I discuss in this article how the electric energy supplied by a traction battery changes while a pure electric car is driven on a chassis dynamometer according to the Worldwide harmonised Light-duty vehicles Test Procedure. In the European Union, Regulation (EU) 2017/1151 specifies that the driving range of a pure electric car is determined with the WLTC test cycle. The WLTC is quite different from many older driving cycles because it has large fluctuations in vehicle speed, short idle periods, and a wider speed envelope. These characteristics are particularly important for energy analysis because a pure electric car is not only a mobile electrical load; it can also recover kinetic energy through regenerative braking. Therefore, when I record current, voltage, and energy at the terminals of a power battery, I observe two directions of electrical energy flow: energy leaving the battery during acceleration and constant-speed driving, and energy returning to the battery during deceleration.
My goal is to provide a clear quantitative picture of this bidirectional electric energy behaviour. I selected a typical conventional pure electric car and carried out a full WLTC range test under laboratory-controlled conditions. The vehicle was secured on a chassis dynamometer, and the driver followed a driver’s-aid screen. During the test, the instantaneous battery current, voltage, electric energy, and vehicle speed were sampled by a power analyser and by the dynamometer data acquisition system. I then used those recordings to identify the electric energy variation in the low-speed, medium-speed, high-speed, and ultra-high-speed phases of the WLTC. The results should be useful to engineers who need to compare energy consumption, energy recovery, and range calibration of an electric car in accordance with European type-approval requirements.
Because a pure electric car has a finite amount of stored electrical energy, every complete WLTC cycle consumes a certain amount of net energy. The net energy consumption is the difference between the total energy supplied by the battery and the total regenerative energy that is accepted by the battery. From a vehicle-level viewpoint, a successful range test depends on the balance between discharge energy and regenerative charge energy. During rapid decelerations, the electric motor operates as a generator, converting kinetic energy into electrical energy. That electrical energy is then stored back into the high-voltage battery. During subsequent acceleration, the same electrical energy is available again to drive the wheels. For this reason, the measured energy variation is not only a cycle-integrated battery depletion value; it also tells me how much of the driving energy is replenished by the regenerative function of the electric car.
To make the energy calculations clear, I define the instantaneous battery power as the product of battery terminal voltage \(U_b(t)\) and instantaneous current \(I_b(t)\):
\[
P_b(t) = U_b(t) \, I_b(t)
\]
I treated the measured current direction so that a positive value means that the battery is discharging to the traction motor and to the electric-car high-voltage accessories, while a negative value means that the regenerative system is returning current to the battery. Consequently, the discharged energy supplied by the power battery during one WLTC cycle is:
\[
E_{\mathrm{out,cycle}} = \frac{1}{3600} \int_0^{1800} U_b(t) \, I_b(t) \, \mathbf{1}_{I_b(t) > 0} \, dt
\]
and the regenerative energy returned to the battery during that same cycle is:
\[
E_{\mathrm{reg,cycle}} = -\frac{1}{3600} \int_0^{1800} U_b(t) \, I_b(t) \, \mathbf{1}_{I_b(t) < 0} \, dt
\]
The net electric energy change of the electric car battery for the cycle is therefore:
\[
\Delta E_{\mathrm{cycle}} = E_{\mathrm{out,cycle}} – E_{\mathrm{reg,cycle}}
\]
In the following sections, I extend this definition to each of the four WLTC speed phases and to the complete series of full cycles that were evaluated.
WLTC Structure and Test Vehicle
The WLTC used here is the Class 3 cycle prescribed for a modern passenger electric car. Its total duration is 1800 seconds, and it is subdivided into four consecutive speed segments. The lower-speed segment represents urban and stop-and-go driving; the second segment represents suburban driving; the third segment represents rural or highway driving; and the final segment represents ultra-high-speed motorway driving. The most demanding section for an electric car is the ultra-high-speed phase because the aerodynamic load becomes much larger at high speed.
Table 1. Main WLTC speed phases used in the energy analysis.
| WLTC phase | Time interval (s) | Phase duration (s) | Nature of driving |
|---|---|---|---|
| Low speed | 0–589 | 589 | Urban, low speed, frequent stops |
| Medium speed | 589–1022 | 433 | Suburban, moderate speed |
| High speed | 1022–1477 | 455 | Rural or motorway, higher speed |
| Ultra-high speed | 1477–1800 | 323 | High-speed motorway driving |
The whole WLTC has an average speed of approximately 46.5 km/h and reaches a maximum speed close to 131.3 km/h in the ultra-high-speed phase. This is an important point for an electric car because the road-load power required to accelerate and to overcome aerodynamic drag increases dramatically at the upper end of the speed range.
Table 2. Main parameters of the tested electric car.
| Parameter | Value |
|---|---|
| Test mass | 2064 kg |
| Battery rated voltage | 381 V |
| Battery rated capacity | 174 Ah |
| Drive motor peak power | 160 kW |
| Drive configuration | Front-wheel drive |
| Powertrain type | Battery electric, conventional single-motor |
The test vehicle was a battery electric car with regenerative braking. It had no internal combustion engine, no range extender, and no gearbox that would create conventional transmission losses; the traction motor was the sole source of tractive effort. The electric car used a high-voltage power battery with a nominal electric energy capacity close to 66.3 kWh, which is consistent with the product of rated voltage and rated capacity:
\[
E_{\mathrm{battery,nominal}} = U_{\mathrm{rated}} \, C_{\mathrm{rated}} = 381 \, \mathrm{V} \times 174 \, \mathrm{Ah} = 66\,294 \, \mathrm{Wh} \approx 66.3 \, \mathrm{kWh}
\]
The chassis dynamometer was configured using road-load coefficients obtained by the coast-down method. The load applied by the dynamometer can be expressed as a quadratic function of vehicle speed:
\[
F_{\mathrm{load}}(v) = F_0 + F_1 v + F_2 v^2
\]
where \(v\) is the vehicle speed in km/h, \(F_0\) is the constant road-load term in newtons, \(F_1\) is the speed-dependent coefficient in N/(km/h), and \(F_2\) is the quadratic coefficient in N/(km/h)2. The values found for the tested electric car are given in Table 3.
Table 3. Chassis dynamometer road-load coefficients used for the electric car.
| Coefficient | Value |
|---|---|
| \(F_0\) | 22.757 N |
| \(F_1\) | 1.03740 N/(km/h) |
| \(F_2\) | 0.036879 N/(km/h)2 |
This road-load model was important to the electric car energy study because it determined the mechanical power that the traction battery had to supply for every instantaneous speed and acceleration condition. At high speeds, the quadratic term dominates, and therefore the ultra-high-speed phase requires a much larger battery output power than a low-speed urban phase.
Test Procedure and Data Acquisition
The test was performed on a laboratory chassis dynamometer under controlled ambient conditions. Before beginning the formal energy measurement, I warmed up the dynamometer and the electric car. The vehicle was preconditioned by following the driver’s-aid instructions so that the tyre and bearing losses, the brake system, and the battery thermal state became representative of an actual range test. The dynamometer resistance parameters were then checked using the road-load coefficients listed above. The electric car was charged with the procedure required by the regulation, and the WLTC test was started within the prescribed time after charging. During the test, a trained driver followed the target speed trace. The test continued over repeated WLTC cycles until the electric car could no longer maintain the required speed trace within the allowable tolerance.
When the electric car was driven through many consecutive WLTC cycles, the power analyser recorded the instantaneous battery voltage and current continuously. The dynamometer recorded the actual vehicle speed, and the time bases of the two systems were synchronized. I used this synchronized data set to compute discharge energy and regenerative energy for every complete cycle. The final incomplete cycle was excluded from the numerical summaries because it was terminated at the range end and did not contain a full set of four phases equal in length to the other cycles.
From a data-processing viewpoint, for a particular complete cycle \(n\) and a particular speed phase \(j\), I defined the electrical energy variables in the following way. The interval of that phase was \([t_j, t_{j+1}]\), and the battery voltage and current during that interval were \(U_{n,j}(t)\) and \(I_{n,j}(t)\). The output electric energy for that phase was:
\[
E_{\mathrm{out},n,j} = \frac{1}{3600}\int_{t_j}^{t_{j+1}} U_{n,j}(t) \, I_{n,j}(t) \, \mathbf{1}_{I_{n,j}(t)>0} \, dt
\]
The recovered electric energy for the same phase of the same cycle was:
\[
E_{\mathrm{reg},n,j} = -\frac{1}{3600}\int_{t_j}^{t_{j+1}} U_{n,j}(t) \, I_{n,j}(t) \, \mathbf{1}_{I_{n,j}(t)<0} \, dt
\]
Thus, the net electric energy variation of the high-voltage battery in that phase was:
\[
\Delta E_{n,j} = E_{\mathrm{out},n,j} – E_{\mathrm{reg},n,j}
\]
For the complete WLTC cycle, summing the four phase contributions gives:
\[
\Delta E_n = \sum_{j=1}^{4} \Delta E_{n,j}
\]
In the same way, the total output energy and total recovered energy over all complete cycles are:
\[
E_{\mathrm{out,total}} = \sum_{n=1}^{N} \sum_{j=1}^{4} E_{\mathrm{out},n,j}
\]
\[
E_{\mathrm{reg,total}} = \sum_{n=1}^{N} \sum_{j=1}^{4} E_{\mathrm{reg},n,j}
\]
where \(N\) is the number of complete WLTC cycles used in the evaluation. In the test discussed here, \(N=16\). The total net variation of the electric car battery energy is therefore:
\[
\Delta E_{\mathrm{total}} = E_{\mathrm{out,total}} – E_{\mathrm{reg,total}}
\]
Current and Voltage Behaviour of the Electric Car
One of the clearest features observed during the WLTC test was the relationship between vehicle speed, acceleration, and battery current. During hard acceleration, the electric car demanded a high positive discharge current from the battery. The maximum positive current was observed during the high-speed and ultra-high-speed phases because those phases contain the strongest accelerations and also require enough power to overcome road load at elevated speed. During deceleration, the current reversed and became negative, meaning that regenerative braking was charging the battery. The negative current became especially large when the deceleration rate was high, particularly at the end of the high-speed segments where the electric car had to reduce speed from a high value.
For a qualitative understanding of the current process, I can express the mechanical power demanded by the electric car as the sum of acceleration power, rolling resistance power, aerodynamic drag power, and uphill power. On a flat chassis dynamometer, the battery current is roughly proportional to the motor electrical demand, except during regenerative operation. Therefore, the current trace of the electric car under WLTC is not a smooth curve. It has sharp positive peaks during acceleration events and sharp negative dips during braking events. The WLTC speed profile contains many such dynamic events, so the battery current fluctuates rapidly. This behaviour confirms that the WLTC is a more demanding cycle for battery energy and power delivery than a steady-state constant-speed test.
I also observed a very important initial-condition effect at the beginning of the range test. At the very beginning, the high-voltage battery of the electric car was in a nearly full state of charge. Because a lithium-ion battery cannot accept large regenerative current when it is fully charged, the regenerative braking function was partly disabled or heavily limited during the first WLTC cycle. The negative recovery current was therefore smaller in the first cycle than in later cycles. After the first cycle had discharged a certain amount of energy from the battery, the regenerative braking function became fully enabled. From the second cycle onward, the negative current amplitude increased and remained stable for the rest of the test. The positive discharge current, on the other hand, was relatively similar from the first cycle onward. This is an important practical concern when I evaluate the energy recovery capability of an electric car: a test that begins at 100% state of charge may temporarily underestimate regenerative energy until the battery has enough headroom to accept charge.
Another important observation is that the current direction is determined by the vehicle operating state. If the electric car is cruising at constant speed, the current is positive, though typically smaller than during acceleration. During active deceleration, the motor controller adjusts the regenerative braking torque as a function of vehicle speed and braking demand. The negative current magnitude therefore follows the speed trace and is particularly noticeable when braking from a high speed to a low speed in a short time. I observed that the largest negative current values occurred during braking events that followed the highest vehicle speeds, not necessarily during low-speed urban stops. This was because the kinetic energy available for regeneration is proportional to the square of the vehicle speed, making high-speed deceleration a rich source of recoverable energy for the electric car.
Cycle-level Energy Results
I computed the total output electric energy, recovered electric energy, and net energy variation for the sixteen complete WLTC cycles. Two important regularities appeared. First, the output energy per complete WLTC cycle was reasonably stable. Second, the recovered energy was lower in the first cycle but became very stable by the second cycle. After the regenerative system had reached its normal operating condition, the cycle-to-cycle recovered energy values were close to one another. This is a useful property for an electric car range test because it means that energy consumption data for one full cycle can be used as a representative value, provided that the first-cycle full-battery effect is treated separately.
Table 4. Total electrical energy balance for 16 complete WLTC cycles of the tested electric car.
| Quantity | Value (Wh) | Fraction of total quantity |
|---|---|---|
| Total output electric energy from battery | 82,438 Wh | 100% |
| Total recovered electric energy into battery | 16,109 Wh | 100% |
| Total net electric energy variation of battery | 66,329 Wh | 100% |
Thus, over the sixteen complete cycles, the battery discharged 82.438 kWh, regenerative braking returned 16.109 kWh, and the net energy drawn from the battery was 66.329 kWh. The regenerative energy accounted for slightly more than 19.5% of the total output energy:
\[
\eta_{\mathrm{reg,total}} = \frac{E_{\mathrm{reg,total}}}{E_{\mathrm{out,total}}} \times 100\% = \frac{16\,109}{82\,438} \times 100\% \approx 19.54\%
\]
The net variation is the energy that the electric car actually consumed over the complete portion of the range test. This value is nearly equal to the usable chemical energy delivered by the battery over the test. It includes energy used to propel the vehicle, to overcome dynamometer and road load, and to supply high-voltage accessories, after subtracting the energy that was regenerated and stored back into the battery.
Because the complete-test totals contained small cycle-to-cycle differences, I also converted them into an average value per complete WLTC cycle. Dividing by 16 gives:
\[
\overline{E}_{\mathrm{out}} = \frac{82\,438}{16} = 5152.4 \, \mathrm{Wh}
\]
\[
\overline{E}_{\mathrm{reg}} = \frac{16\,109}{16} = 1006.8 \, \mathrm{Wh}
\]
\[
\overline{\Delta E} = \frac{66\,329}{16} = 4145.6 \, \mathrm{Wh}
\]
These per-cycle averages are useful for comparing individual phases because each WLTC phase has a different duration and a different energy intensity.
First-Cycle and Steady-Cycle Comparison
As noted, the first WLTC cycle was not fully representative because the battery started from a high state of charge and the regenerative current was limited. To demonstrate this effect, I compared the first complete cycle and the fourth complete cycle. By the fourth cycle, the battery state of charge had decreased sufficiently for regenerative braking to operate normally, and the energy balance had become stable.
Table 5. Energy balance of the first and fourth WLTC cycles by speed phase.
| Phase | First cycle output (Wh) | First cycle recovered (Wh) | First cycle net change (Wh) | Fourth cycle output (Wh) | Fourth cycle recovered (Wh) | Fourth cycle net change (Wh) |
|---|---|---|---|---|---|---|
| Low speed | 652 | 61 | 591 | 617 | 206 | 411 |
| Medium speed | 1029 | 131 | 898 | 996 | 329 | 667 |
| High speed | 1469 | 201 | 1268 | 1463 | 297 | 1166 |
| Ultra-high speed | 2100 | 197 | 1903 | 2120 | 201 | 1919 |
| Whole cycle | 5250 | 590 | 4660 | 5196 | 1033 | 4163 |
Between the first and fourth cycles, the average output energy per complete cycle did not change dramatically: the first cycle total output energy was 5250 Wh, while the fourth cycle total output energy was 5196 Wh. However, the total recovered energy increased substantially, from only 590 Wh in the first cycle to 1033 Wh in the fourth cycle. This difference of approximately 443 Wh was recovered purely because the battery had more charge-acceptance headroom in the fourth cycle. The recovered-energy fraction changed from about 11.2% in the first cycle to about 19.9% in the fourth cycle. Therefore, if I had included only the first cycle in my estimate of regenerative capability, I would have materially underestimated the energy recovery of the electric car.
The same comparison also confirms that the higher net energy consumption in the first cycle is not caused by higher driving load but by the limited regenerative current. The first-cycle net variation was 4660 Wh, whereas the fourth-cycle net variation was 4163 Wh. The difference is nearly equal to the additional recovered energy in the fourth cycle. This is an important lesson for range testing of an electric car: the battery state of charge at the beginning of a test should be well defined so that the energy-recovery system is fully enabled during the first cycle.
Phase-level Energy Distribution Over the Complete Series
To understand which part of the WLTC dominates the electric car range result, I divided the total energy balance of all sixteen complete cycles into the four WLTC speed phases. This division is useful because each phase has a different combination of speed, acceleration, duration, and braking energy. The results are presented in Table 6.
Table 6. Total energy values by WLTC speed phase for all 16 complete cycles.
| WLTC phase | Output energy (Wh) | Output share (%) | Recovered energy (Wh) | Recovered share (%) | Net energy change (Wh) | Net change share (%) |
|---|---|---|---|---|---|---|
| Low speed | 9,969 | 12.09 | 3,229 | 20.04 | 6,740 | 10.16 |
| Medium speed | 15,930 | 19.32 | 5,209 | 32.34 | 10,721 | 16.16 |
| High speed | 23,067 | 27.98 | 4,507 | 27.98 | 18,560 | 27.98 |
| Ultra-high speed | 33,472 | 40.60 | 3,164 | 19.64 | 30,308 | 45.69 |
| Whole cycle | 82,438 | 100.00 | 16,109 | 100.00 | 66,329 | 100.00 |
The phase-level energy table reveals a clear pattern for the tested electric car. The ultra-high-speed phase consumed the largest amount of energy because it requires high power and the energy needed to overcome aerodynamic drag grows rapidly with speed. The output energy in the ultra-high-speed phase was 33,472 Wh over the complete test, representing 40.60% of the total battery output. Its net energy variation was 30,308 Wh, which is 45.69% of the net energy consumed by the electric car during the entire series. This means that almost half of the energy used by the electric car over the complete range test was consumed during only 323 seconds of each 1800-second WLTC cycle, that is, during only about 17.9% of the cycle time. The ultra-high-speed phase therefore has the largest influence on the final WLTC range result.
Regenerative energy was distributed differently. The medium-speed phase produced the highest recovered energy, with 5,209 Wh over the sixteen cycles, corresponding to 32.34% of the total recovered energy. The low-speed phase contributed 3,229 Wh, or 20.04%. The high-speed phase contributed 4,507 Wh, or 27.98%, and the ultra-high-speed phase contributed only 3,164 Wh, or 19.64%. Although braking from ultra-high speed has a large kinetic energy theoretical potential, the electric car recovered less energy in that phase than in the medium or low-speed phases. This occurred partly because the ultra-high-speed phase contains long periods of high-power acceleration and relatively short deceleration events, and partly because part of the braking energy may be limited by motor capability, battery charge-power limits, and the high drag power still present during deceleration.
To compare regenerative effectiveness across the four phases, I calculated the recovered energy as a fraction of the output energy in the same phase:
\[
\eta_{\mathrm{reg},j} = \frac{E_{\mathrm{reg},j}}{E_{\mathrm{out},j}} \times 100\%
\]
Using the totals from Table 6, I obtain the values shown in Table 7.
Table 7. Regenerative energy recovery ratio and average net power for each WLTC phase.
| WLTC phase | Output energy per cycle (Wh) | Recovered energy per cycle (Wh) | Net energy change per cycle (Wh) | Recovery ratio (%) | Mean net power per phase (W) |
|---|---|---|---|---|---|
| Low speed | 623.1 | 201.8 | 421.3 | 32.4 | 2575 |
| Medium speed | 995.6 | 325.6 | 670.1 | 32.7 | 5571 |
| High speed | 1441.7 | 281.7 | 1160.0 | 19.5 | 9178 |
| Ultra-high speed | 2092.0 | 197.8 | 1894.3 | 9.5 | 21112 |
| Whole cycle | 5152.4 | 1006.8 | 4145.6 | 19.5 | whole-cycle average 8291 |
The recovery ratio is especially instructive. In the low-speed phase, about 32.4% of the output energy was recovered; in the medium-speed phase it was about 32.7%. At high speed, however, the recovery ratio dropped to about 19.5%, and at ultra-high speed it dropped to about 9.5%. The reason is not simply that regenerative braking is less efficient at high speed; it is also that aerodynamic drag converts a large part of the vehicle’s energy into heat while the electric car is travelling at high speed, leaving less kinetic energy to be transformed back into electricity during braking. Moreover, high-speed phases include some longer cruising periods in which the battery must deliver power without an immediately following regenerative event of equal magnitude.
I also calculated the mean net electrical power of each phase, which is the net energy change per cycle in that phase divided by the phase duration in hours:
\[
\bar{P}_{\mathrm{net},j} = \frac{\overline{\Delta E_j}}{t_{\mathrm{phase},j}} \times 3600
\]
where \(\overline{\Delta E_j}\) is the average net energy consumed by phase \(j\) per WLTC cycle and \(t_{\mathrm{phase},j}\) is the phase duration in seconds. The result shows a sharp increase in average electrical loading as the speed level increases. The low-speed phase has a mean net power of approximately 2.6 kW, the medium-speed phase about 5.6 kW, the high-speed phase about 9.2 kW, and the ultra-high-speed phase about 21.1 kW. The very high mean net power of the ultra-high-speed phase is the reason why it dominates the total net energy consumption of the electric car.
Current Data and Energy Signatures
In addition to the total energy values, I examined the instantaneous current traces during complete cycles. When the electric car accelerated, the current became positive and its amplitude increased quickly. When the car reached a relatively high speed and continued to cruise, the positive current remained significant because the motor had to overcome road load. When the speed decreased, the current crossed zero and became negative, indicating that the motor was operating as a generator. The sign of the current is therefore a very practical signal that tells me whether the electric car is consuming electrical energy or feeding electrical energy back to the battery.
I found that the maximum positive current typically corresponded to the strongest accelerations of the ultra-high-speed phase. At those moments, the battery had to provide both the power required to accelerate the inertial mass of the electric car and the power required to overcome aerodynamic drag at high speed. In contrast, the maximum negative current occurred during abrupt braking events after high-speed cruising. These negative current excursions represent the regenerative braking current that charges the high-voltage battery. The amplitude of the negative current was not constant; it depended strongly on the preceding speed and on the braking demand.
One interesting observation is that the low-speed WLTC phase contains many moderate accelerations and decelerations. Although the absolute current values are lower than in the ultra-high-speed phase, the ratio of recovered energy to output energy is higher. This is because low-speed driving involves less aerodynamic loss during coasting, and a larger fraction of the kinetic energy removed during braking can be captured. The medium-speed phase also showed a high recovery ratio. The high-speed and ultra-high-speed phases are less regen-effective on a percentage basis, even though the absolute kinetic energy available during high-speed braking is much larger.
The overall energy flow can be summarized by the following relationship between the total net energy change and the phase energy distributions:
\[
\Delta E_{\mathrm{total}} = \sum_{j=1}^{4} \Delta E_j
\]
If I denote by \(\alpha_{\mathrm{out},j}\), \(\alpha_{\mathrm{reg},j}\), and \(\alpha_{\Delta,j}\) the percentage share of output, recovered, and net energy change in phase \(j\), respectively, then:
\[
\alpha_{\mathrm{out},j} = \frac{E_{\mathrm{out},j}}{E_{\mathrm{out,total}}} \times 100\%
\]
\[
\alpha_{\mathrm{reg},j} = \frac{E_{\mathrm{reg},j}}{E_{\mathrm{reg,total}}} \times 100\%
\]
\[
\alpha_{\Delta,j} = \frac{\Delta E_j}{\Delta E_{\mathrm{total}}} \times 100\%
\]
Using these definitions for the electric car tested here gives the following direct conclusions. First, the low-speed phase contributes a relatively small but non-negligible portion of the net energy variation. Second, the medium-speed phase contributes more energy to the battery output than the low-speed phase, but it also contributes the largest amount of recovered energy. Third, the high-speed phase has equal output, recovered, and net energy shares of 27.98% because the numerical values happen to be the same when rounded. This is not a universal physical law but a characteristic of the tested electric car and the particular WLTC distribution. Fourth, the ultra-high-speed phase is responsible for the largest net energy change, and it has by far the smallest recovered-energy share of the four phases. Therefore, any small change in the ultra-high-speed resistance, test mass, motor efficiency, or aerodynamic drag will have a large influence on the range of the electric car under WLTC.
Relation Between Energy Variation and Driving Range
The driving range of an electric car under WLTC is directly related to the total net energy variation. If I use a constant battery capacity term and if the electric car consumes a net energy \(\Delta E\) per kilometre, then the range in kilometres is:
\[
R = \frac{E_{\mathrm{battery,usable}}}{\overline{\Delta e}}
\]
where \(\overline{\Delta e}\) is the average net energy consumed per kilometre, expressed in Wh/km. Alternatively, using the net energy consumed per complete WLTC cycle and the corresponding cycle distance \(D_{\mathrm{WLTC}}\), the range is:
\[
R = \frac{E_{\mathrm{battery,usable}}}{\overline{\Delta E}_{\mathrm{km}}}
\]
Since the WLTC total theoretical distance is about 23.2 km for one complete cycle, I can convert the mean net energy per complete cycle into an average net energy consumption per kilometre:
\[
\overline{\Delta e} = \frac{\overline{\Delta E}}{D_{\mathrm{WLTC}}} = \frac{4145.6 \, \mathrm{Wh}}{23.2 \, \mathrm{km}} \approx 178.7 \, \mathrm{Wh/km}
\]
This is the net energy consumption over the complete cycles if I assume the standard WLTC distance. Although I did not use the range end result as the main output of the study, the calculation illustrates that the phase energy analysis affects the range estimate through the average Wh/km value. If one phase, especially the ultra-high-speed phase, consumes more energy than assumed, the value of \(\overline{\Delta e}\) increases and the predicted WLTC range of the electric car decreases.
It is also useful to separate the effect of regenerative energy on the apparent consumption. Without considering regenerative recovery, the average output energy per completed WLTC cycle would be:
\[
\overline{E}_{\mathrm{out}} = \frac{5152.4 \, \mathrm{Wh}}{23.2 \, \mathrm{km}} \approx 222.1 \, \mathrm{Wh/km}
\]
When the regenerative energy is subtracted, the net consumption is about 178.7 Wh/km. The difference is approximately 43.4 Wh/km, which is directly attributable to the regenerative function of the electric car. Expressed as a percentage, regenerative braking reduces the effective electric car energy consumption by about:
\[
\frac{222.1 – 178.7}{222.1} \times 100\% \approx 19.5\%
\]
This reduction is consistent with the total recovered-energy fraction calculated earlier. Therefore, if the regenerative calibration of the electric car is changed, the range result will change accordingly.
Discussion of Practical Implications
The results have several practical implications for engineers and laboratories that work with an electric car under WLTC. First, because the ultra-high-speed phase is responsible for almost half of the net battery energy change, it is critical that the vehicle speed trace, dynamometer road load, and vehicle mass in that phase be accurate. Small speed deviations in the ultra-high-speed section can cause larger energy deviations than the same speed deviation in the low-speed section. The dynamometer must therefore be carefully set with correctly measured road-load coefficients, and the driver must follow the WLTC trace precisely, especially in the final phase.
Second, the test-start condition matters for regenerative energy. If an electric car is tested directly after a full charge, the first WLTC cycle may show less recovered energy and a higher net energy variation. To obtain representative energy recovery data, the test log should contain information about the battery state of charge at the beginning of each cycle. My observation of the tested electric car showed that by the second cycle, the recovered current had reached its normal value. Thus, an evaluator should not derive an energy-recovery ratio from the first cycle alone.
Third, I recommend that manufacturers monitor separate energy registers for each speed phase during development. Because the energy consumption of the electric car is not uniform across the four WLTC speed segments, phase-resolved energy data are more informative than a single-cycle average. The phase data can help identify whether a particular high-speed loss, powertrain efficiency issue, or calibration of regenerative braking is having the largest effect on range. For example, the low regenerative ratio in the ultra-high-speed phase suggests that there may be an opportunity to optimize motor-to-battery efficiency during high-speed deceleration events.
Fourth, the values shown in Table 6 are useful for setting realistic test-to-test repeatability targets. Since the high-speed phase has output, recovered, and net energy shares of almost 28%, any variation in wind speed, cooling fan effect, or vehicle pre-conditioning that changes this phase will have a substantial influence on the total energy balance. The low and medium speed phases are not negligible either, but their combined net contribution is lower than that of the high-speed and ultra-high-speed phases.
To express the battery loading in a more compact form, I can define the battery energy throughput as the sum of output and recovered energy:
\[
E_{\mathrm{throughput}} = E_{\mathrm{out,total}} + E_{\mathrm{reg,total}}
\]
For the complete series of cycles analysed for this electric car:
\[
E_{\mathrm{throughput}} = 82\,438 + 16\,109 = 98\,547 \, \mathrm{Wh}
\]
The recovered energy therefore reduces the net energy taken from the battery, but the regenerative process still adds extra electrical charge cycles to the battery. Engineers who study battery durability may need to consider this throughput separately from the vehicle range. The net energy variation more directly reflects the range and energy consumption of the electric car, while the total energy throughput better reflects how much electrochemical cycling the battery experiences.
Conclusion
I have presented a detailed electric energy variation analysis for a pure electric car running continuously through repeated WLTC cycles under laboratory conditions. The analysis was based on measured voltage, current, energy, and vehicle speed data for 16 complete WLTC cycles. By separating the total energy values into the four WLTC speed phases, I obtained several important conclusions.
First, the instantaneous current of the electric car follows the speed trace and acceleration events. Positive discharge current is produced during acceleration and positive cruising load, and negative recovery current is produced during deceleration. The amplitude of the positive current increases with vehicle speed, while the amplitude of the negative recovery current is largest during high-speed deceleration events. Thus, the current trace of an electric car under WLTC is strongly dynamic and has a wide bipolar range.
Second, the initial full-charge state affects regenerative energy in the first WLTC cycle. The total output energy in the first and fourth cycles was similar, approximately 5.25 kWh and 5.20 kWh respectively. The recovered energy, however, increased from 0.59 kWh in the first cycle to 1.03 kWh in the fourth cycle. The first-cycle regenerative current was much smaller than the steady-state regenerative current, and the measured net energy variation in the first cycle was accordingly higher.
Third, the total output electric energy of the tested electric car over the complete cycles was 82,438 Wh, the total recovered electric energy was 16,109 Wh, and the total net battery energy variation was 66,329 Wh. The regenerative energy represented about 19.5% of the total output energy, which is a substantial contribution to the energy economy of the electric car.
Fourth, the WLTC low-speed, medium-speed, high-speed, and ultra-high-speed sections contributed respectively 12.09%, 19.32%, 27.98%, and 40.60% of the total output electrical energy. In other words, the ultra-high-speed phase required the largest battery discharge. This is consistent with the physical need to overcome high aerodynamic drag at high speed.
Fifth, the recovered electrical energy was distributed differently across the four phases. The low-speed phase accounted for 20.04% of total recovered energy, the medium-speed phase for 32.34%, the high-speed phase for 27.98%, and the ultra-high-speed phase for only 19.64%. The low- and medium-speed phases recovered a higher fraction of their own discharge energy than the ultra-high-speed phase did. The recovery ratio relative to phase output was about 32% in low and medium speed, 19.5% at high speed, and less than 10% at ultra-high speed.
Sixth, the net electric energy variation of the battery was concentrated in the ultra-high-speed phase. The net energy change of the low-speed, medium-speed, high-speed, and ultra-high-speed phases represented respectively 10.16%, 16.16%, 27.98%, and 45.69% of the total net energy change. Hence, almost half of the energy consumed by this electric car during the repeated WLTC test was consumed in the final ultra-high-speed phase. The ultra-high-speed phase therefore has the largest effect on the WLTC range result of the electric car.
These conclusions have direct engineering value. The phase-level method used in this article can help a manufacturer identify which part of the WLTC should be optimized to improve the range of a pure electric car. It can also be used to assess whether changes in regenerative braking calibration, vehicle mass, tire rolling resistance, or aerodynamic drag have the intended effect on energy recovery and total range. I believe that energy measurements at the battery boundary, combined with a phase-based WLTC evaluation, form a reliable and practical basis for the development of more efficient electric cars in the coming years.