When I began this investigation, my central goal was to understand how waste heat from the battery pack and the traction motor could be used inside an electric car cabin heating system. Unlike an internal-combustion-engine vehicle, an electric car does not always have a large and easily available hot coolant stream from an engine block. In winter, the thermal management system must therefore find a different source of useful heat or pay for the heat from the battery. The most direct way to reduce this penalty is to recover heat that is already generated during driving. In this study, I focused on the low-temperature heating performance of an electric car equipped with a waste-heat recovery loop operating together with a positive temperature coefficient heater, and I compared this arrangement with a system that used only the PTC heater.
1. Introduction and Motivation
The popularity of electric cars has increased rapidly in the past decade, but winter driving still creates a serious challenge. In an electric car, the same battery that supplies traction energy also supplies cabin heating energy. When ambient temperature drops below a comfortable level, the heating load can become extremely large compared with the auxiliary loads of a conventional car. Earlier studies have shown that the use of a PTC heater in cold conditions can reduce driving range by tens of percent. This is particularly important in China, where many regions experience winter temperatures below -10 °C and sometimes as low as -25 °C.
From my point of view, the electric car thermal management system must do more than simply convert battery electric energy into heat through a resistive heater. The motor and the battery produce heat whenever the vehicle is driven, and that heat is often rejected to the surrounding air unnecessarily. In a heat-pump system, this waste heat can be absorbed by the refrigerant, but the system I examined uses a simpler architectural idea: the fresh air entering the cabin is first passed through a heat exchanger connected to the battery and motor cooling loop; only if the air temperature after this heat exchanger is still lower than the desired supply temperature is the PTC heater energized. This is an “air-to-liquid” waste-heat recovery strategy, which can be combined with a PTC heater to maintain the desired cabin temperature even in severe cold.
In this work, I selected three driving cycles: WLTC, NEDC and CLTC-P. I used these cycles because they represent different traffic conditions and different levels of dynamic acceleration. A fixed waste-heat power assumption can be misleading, because electric-car waste heat is strongly influenced by speed, acceleration and braking. Therefore, I obtained the dynamic response of battery and motor losses in every time step and then used those losses as the available waste heat. I evaluated the waste-heat recovery heating mode at ambient temperatures of -10 °C, -15 °C, -20 °C and -25 °C. Finally, I compared the SOC of the battery after one complete driving cycle in two configurations: waste heat + PTC heating and PTC-only heating.
2. System Architecture and Control Logic
2.1 Overall Thermal System
The investigated electric car thermal management system contains the following major components: the vehicle control unit, the thermal management control unit, the battery cooling loop, the motor cooling loop, an air-side waste-heat exchanger, a PTC air heater, a blower and a set of valves. The driver command enters the vehicle control unit, which controls the electric machine. The thermal management control unit then receives the passenger-cabin temperature requirement and calculates the heating demand.
In my simulation, the cabin temperature target was 25 °C. When the cabin temperature fell below 25 °C, the blower was switched on to deliver warm air into the passenger compartment. When the cabin temperature rose above 25 °C, the blower was switched off. This is a practical modulation strategy that keeps the average cabin temperature near the comfort target without continuously operating the blower. While the blower was active, the controller tried to supply air at approximately 40 °C to the cabin. The supply-air temperature after the waste-heat exchanger was monitored, and the PTC heater was controlled with PWM so that the final discharge temperature reached the 40 °C setpoint.
2.2 Heating Control Modes
I modelled three distinct heating control states, as summarized below. The first state is the pure waste-heat mode. If the fresh air that passes over the waste-heat exchanger has an outlet temperature equal to or greater than 40 °C, then the cabin can be supplied with warm air without additional PTC energy. In this state the PTC is turned off. If the waste-heat loop temperature is too high, part of the battery cooling loop is opened so that surplus heat can be rejected outside the car, preventing the supply temperature from becoming excessive.
The second state is the combined waste-heat + PTC mode. When the outlet temperature of the waste-heat exchanger is below 40 °C, the thermal management control unit sends a PWM signal to the PTC heater. The PTC adds the missing heat until the supply-air temperature reaches the desired 40 °C. This state is important at all ambient temperatures considered in this study, because the amount of waste heat generated by the battery and motor is usually insufficient to fully satisfy the ventilation heating demand at -25 °C.
The third state is the off/circulation state. If the cabin temperature is above 25 °C, the blower is disabled. The PTC heater is also disabled, regardless of the waste-heat availability, because no additional heating is needed. This prevents overheating and reduces unnecessary electric power consumption.
| Control state | Condition | PTC operation | Blower operation |
|---|---|---|---|
| Waste-heat only | \(T_{\mathrm{waste,out}}\ge40\,^{\circ}\mathrm{C}\) | Off | On if cabin \(<25\,^{\circ}\mathrm{C}\) |
| Waste heat + PTC | \(T_{\mathrm{waste,out}}<40\,^{\circ}\mathrm{C}\) and cabin \(<25\,^{\circ}\mathrm{C}\) | PWM modulated | On |
| Off / blower standby | Cabin \(\ge25\,^{\circ}\mathrm{C}\) | Off | Off |
Mathematically, the heat required from the PTC heater can be expressed as the difference between the required supply-air enthalpy flow and the heat recovered from the battery and motor. If the air mass flow rate is \(\dot m_a\), and the specific heat capacity of air is \(c_{p,a}\), then:
\[
\Phi_{\mathrm{PTC,req}}
=
\dot m_a \, c_{p,a}
\left(40 – T_{\mathrm{waste,out}}\right)
\]
with the constraint that \(\Phi_{\mathrm{PTC,req}}\) is zero whenever \(T_{\mathrm{waste,out}}\ge40\,^{\circ}\mathrm{C}\). Because the PTC heater is controlled by pulse-width modulation, the actual average heating power delivered to the air is:
\[
\Phi_{\mathrm{PTC,avg}}
=
D \, \Phi_{\mathrm{PTC,max}}
\]
where \(D\) is the duty ratio between 0 and 1. The duty ratio can be obtained from the required heating power as:
\[
D
=
\min
\left(
1,\,
\max
\left(
0,\,
\frac{\Phi_{\mathrm{PTC,req}}}{\Phi_{\mathrm{PTC,max}}}
\right)
\right)
\]
3. Models Used in the Simulation
3.1 Battery Model
I represented the battery with an equivalent circuit model. In this model, a voltage source represents the open-circuit voltage \(U_{\mathrm{OCV}}\). The internal resistance is divided into an ohmic resistance \(R_{\mathrm{ohm}}\) and an additional polarization resistance \(R_{\mathrm{add}}\). The additional resistance accounts for charge-transfer and diffusion losses, although in this simplified quasi-static model I neglected the full RC dynamics. The terminal voltage can therefore be written as:
\[
U_t
=
U_{\mathrm{OCV}}
–
I \, R_{\mathrm{ohm}}
–
I \, R_{\mathrm{add}}
\]
In this equation, the current \(I\) is positive when the battery is discharging. Both resistance terms contribute to battery heat generation. The heat losses caused by the ohmic resistance and by the additional polarization resistance are:
\[
\Phi_{\mathrm{ohm}}
=
I^2 \, R_{\mathrm{ohm}}
\]
\[
\Phi_{\mathrm{add}}
=
I^2 \, R_{\mathrm{add}}
\]
The total battery heat loss is therefore:
\[
\Phi_{\mathrm{batt}}
=
\Phi_{\mathrm{ohm}}
+
\Phi_{\mathrm{add}}
=
I^2 \left( R_{\mathrm{ohm}} + R_{\mathrm{add}} \right)
\]
State-of-charge is one of the most important outputs of the model. For a battery with capacity \(Q\) expressed in ampere-hours, the SOC change rate is:
\[
\frac{dSOC}{dt}
=
–
\frac{100 \, \eta_F \, I}{3600 \, Q}
\]
where \(\eta_F\) is the Faraday efficiency and the time derivative is in percent per second. A positive discharge current reduces the SOC. During regenerative braking, the current becomes negative, and the SOC increases. The total SOC change during one driving cycle can be obtained by integrating this differential equation over the cycle time:
\[
\Delta SOC
=
–
\int_{0}^{t_{\mathrm{cycle}}}
\frac{100 \, \eta_F \, I(t)}{3600 \, Q}
\, dt
\]
3.2 Motor Model
The electric machine model used in this study is reversible. It operates as a motor when torque and speed have the same sign, and as a generator during regenerative braking when torque and speed have opposite signs. For an electric car, the power flow between the battery and the wheels can be described by the electrical power \(P_e\), the mechanical power \(P_m\), and the motor heat loss \(\Phi_m\). In each instantaneous operating condition:
\[
\Phi_m
=
P_e
–
P_m
\]
The electrical power is the product of the motor terminal voltage and current:
\[
P_e
=
U_m \, I_m
\]
The mechanical power depends on torque \(T_m\) and rotational speed \(n_m\). If \(n_m\) is expressed in revolutions per minute, the rotational speed in radians per second is:
\[
\omega_m
=
\frac{2\pi \, n_m}{60}
\]
so that:
\[
P_m
=
T_m \, \omega_m
=
\frac{2\pi}{60}
T_m \, n_m
\]
When the electric machine is motoring, \(P_e\) and \(P_m\) are positive, and \(\Phi_m\) is positive because the motor is not perfectly efficient. During regenerative braking, the mechanical power is negative because the machine absorbs kinetic energy from the vehicle, and the electrical power is also negative because energy flows back to the battery. The heat loss \(\Phi_m\) remains positive and represents the fraction of braking energy that is not converted into electricity. That heat loss is available for the waste-heat recovery loop, which can be particularly useful at low ambient temperatures.
3.3 PTC Heater Model
The PTC heater is modelled as a temperature-dependent resistance. Its instantaneous heat-release rate can be expressed in either of the following forms:
\[
\Phi_{\mathrm{PTC}}
=
\frac{U_{\mathrm{PTC}}^2}{R_{\mathrm{PTC}}}
\]
\[
\Phi_{\mathrm{PTC}}
=
I_{\mathrm{PTC}}^2 \, R_{\mathrm{PTC}}
\]
The PTC heater used in my simulation had a peak heating capacity of approximately 8.0 kW. The input voltage range was 700 to 800 V. Because the resistance of a PTC element increases with temperature, the heater naturally limits its current and tends to operate at a roughly constant temperature. However, in the simulation, I controlled the effective output power by applying a PWM duty ratio. This allowed a linerized control model to maintain the outlet air temperature at the required setpoint.
3.4 Cabin Air Heating Balance
At any given moment, the energy delivered to the cabin air can be divided into two parts: the waste heat transferred from the battery/motor cooling water to the air and the heating power of the PTC element. Thus,
\[
\Phi_{\mathrm{heating}}
=
\Phi_{\mathrm{waste,used}}
+
\Phi_{\mathrm{PTC}}
\]
The useful waste-heat fraction is one of the most important measures in this paper. I define it as:
\[
\eta_{\mathrm{wh}}
=
\frac{
\int_{0}^{t_{\mathrm{cycle}}}
\Phi_{\mathrm{waste,used}}(t)\,dt
}{
\int_{0}^{t_{\mathrm{cycle}}}
\left[
\Phi_{\mathrm{waste,used}}(t)
+
\Phi_{\mathrm{PTC}}(t)
\right]
dt
}
\]
This fraction shows how much of the total heating energy supplied to the passenger compartment comes from recovered battery and motor heat. It is not constant because the motor heat loss changes constantly with vehicle speed and acceleration.
4. Driving Cycles and Thermal Loads
4.1 Characteristics of the Selected Cycles
I used WLTC, NEDC and CLTC-P driving cycles in this article. The WLTC is a highly dynamic cycle developed by the Worldwide harmonized Light vehicles Test Procedure. It contains low-, medium-, high- and extra-high-speed sections. The NEDC is an older and less dynamic cycle with an urban part and an extra-urban part. The CLTC-P is the Chinese light-duty vehicle test cycle and contains more low-speed and medium-speed phases, which are representative of congested urban driving in Chinese cities.
| Cycle | Time (s) | Distance (km) | Maximum speed (km/h) | Main characteristic |
|---|---|---|---|---|
| WLTC | 1800 | 23.27 | 131.3 | Low, medium, high and extra-high speed dynamic segments |
| NEDC | 1180 | 11.04 | 120 | Four repeated urban cycles followed by one extra-urban cycle |
| CLTC-P | 1800 | 14.48 | 114 | Low-, medium- and high-speed segments representing Chinese traffic |
The dynamic content of the cycles has a direct influence on waste heat. During the WLTC extra-high-speed section, the motor operates at high speed and high torque more frequently, producing a large amount of heat. In contrast, during the low-speed segments of CLTC-P, the average motor power is low and the waste heat is relatively small. Therefore, each cycle offers a different opportunity for waste-heat recovery in an electric car.
4.2 Simulated Waste-Heat Availability
In the simulations, I observed several important trends. In the WLTC, the motor average heat loss over the entire cycle was about 0.57 kW, while the battery average heat loss was about 0.10 kW. In the extra-high-speed section, the average motor loss increased to about 1.50 kW and the average battery loss was 0.37 kW. This shows that high-speed driving can generate significant waste heat, but the low-speed municipal segment generates much less.
In the NEDC, the urban section was considerably less demanding. During the urban part, the peak motor heat loss was about 0.58 kW and the peak battery heat loss was about 0.14 kW. During the high-speed extra-urban portion, the peak motor heat loss reached 2.3 kW and the battery peak loss was around 1.0 kW. The average motor and battery heat losses in the high-speed section were approximately 0.68 kW and 0.11 kW.
The CLTC-P, because of its long low-speed and medium-speed sections, produced a more moderate thermal load. In the medium-speed portion, the combined average heat loss from the motor and battery was roughly 0.33 kW. In the high-speed portion, the combined average heat loss increased to about 0.65 kW. The highest instantaneous total heat loss that I observed in the CLTC-P simulation was about 2.3 kW.
| Cycle or cycle section | Average motor heat loss (kW) | Average battery heat loss (kW) | Observation |
|---|---|---|---|
| WLTC, full cycle | 0.57 | 0.10 | Low-speed segments generate relatively little heat |
| WLTC, extra-high section | 1.50 | 0.37 | High motor torque produces strong waste heat |
| NEDC, urban section | 0.58 peak | 0.14 peak | Urban operation is less dynamic |
| NEDC, extra-urban section | 0.68 average | 0.11 average | Sustained high speed increases motor loss |
| CLTC-P, medium-speed portion | combined average 0.33 | — | Motor and battery produce limited heat |
| CLTC-P, high-speed portion | combined average 0.65 | — | Maximum instantaneous heat loss around 2.3 kW |
5. Results and Discussion
5.1 Thermal Comfort Achieved by the Waste-Heat Recovery System
In order to assess the system correctly, I first checked that the control strategy satisfied the passenger-cabin comfort requirement. For every ambient temperature from -10 °C down to -25 °C, the cabin temperature remained within \(25 \pm 2\,^{\circ}\mathrm{C}\). The supply-air temperature after the PTC heater remained within \(40 \pm 3\,^{\circ}\mathrm{C}\). Thus, the waste-heat recovery system did not sacrifice thermal comfort while reducing energy consumption.
The total heating requirement naturally increased as the ambient temperature decreased. In my simulations, the required cabin heating power increased from about 4.1 kW at -10 °C to about 5.3 kW at -25 °C. This happened because the ventilation air had to be heated from a much colder inlet condition, and the heat loss through the vehicle body also became larger. At the same time, the available waste heat did not increase enough to match this growing demand. Consequently, the PTC heater had to provide a larger share of the total heating load when the ambient temperature became very low.
The waste-heat share under WLTC conditions is a good example. At -10 °C the waste heat recovered from the battery and motor supplied about 18% of the heating energy. When the ambient temperature dropped to -25 °C, the waste-heat share decreased to about 15%. The absolute amount of recovered heat did not disappear completely, but the total demand increased more rapidly than the waste heat. Therefore, the PTC heater was required more often and with a higher average power at lower ambient temperatures.
5.2 Waste-Heat Share for Different Driving Cycles and Ambient Temperatures
One of the most important results in my study is the comparison among WLTC, NEDC and CLTC-P. The table below summarizes the waste-heat share at -10 °C and -25 °C. At -10 °C, WLTC had the largest waste-heat share among the three cycles, equal to 18.1%. NEDC had the smallest waste-heat share at -10 °C, equal to 12.3%. CLTC-P was between them, with a share of 14.6%. At -25 °C, the order changed slightly: WLTC still provided the largest waste-heat fraction, 15.0%, while NEDC and CLTC-P had very similar values of 9.4% and 9.3%, respectively.
| Ambient temperature | WLTC waste-heat share | NEDC waste-heat share | CLTC-P waste-heat share |
|---|---|---|---|
| -10 °C | 18.1% | 12.3% | 14.6% |
| -25 °C | 15.0% | 9.4% | 9.3% |
Why did WLTC have a larger waste-heat share than NEDC and CLTC-P? The reason is related to the dynamic content of the cycles. WLTC contains aggressive acceleration events and a prolonged extra-high-speed section, causing both the motor and battery to generate more heat per kilometer. NEDC, although it contains a high-speed extra-urban segment, has much lower acceleration and therefore lower battery losses. CLTC-P contains substantial medium-speed driving in which the average waste heat is low. Thus, when the total heating demand is considered, WLTC provides more opportunities for recovery.
As the ambient temperature falls from -10 °C to -25 °C, the waste-heat fraction falls for all cycles. The decrease is not caused by a fall in theoretical waste heat only; rather, it is caused by the rapid rise in the cabin heating requirement. The same amount of recovered heat becomes a smaller portion of the total heat supplied to the cabin. This finding suggests that for very cold regions, an electric car cannot rely solely on waste-heat recovery to eliminate PTC energy consumption. The battery and motor waste heat should instead be viewed as a useful range-extending measure that lowers the required PTC power.
5.3 Battery SOC Comparison
The next part of my analysis examines battery energy consumption. The most relevant comparison is between a configuration that uses waste heat plus PTC and a baseline configuration that uses PTC alone. I compared the battery SOC reduction after one complete driving cycle at the same ambient temperature and with the same cabin thermal-comfort target. The SOC reduction in the waste-heat recovery mode is always smaller because part of the heating energy comes from battery and motor losses that would otherwise be wasted.
The SOC reduction benefit is summarized in the table below. I express the benefit as the difference between the SOC reduction of the PTC-only mode and the SOC reduction of the waste-heat + PTC mode. A larger number indicates that the waste-heat recovery system preserved more battery energy.
| Driving cycle | SOC saving range of waste heat + PTC versus PTC-only (percentage points) |
|---|---|
| WLTC | 6.0–7.5 |
| NEDC | 4.9–6.6 |
| CLTC-P | 2.3–6.1 |
In every cycle, the larger SOC saving appeared at the warmer end of the tested temperature interval, near -10 °C, while the smaller saving appeared at the coldest end, near -25 °C. For example, with the WLTC, the battery SOC decreased by 7.5 percentage points less in the combined mode than in the PTC-only mode at -10 °C. When the ambient temperature fell to -25 °C, this advantage reduced to approximately 6.0 percentage points. A similar trend was visible with NEDC and CLTC-P. This trend is consistent with the earlier observation that waste heat covers a smaller share of the total heating demand as ambient temperature decreases.
The NEDC results deserve special attention because NEDC contains a rather low number of acceleration events compared to WLTC. Even so, the waste-heat recovery system reduced the SOC drop by 4.9 to 6.6 percentage points. This means that even in a relatively conservative driving cycle, energy from the motor and battery is meaningfully useful for cabin heating. At -25 °C, CLTC-P produced the smallest saving, about 2.3 percentage points. This is because CLTC-P has a higher proportion of low-speed and medium-speed operation, where the generated waste heat is insufficient for the high heating demand at such a low ambient temperature.
For completeness, I define the SOC saving as follows. Let \(\Delta SOC_{\mathrm{PTC}}\) denote the SOC reduction in the PTC-only mode after one complete cycle, and let \(\Delta SOC_{\mathrm{WH+PTC}}\) denote the SOC reduction in the combined waste-heat and PTC mode. Then,
\[
\delta_{\mathrm{SOC}}
=
\Delta SOC_{\mathrm{PTC}}
–
\Delta SOC_{\mathrm{WH+PTC}}
\]
Because \(\Delta SOC_{\mathrm{WH+PTC}}\) is always smaller than \(\Delta SOC_{\mathrm{PTC}}\), the value of \(\delta_{\mathrm{SOC}}\) is positive. This positive value represents the additional battery charge retained by the electric car over one full driving cycle as a result of waste-heat recovery. The energy that corresponds to this retained SOC can be estimated if the total usable battery energy \(E_{\mathrm{batt}}\) is known:
\[
E_{\mathrm{saved}}
=
\frac{\delta_{\mathrm{SOC}}}{100}
E_{\mathrm{batt}}
\]
For example, if an electric car has a usable battery energy of 80 kWh and \(\delta_{\mathrm{SOC}}\) is 5.0 percentage points, then the energy saved in one cycle would be 4.0 kWh. In a real vehicle, this energy would directly extend the driving range in winter.
5.4 Why the Combined Mode Loses Some Advantage at Low Ambient Temperature
At this point, readers may ask why the SOC advantage does not become larger when the ambient temperature is lower. After all, in very cold weather, the battery and motor may need more cooling or may deliver more waste heat. However, there are several physical processes working in the opposite direction.
First, the cabin heating demand increases with decreasing ambient temperature. At -25 °C, the inlet air is much colder, and the heat loss through the windows and body panels is larger. The total heat that must be supplied to the cabin is therefore much higher than at -10 °C. Second, the waste heat generated by the battery and motor does not increase in proportion to the heating demand. The battery may become less efficient at lower temperatures, which does generate additional heat, but the total heat produced by the battery is not enough to offset the large increase in the cabin demand. Third, at very low temperatures, the thermal management controller must protect the battery and may divert some cooling-loop energy to keep the battery warm. This reduces the fraction of waste heat that can be sent directly to the cabin.
For all of these reasons, the PTC heater has to work harder at -25 °C than at -10 °C. In the WLTC case at -25 °C, for instance, the average PTC heating power was approximately 4.5 kW, accounting for about 85% of the total supplied heating power. The remaining 15% came from recovered waste heat. This explains why the SOC saving in the combined mode is still positive but smaller in relative terms when the ambient temperature is extremely low.
6. Further Design Considerations for an Electric Car
Based on my simulation results, I believe that a waste-heat recovery system should be designed together with the battery thermal management system. If the battery is cold at start-up, the first priority should be to warm the battery enough to allow satisfactory discharge performance. During this warm-up phase, much of the heat generated internally by the battery may be retained in the battery rather than being transferred to the cabin air. Once the battery reaches a suitable operating temperature, the waste heat recovery loop can provide more heat to the cabin.
The potential for waste heat recovery is also dependent on the powertrain control strategy. In an electric car, regenerative braking has a large influence on the amount of energy that flows through the motor. In urban driving, frequent regenerative braking events can generate additional motor losses that are not present in a vehicle that relies only on friction braking. Those motor losses are captured in my cycle simulations, which is another reason why dynamic cycles such as WLTC show more waste heat than the less dynamic NEDC. It is therefore important to evaluate an electric car waste-heat system over the actual customer driving profile rather than only over one legislative cycle.
| Parameter | Symbol | Impact on electric car heating |
|---|---|---|
| Battery internal resistance | \(R_{\mathrm{ohm}}, R_{\mathrm{add}}\) | Higher resistance produces more battery heat but also reduces available power |
| Motor efficiency loss | \(\Phi_m\) | Large during acceleration and high-speed cruising |
| Regenerative braking | \(P_m<0\) | Adds motor losses and returns energy to battery |
| PTC heater capacity | \(\Phi_{\mathrm{PTC,max}}\) | Determines ability to reach 40 °C outlet temperature in extreme cold |
| Air flow rate | \(\dot m_a\) | Controls heat delivery rate and fan power consumption |
| Cabin setpoint | 25 °C | Lower setpoint reduces heating demand and increases range |
7. Limitations and Future Work
The results discussed above were obtained with a modular system simulation rather than with a complete production vehicle on a chassis dynamometer. In my model, I simplified the battery by ignoring the dynamic response of the RC networks and used a quasi-static representation of resistance and open-circuit voltage. The motor model also uses a loss calculation based on the difference between electrical and mechanical power, rather than a full electromagnetic loss map. These simplifications affect the precision of the instantaneous heat-flow predictions, but they are unlikely to change the main conclusion that waste-heat recovery is beneficial for an electric car in winter.
In future work, I would like to add a heat-pump cycle to the waste-heat recovery system. A heat pump can raise the temperature of the recovered thermal energy before it enters the passenger cabin. This is important because the cooling-loop temperature may be lower than the desired cabin supply temperature in some ambient conditions. With a heat-pump cycle, the waste heat can be absorbed by the refrigerant at low temperature and then rejected into the cabin air at a higher temperature. This arrangement can further reduce the electric power required by the PTC heater.
Another promising direction is to optimize the valve schedule and the blower speed profile. In the present strategy, the blower stops whenever the cabin temperature exceeds 25 °C. A continuous low-speed blower may provide better average temperature uniformity and can also increase the opportunity to extract waste heat from the cooling loop. The trade-off is increased fan power. Therefore, a system-level optimization should be performed to balance thermal comfort, fan power and PTC energy consumption.
Finally, the influence of thermal soak and initial cabin temperature is significant. In my simulation, the initial cabin temperature was close to the ambient temperature because the vehicle was soaked overnight outside. If the vehicle is preconditioned while being charged, the waste-heat recovery can begin from a warmer initial state. The comparison between waste-heat + PTC and PTC-only heating may then show different absolute SOC savings. Preconditioning therefore deserves a separate study, especially for an electric car used in severe winter conditions.
8. Conclusions
In this paper, I investigated the low-temperature heating performance of an electric car waste-heat recovery system. Instead of fixing the waste heat as a constant value, I calculated battery and motor heat losses dynamically from WLTC, NEDC and CLTC-P drive cycles. The recovered waste heat was then used to preheat the fresh air before a PTC heater. My simulation covered ambient temperatures from -10 °C to -25 °C. The main conclusions are summarized below.
First, from the perspective of powertrain heat losses, different driving cycles create different waste-heat resources. In the WLTC, the motor average heat loss was 0.57 kW and the battery average heat loss was 0.10 kW, but in the extra-high-speed section the motor loss rose to 1.50 kW. The NEDC showed lower heat loss in its urban section but significant loss during the extra-urban high-speed section. CLTC-P had lower average heat loss but still produced enough waste heat to reduce the required PTC power.
Second, when the waste-heat recovery mode is used, the waste-heat share decreases as the ambient temperature decreases. When the ambient temperature fell from -10 °C to -25 °C, the waste-heat share based on WLTC decreased from 18.1% to 15.0%. The corresponding shares for NEDC were 12.3% and 9.4%, while the shares for CLTC-P were 14.6% and 9.3%. The total cabin heating demand increased from 4.1 kW to 5.3 kW over the same temperature range, so the PTC heater necessarily contributed more energy.
Third, the waste-heat + PTC combined mode always reduced the battery SOC drop compared with the PTC-only mode. After one WLTC cycle, the SOC reduction in the combined mode was 6.0 to 7.5 percentage points smaller. After one NEDC cycle, the combined mode reduced SOC loss by 4.9 to 6.6 percentage points. After one CLTC-P cycle, the reduction was 2.3 to 6.1 percentage points. Therefore, I conclude that waste-heat recovery is an effective and practical approach for improving the low-temperature heating performance of an electric car.
Overall, this investigation shows that an electric car should not be treated as a vehicle without a usable heat source. Although no engine block is available, the traction battery, the motor and the power electronics all generate heat whenever the vehicle operates. By capturing this heat and sending it into the cabin air stream, an electric car can reduce PTC power consumption, retain more SOC, and extend winter driving range. In future vehicle programs, waste-heat recovery should be regarded as a core feature of the thermal management architecture rather than as an optional accessory.