184	44.50	12.36	1.06	0.00
185	47.50	13.19	0.89	0.00
186	50.90	14.14	0.92	0.00
187	54.10	15.03	0.75	0.00
188	56.30	15.64	0.56	0.00
189	58.10	16.14	0.49	0.00
190	59.80	16.61	0.42	0.00
191	61.10	16.97	0.32	0.00
192	62.10	17.25	0.24	0.00
193	62.80	17.44	0.17	0.00
194	63.30	17.58	0.11	0.00
195	63.60	17.67	0.10	0.00
196	64.00	17.78	0.15	0.00
197	64.70	17.97	0.17	0.00
198	65.20	18.11	0.08	0.00
199	65.30	18.14	0.01	0.00
200	65.30	18.14	0.01	0.00
201	65.40	18.17	0.06	0.00
202	65.70	18.25	0.08	0.00
203	66.00	18.33	-0.01	0.00
204	65.60	18.22	-0.35	6.17
205	63.50	17.64	-0.82	170.14
206	59.70	16.58	-1.24	557.10
207	54.60	15.17	-1.44	1003.47
208	49.30	13.69	-1.35	1083.72
209	44.90	12.47	-0.97	746.91
210	42.30	11.75	-0.49	260.80
211	41.40	11.50	-0.14	31.25
212	41.30	11.47	0.10	0.39
213	42.10	11.69	0.47	0.00
214	44.70	12.42	0.88	0.00
215	48.40	13.44	0.93	0.00
216	51.40	14.28	0.60	0.00
217	52.70	14.64	0.22	0.00
218	53.00	14.72	-0.03	0.00
219	52.50	14.58	-0.24	9.65
220	51.30	14.25	-0.39	55.56
221	49.70	13.81	-0.54	98.77
222	47.40	13.17	-0.83	204.09
223	43.70	12.14	-1.07	528.16
224	39.70	11.03	-1.14	617.28
225	35.50	9.86	-1.19	680.56
226	31.10	8.64	-1.28	746.91
227	26.30	7.31	-1.28	888.89
228	21.90	6.08	-1.15	746.91
229	18.00	5.00	-0.68	586.81
230	17.00	4.72	0.00	38.58
231	18.00	5.00	0.61	0.00
232	21.40	5.94	0.94	0.00
233	24.80	6.89	0.90	0.00
234	27.90	7.75	0.83	0.00
235	30.80	8.56	0.71	0.00
236	33.00	9.17	0.60	0.00
237	35.10	9.75	0.57	0.00
238	37.10	10.31	0.53	0.00
239	38.90	10.81	0.60	0.00
240	41.40	11.50	0.71	0.00
241	44.00	12.22	0.68	0.00
242	46.30	12.86	0.51	0.00
243	47.70	13.25	0.26	0.00
244	48.20	13.39	0.14	0.00
245	48.70	13.53	0.15	0.00
246	49.30	13.69	0.15	0.00
247	49.80	13.83	0.13	0.00
248	50.20	13.94	0.15	0.00
249	50.90	14.14	0.22	0.00
250	51.80	14.39	0.22	0.00
251	52.50	14.58	0.21	0.00
252	53.30	14.81	0.28	0.00
253	54.50	15.14	0.33	0.00
254	55.70	15.47	0.28	0.00
255	56.50	15.69	0.15	0.00
256	56.80	15.78	0.07	0.00
257	57.00	15.83	0.06	0.00
258	57.20	15.89	0.10	0.00
259	57.70	16.03	0.21	0.00
260	58.70	16.31	0.33	0.00
261	60.10	16.69	0.33	0.00
262	61.10	16.97	0.22	0.00
263	61.70	17.14	0.17	0.00
264	62.30	17.31	0.17	0.00
265	62.90	17.47	0.14	0.00
266	63.30	17.58	0.07	0.00
267	63.40	17.61	0.03	0.00
268	63.50	17.64	0.15	0.00
269	64.50	17.92	0.32	0.00
270	65.80	18.28	0.32	0.00
271	66.80	18.56	0.22	0.00
272	67.40	18.72	0.28	0.00
273	68.80	19.11	0.51	0.00
274	71.10	19.75	0.49	0.00
275	72.30	20.08	0.24	0.00
276	72.80	20.22	0.15	0.00
277	73.40	20.39	0.25	0.00
278	74.60	20.72	0.36	0.00
279	76.00	21.11	0.28	0.00
280	76.60	21.28	0.07	0.00
281	76.50	21.25	-0.06	0.39
282	76.20	21.17	-0.10	3.47
283	75.80	21.06	-0.11	6.17
284	75.40	20.94	-0.14	6.17
285	74.80	20.78	-0.21	13.89
286	73.90	20.53	-0.29	31.25
287	72.70	20.19	-0.36	55.56
288	71.30	19.81	-0.32	75.62
289	70.40	19.56	-0.18	31.25
290	70.00	19.44	-0.06	6.17
291	70.00	19.44	-0.14	0.00
292	69.00	19.17	-0.28	38.58
293	68.00	18.89	-0.14	38.58
294	68.00	18.89	0.00	0.00
295	68.00	18.89	0.01	0.00
296	68.10	18.92	0.06	0.00
297	68.40	19.00	0.07	0.00
298	68.60	19.06	0.04	0.00
299	68.70	19.08	-0.01	0.00
300	68.50	19.03	-0.08	1.54
301	68.10	18.92	-0.17	6.17
302	67.30	18.69	-0.26	24.69
303	66.20	18.39	-0.35	46.68
304	64.80	18.00	-0.36	75.62
305	63.60	17.67	-0.31	55.56
306	62.60	17.39	-0.21	38.58
307	62.10	17.25	-0.10	9.65
308	61.90	17.19	-0.03	1.54
309	61.90	17.19	-0.01	0.00
310	61.80	17.17	-0.06	0.39
311	61.50	17.08	-0.13	3.47
312	60.90	16.92	-0.25	13.89
313	59.70	16.58	-0.88	55.56
314	54.60	15.17	-1.44	1003.47
315	49.30	13.69	-1.35	1083.72
316	44.90	12.47	-0.97	746.91
317	42.30	11.75	-0.49	260.80
318	41.40	11.50	-0.14	31.25
319	41.30	11.47	0.10	0.39
320	42.10	11.69	0.47	0.00
321	44.70	12.42	0.88	0.00
322	48.40	13.44	0.93	0.00
323	51.40	14.28	0.60	0.00
324	52.70	14.64	0.36	0.00
325	54.00	15.00	0.60	0.00
326	57.00	15.83	0.57	0.00
327	58.10	16.14	0.31	0.00
328	59.20	16.44	0.13	0.00
329	59.00	16.39	-0.01	1.54
330	59.10	16.42	0.07	0.00
331	59.50	16.53	0.19	0.00
332	60.50	16.81	0.39	0.00
333	62.30	17.31	0.47	0.00
334	63.90	17.75	0.39	0.00
335	65.10	18.08	0.03	0.00
336	64.10	17.81	-0.33	38.58
337	62.70	17.42	-0.29	75.62
338	62.00	17.22	-0.19	18.90
339	61.30	17.03	-0.15	18.90
340	60.90	16.92	-0.11	6.17
341	60.50	16.81	-0.10	6.17
342	60.20	16.72	-0.10	3.47
343	59.80	16.61	-0.11	6.17
344	59.40	16.50	-0.17	6.17
345	58.60	16.28	-0.26	24.69
346	57.50	15.97	-0.28	46.68
347	56.60	15.72	-0.21	31.25
348	56.00	15.56	-0.15	13.89
349	55.50	15.42	-0.14	9.65
350	55.00	15.28	-0.15	9.65
351	54.40	15.11	-0.13	13.89
352	54.10	15.03	-0.06	3.47
353	54.00	15.00	-0.03	0.39
354	53.90	14.97	-0.01	0.39
355	53.90	14.97	0.01	0.00
356	54.00	15.00	0.04	0.00
357	54.20	15.06	0.14	0.00
358	55.00	15.28	0.22	0.00
359	55.80	15.50	0.17	0.00
360	56.20	15.61	0.04	0.00
361	56.10	15.58	-0.15	0.39
362	55.10	15.31	-0.47	38.58
363	52.70	14.64	-0.93	222.22
364	48.40	13.44	-1.33	713.35
365	43.10	11.97	-1.47	1083.72
366	37.80	10.50	-1.47	1083.72
367	32.50	9.03	-1.47	1083.72
368	27.20	7.56	-1.03	1083.72
369	25.10	6.97	-0.17	170.14
370	26.00	7.22	0.58	0.00
371	29.30	8.14	1.19	0.00
372	34.60	9.61	1.54	0.00
373	40.40	11.22	1.49	0.00
374	45.30	12.58	1.19	0.00
375	49.00	13.61	0.81	0.00
376	51.10	14.19	0.43	0.00
377	52.10	14.47	0.15	0.00
378	52.20	14.50	0.00	0.00
379	52.10	14.47	-0.07	0.39
380	51.70	14.36	-0.17	6.17
381	50.90	14.14	-0.35	24.69
382	49.20	13.67	-0.69	111.50
383	45.90	12.75	-1.19	420.14
384	40.60	11.28	-1.47	1083.72
385	35.30	9.81	-1.47	1083.72
386	30.00	8.33	-1.47	1083.72
387	24.70	6.86	-1.49	1083.72
388	19.30	5.36	-1.21	1125.00
389	16.00	4.44	-0.85	420.14
390	13.20	3.67	-0.74	302.47
391	10.70	2.97	-0.61	241.13
392	8.80	2.44	-0.49	139.27
393	7.20	2.00	-0.46	98.77
394	5.50	1.53	-0.56	111.50
395	3.20	0.89	-0.61	204.09
396	1.10	0.31	-0.44	170.14
397	0.00	0.00	-0.15	46.68
398	0.00	0.00	0.00	0.00
399	0.00	0.00	0.00	0.00
400	0.00	0.00	0.00	0.00
				45248.84

Braking energy calculated for each seconds during deceleration using the IF function. Which can be observed in the table. Formula used for Braking Energy is `1/2 M V^2`

M = Mass of Vehicle, taken as 1000kg

V= difference of inital velocity and final velocity.

Total braking energy used = 45.25kJ

2. Why electric motor can’t develop braking torque at high speed similar to starting?

You cannot attain the maximum torque after accelerating. At high speeds, the back EMF is too near to the Motor supply voltage, therefore current cannot rise so much by raising the PWM duty cycle. Current is proportional to torque and hence Torque is not much produced. Due to the fact that the majority of the torque is utilised to increase the kinetic energy of the load, this condition does not arise at the start of an acceleration (and motor). However, it is impossible to increase the torque while the speed is already high and no additional load is being added.

Electrical & Mechanical Brake coordination

According to the Brake Control Strategy, it sis classified into Series and Parallel Braking

Series Braking: In this type of braking control, Mechanical and Regenerative braking are applied one after another. When acceleration stopped for a vehicle running at a speed, as far as acceleration stopped, Motor will acts as generator regeneration happens and speed reduces. Mechanical braking applied after slowing down to completely stop the vehicle.

Parallel braking: In this type of braking, after acceleration is stopped, mechanical brake is applied and regenerative braking is happening at the same time.

3. Contour plot of given motor speed, torque and efficiency

MATLAB Script Code

clear all;
close all;
clc;

%setup arrays for range
x=linspace(1,1500); %speed rad/sec
y=linspace(1,750); %0 to 40 Nm

kc=0.2; %Copper loss constant
ki=0.008; %Iron loss constant
kw=0.00001; %Windage loass constant
ConL=20; %Constant loss

[X,Y]=meshgrid(x,y); %Make mesh
Outputpower=(X.*Y); %Torque x Speed = Power
B=(Y.^2)*kc; %Copper loss
C=X*ki; %Iron loss
D=(X.^3)*kw; %Windage loss
Inputpower=Outputpower+B+C+D+ConL;
Z=Outputpower./Inputpower;
%Set the efficiencies for which a contour will be plotted
V=[0.70,0.80,0.85,0.90,0.91,0.92,0.925,0.93];
box off
grid off
contour (X,Y,Z,V);
xlabel('Speed (rad/sec)'), ylabel('Torque (N.m)');
hold on

Contour Plot