Mathematical Modeling, Analysis, and Advanced Control of Complex Dynamical Systems
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Energy Flow ChartBased Energy Efficiency Analysis of a RangeExtended Electric Bus
Abstract
This paper puts forward an energy flow chart analysis method for a rangeextended electric bus. This method uses dissipation and cycle energy, recycle efficiency, and fueltraction efficiency as evaluation indexes. In powertrain energy efficiency analysis, the rangeextended electric bus is developed by Tsinghua University, the driving cycle based on that of Harbin, a northern Chinese city. The CDCS and blended methods are applied in energy management strategies. Analysis results show with average daily range of 200 km, auxiliary power of 10 kW, CDCS strategy, recycle ability and fueltraction efficiency are higher. The inputrecycled efficiency using the blended strategy is 24.73% higher than CDCS strategy, while the outputrecycled efficiency when using the blended strategy is 7.83% lower than CDCS strategy.
1. Introduction
Compared with conventional fuel vehicles, application of electric vehicle decreases the dependency on petroleum and has the advantages of high energy efficiency and low environmental impact [1–3]. For a pure electric bus, the cost of a battery pack that can meet the driving range is too high; meanwhile, vehicle weight is too large for adding a large battery pack. A rangeextended electric vehicle is regarded as one of the most suitable solutions for powertrain schemes, because of the maximum utility of the electric drive and the minimum capacity requirement of battery packs.
The main powertrain configurations of rangeextended electric vehicles are series plugin hybrid electric vehicles [4] and the Chevrolet Volt, produced by General Motors Corporation (GM) [5]. This paper will analyze a series plugin hybrid electric bus.
In the studies of energy efficiency and fuel economy of rangeextended electric vehicles, vehicle performance is analyzed on the basis of energy consumption and greenhouse gas emissions on the welltowheel and tanktowheel paths [6, 7]. Welltowheel fuel economy and greenhouse gas emissions data were obtained using the greenhouse gases, regulated emissions, and energy use in transportation (GREET) software model. The tanktowheel process is characterized by the recuperation and fueltraction efficiencies, which are quantified and compared for two optimizationbased energy management strategies.
The improvement of fuel economy for a rangeextended electric vehicle can be realized by matching powertrain parts and a model selection method [8–12]. An optimal genset operating line method can minimize fuel consumption at a set level of electric output power. Series hybrid vehicles with direct injected stratified charge (DISC) rotary engines are proven to be more efficient in pure electric mode in terms of energy consumption and greenhouse gases (GHG) emissions than in vehicles with reciprocating engines.
Energy efficiency and fuel economy of rangeextend electric vehicles can be improved by studying energy management strategy [13–16]. Researchers use dynamic programming strategies and equivalent consumption minimization strategies as well as Pontryagin’s minimum principle strategy to analyze energy efficiency and fuel economy of rangeextended electric vehicles, and results show that optimized energy management strategy can improve energy efficiency and fuel economy to a certain extent.
In conclusion, current studies on configuration analysis and energy management strategy on rangeextended electric vehicles mainly focus on passenger vehicles, but work is rarely conducted into rangeextended electric buses. Reference [17] asserts that a driving cycle significantly influences the energy efficiency and fuel economy of the vehicle. It proposes that construction and optimization of energy management strategy should consider different driving cycles. A system of energy efficiency analysis based on a certain driving cycle is the foundation of an optimal control strategy.
This paper focuses on the application requirements of the rangeextended electric bus developed by Tsinghua University in Harbin and establishes the powertrain model of the bus based on the construction of the Harbin driving cycle. It examines the energy efficiency of the rangeextended electric bus with two different energy management strategies (CDCS and blended) and proposes improvement methods for energy efficiency.
2. Configuration and Principle of the RangeExtended Electric Bus
The rangeextended electric vehicle lies between the plugin hybrid electric vehicle and pure electric vehicle. Compared with a pure electric vehicle, a rangeextended electric vehicle is supplemented with an onboard power generation system (rangeextender) [18, 19]. The rangeextender consists of engine, generator, and rectifier. The engine continually charges the power battery, so the driving range can be greatly increased to the level of a conventional internal combustion engine vehicle. The engine and power battery of a rangeextended electric bus can be optimized at the same time. The working area of the engine can be optimized according to the driving cycle and the engine efficiency can be improved. The engine can operate with low pollution and fuel consumption. As for the battery, working condition of the power battery can also be optimized. If the power battery can continually work in good condition without overcharging or overdischarging, battery life can be extended. Braking energy can be recycled and energy consumption is decreased. The rangeextender solves the problems of the energy consumption of airconditioning, lighting, heating, and other electric auxiliaries, making the rangeextended electric bus the most suitable solution for city buses.
A typical rangeextended electric powertrain is shown in Figure 1. In a rangeextended electric vehicle, wheels are driven directly by an electric motor. The motor draws energy from a battery pack and drives in pure electric mode when battery energy is available. Once the battery has been mostly depleted, the motor draws power from the rangeextender, composed of an internal combustion engine and generator, in conjunction with a battery. Rangeextended electric vehicles are designed with a predetermined allelectric range (AER). The AER represents the distance that the vehicle can travel using the energy stored in its battery only, without the engine and generator. Vehicles with a higher AER must have larger, heavier, and more expensive battery systems. The rangeextended electric powertrain configuration is one of the most attractive applications for the diesel engine.
We can see the powertrain configuration of the rangeextended electric bus discussed in this paper; the energy flow conditions of different driving modes are analyzed, as is shown in Figure 2. There are three driving modes: pure electric drive mode, rangeextended mode, and regenerative brake mode.
(a) Pure electric drive mode
(b) Rangeextended mode
(c) Regenerative brake mode
Pure electric drive mode is shown in Figure 2(a). If SOC is high, the powertrain begins pure electric mode, whereby the engine stops and the motor will be driven by a power battery. Cheaper electric energy from the power grid is fully utilized. Fuel consumption and pollution are reduced in this mode. If SOC decreases to the set starting value, the rangeextender begins and the powertrain works in rangeextended mode.
Powertrain working in rangeextended is shown in Figure 2(b). To increase driving range, if SOC decreases to the set starting value, the rangeextender starts to generate power, reducing the rate of electricity loss and ensuring the motor can work to drive the bus. This mode can be divided into two kinds. One, if the output power of rangeextender is lower than the motor required power, the lacking electric energy is provided by battery; the battery discharges. Two, if the output power of the rangeextender is higher than the required motor power, the redundant electric energy is reserved in battery, charging the battery. The output power of the rangeextender is not directly influenced by the driving conditions and can be optimized in the high efficiency working areas of the engine and motor.
If the bus is braking, the motor can work in regenerative brake mode, as is shown in Figure 2(c). The motor provides braking torque for the vehicle wheels, and braking energy is transferred into electric energy reserved in the battery. Braking energy is not transferred into heat and lost; it is recycled.
For an individual axle drive bus, only wheels driven by the motor can recycle braking energy. Other wheels are stopped by mechanical braking. Braking energy is partly recycled and mechanical braking is also used on driven wheels for safety.
The rangeextended electric bus analyzed in this paper is developed by Tsinghua University, shown in Figure 3. The powertrain is designed based on matching powertrain parts and model selection found in [20]. The generator is a permanent magnet generator and the traction motor is an asynchronous motor. Key parameters of the powertrain are listed in Table 1.

3. System Modeling of the RangeExtended Electric Bus
To analyze energy efficiency and fuel economy of the rangeextended electric bus, system models based on benchmarks and modeling lines of [21–24] are built. The basic model of the rangeextended electric system can be divided into four modules: rangeextender module, traction motor module, power battery module, and the vehicle longitudinal dynamics module. Considering the high complexity of a diesel engine, permanent magnet synchronous generator, and the rectifier and driving motor, relevant components are tested by benchmarks and the characteristics MAP are determined according to the test results. Then, the simulation models are built based on the MAP, which replaces the complex mathematical description, reduces modeling complexity, and therefore improves model credibility.
3.1. RangeExtender
The rangeextender includes a diesel engine, a permanent magnet synchronous generator, and rectifier. System features can be described by the following equations: where is the accelerator characteristic MAP of the engine, is fuel consumption characteristic MAP of the engine, is the generator efficiency MAP, is the engine’s target speed, is a time constant, is the accelerator signal, is the engine’s actual speed, is the engine torque, is the generator loading rate, is the rectifier efficiency, is the engine’s instantaneous fuel consumption, and is the total rate of the generator and rectifier.
3.2. Traction Motor
The traction motor module includes the motor and motor controller. The motor model consists of the steady state efficiency characteristic MAP and a firstorder process: where is the motor’s electric efficiency, is the motor’s rotational speed, is a time constant, and , , and are the motor’s actual torque, target torque, and torque capacity, respectively. The function denotes the motor’s efficiency MAP, and denotes the motor’s maximum output torque characteristic MAP.
3.3. Power Battery
The power battery model is built based on the model, which is equivalent to a variable voltage source and a variable resistance in series. According to the battery internal resistance equivalent circuit, the following equation can be established: where SOC is the state of charge of the battery, is the temperature, and is the battery current. stands for the open circuit voltage of the battery, which is a function of SOC, is determined by the test, and is the internal resistance of the battery.
In this model, the battery’s SOC state uses amperehour integral method to estimate [25]. That is, when the vehicle is in operation, it will use SOC as and at moment it will use SOC formula (4) to decide the following: where is rated capacity, is the battery’s columbic capacity, and is its charging and discharging current.
3.4. Vehicle Longitudinal Dynamics
The road load characteristic is assumed to be ideal in simulation, that is, zero air speed and good adhesion. As the vehicle is traveling on the road, traction motor needs to overcome driving resistance (), rolling resistance (), air resistance (), slope resistance (), and acceleration resistance (). Consider where is the rolling resistance coefficient, is the vehicle mass, is the acceleration of gravity, is the road slope, is the coefficient of air resistance, is the windward area, is the air density, is the motor speed, is the correction coefficient of rotating mass, is the overall efficiency of drive system, and is the output power of the traction motor.
4. Energy Efficiency Analysis Using Energy Flow Chart
According to the energy efficiency analysis method of plugin hybrid electric powertrain in [7], energy efficiency analysis can be divided into the following three parts.
4.1. Dissipation and Cycle Energy
Traction power is used to drive the wheels and vehicle auxiliaries; the calculation equation is as follows: where is the power to overcome air resistance, is the air density, is the frontal area, is the air resistance coefficient, is the vehicle speed, is the power to overcome rolling resistance, is the acceleration/deceleration power, is the up/down hill power, is the vehicle speed, is the road gradient, is the battery mass, and is the auxiliaries power, including air condition, battery heat management system, heating (seat heating and windshield heating), lighting, control system, and braking steer consumption. The average power of the auxiliaries is 10 kW [26], assuming airconditioning is working.
can be divided into two parts: one is the dissipated power and the other is conserved power . As the initial and final altitude and speed are the same in a whole driving cycle, the reserved power is zero. If braking energy can be fully recycled, required traction energy should be the same as the dissipated energy where and are initial and final time. If there is no barking energy recycled, where represents the cycle energy , which is the temporal vehicle cycle energy in the form of kinetic or potential energy and ultimately dissipated during friction braking. Therefore, (8) for vehicle without energy recycle can be calculated as
In actual driving, energy balance equation can be calculated as where is the recycled net energy that is usable for traction. According to (7) and (10), it can be found that .
4.2. Recycle Efficiency of Barking Energy
Recycle efficiency is defined as
As can be easily obtained in driving cycle, the key mission is to calculate . Recycle energy consists of two flow methods: input and output. As is shown in Figure 4, recycle ability is determined by energy dissipation, motor torque, current of power battery, and threshold charge value.
Time set is defined as where is physical load in converter. is absolute input energy during and is calculated by
The energy reserved in battery is
The energy loss is
The cycleaverage wheel to battery energy efficiency is
The recycle energy reserved in battery is where is the ratio between and .
Time set is defined as
The associated motor energy loss in propelling is
The average motor efficiency is
The battery energy loss during time is
The battery efficiency in output way is
The cycleaverage battery to wheel energy efficiency is where is the ratio between the power that battery provides to the motor and the power emitted by battery. According to (16) and (23), the recycle energy for traction is
The cycleaverage recycle efficiency is
4.3. FuelTraction Efficiency
Fueltraction efficiency is defined as where is the equal fuel energy, the average consumption of the sum of diesel, and electric energy. is the cycleaverage conversion efficiency from the total consumed energy to the mechanical energy at the wheels and the electrical energy for the auxiliaries. Based on the initial and final SOC, can be divided into diesel energy and electric energy.
An energy flow chart can clearly show the direction of energy flow, showing the sizes of losses from each individual part. It is one of the most effective methods for analyzing flow in the context of system performance. Referring to the analysis method in [27], this paper puts forward a powertrain energy analysis method with energy flow chart for rangeextended electric bus. The powertrain energy flow chart is shown in Figure 5.
5. Analysis Example with the Driving Cycle of Harbin City
To provide a credible reference for the match and control of the rangeextended electric bus, energy efficiency analysis should be carried out within a driving cycle. Based on the authors’ location, the Harbin city driving cycle has been chosen for this paper, and the construction process is shown in Figure 6.
The constructed Harbin city driving cycle is shown in Figure 7; acceleration and deceleration are frequent. The maximum acceleration is 1.94 m/s^{2}, the idle proportion is 22.3%, the maximum speed is 50 km/h, and the average speed is 14.5 km/h.
The analysis process mainly compares the CDCS strategy with the switching control method on the rangeextender and blended strategy with power following control method on the rangeextender. According to the research, the daily average range for Harbin city bus line 101 is 150–180 km, the initial SOC is 100%, and the auxiliaries’ power is 10 kW. SOC curves with the two different driving cycles are shown in Figure 8.
(a) CDCS strategy
(b) Blended strategy
Figure 9 shows the energy flow chart with CDCS strategy, and Figure 10 shows the energy flow chart with blended strategy.
Based on Figure 5, the input and output recycle efficiencies can be obtained, as is shown in Figure 11. The inputrecycled efficiency of the blended strategy is 24.73% higher than that of CDCS strategy. The outputrecycled efficiency of the blended strategy is 7.83% lower than that of the CDCS strategy.
(a) System inputrecycled efficiency
(b) System outputrecycled efficiency
Figure 12 consists of recycle efficiency, fueltraction efficiency, and energy consumption with the two different energy management strategies. As is shown in Figure 12(a), the recycle efficiency is 36.80% with CDCS strategy and 51.32% with blended strategy. With CDCS strategy, the fueltraction efficiency is 38.91%, but, with blended strategy, it is 33.26%. The fueltraction efficiency is limited by engine efficiency and is also influenced by other electric and mechanical losses, such as the battery, power converter, and motor and drive system. Energy consumption is 664.43 kWh with the CDCS strategy and 47.87 kWh lower than that with the blended strategy. The CDCS strategy has a better recycle ability and fueltraction efficiency. It is worth noting that the yearly range of one bus in Harbin is nearly 70000 km, and the energy saved with the CDCS strategy would be considerable.
(a) The recycle efficiency in the two different strategies
(b) The fueltraction efficiency in the two different strategies
(c) The energy consumption in two different strategies
6. Conclusions
For a rangeextended electric bus developed by Tsinghua University, this paper analyzes the energy efficiency with two different energy management strategies (CDCS and blended) using an energy flow chart method. Harbin city driving cycle is taken for analysis. The recycle efficiency and fueltraction efficiency are evaluation indexes.
Analysis results from the energy flow chart show that the energy loss mainly occurs at the engine. Engine energy loss reaches 187.59% of the whole driving energy using the CDCS strategy and 209.47% with the blended strategy. As the CDCS strategy uses a thermostat control method, its charging loss is 3.85% of total driving energy, while the blended strategy only has a 2% charging loss. Of these two energy management strategies, the CDCS strategy can effectively reduce the engine loss but has a higher charging loss compared with the blended strategy.
Energy efficiency results show that over the Harbin city driving cycle, the inputrecycled efficiency of the blended strategy is 24.73% higher than that of the CDCS strategy and that the outputrecycled efficiency of the blended strategy is 7.83% lower than that of the CDCS strategy. With the CDCS strategy, the recycle efficiency is 36.80%, but, with blended strategy, it is 51.32%. Using the CDCS strategy, the fueltraction efficiency is 38.91%, but, with blended strategy, it is 33.26%. In comparison of the two nonoptimized energy management strategies, powertrain energy efficiency is better with CDCS than with blended strategy. We suggest that a CDCS energy management strategy is more appropriate for the driving conditions on urban Harbin roads.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgment
This work is supported by the National Natural Science Foundation (NNSF) of China (Grant no. 51105220).
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Copyright
Copyright © 2014 Xiaogang Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.