Parametric CO2MPAS Model
The present section provides a short description of the parametric CO2MPAS model, which can be found here.
The parametric CO2MPAS model is based on the v1.1.1 version of CO2MPAS (commit: 113b09b). The main difference between the two tools stands on the inputs used and on the various simulation steps. Parametric CO2MPAS consists a "simpler" version of the tool targeting to fleet simulation analysis where test instantaneous data for the simulated vehicles are not available, while the purpose of the Official CO2MPAS tool is well defined as the back-translation of WLTP measured data to the NEDC equivalent values.
In the following sections the reasoning behind the development of this tool is further explained, while on the methodology section the tool is described highlighting the core structure and the core models. Last, on the results section, the validation of the tool on its NEDC and WLTP simulation accuracy is presented for a pool of measured cars.
The main purpose of the present exercise is the development of a vehicle / fleet simulation tool which will be able to simulate, with a good accuracy, fuel consumption and CO2 emissions from fleets, both under real life and test conditions. The tool should be able to capture the effects of various scenarios - e.g. technology penetration scenarios, fleet composition scenarios, etc -, both qualitatively and quantitatively.
Parametric CO2MPAS builds on the Official CO2MPAS Model, which allows the back-translation of a WLTP test to the equivalent NEDC CO2 emission value. Several studies describe the Official CO2MPAS Model, a few are provided here:
- ...
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The current exercise targets the expansion of the official tool's functionalities, mainly adding the capability of running simulations only with "parametric" - e.g. not arrays - input data, and thus by-passing the calibration steps. A detailed explanation of the previous, along with the definition of the additional inputs required to achieve that, is presented bellow.
The following visual presents the main outline of the Parametric CO2MPAS structure.
Parametric CO2MPAS Outline
The tool is structured on three different steps, as further described in the following three paragraphs.
The Inputs part of the tool starts from the raw inputs provided from the user and goes towards the complete pool of input data used in the various Parametric CO2MPAS sub-models. A comprehensive analysis of the Inputs part can be found in the relative section bellow.
The Inputs Model
The Drivetrain part of the Parametric CO2MPAS includes the various sub-models of the vehicle's drivetrain, excluding the engine.
The calculation starts from the velocity profile, and respecting the energy / power equilibriums in the various steps goes backwards from the forces applied to the vehicle and the wheels, to the final drive, the gearbox, (the clutch / torque converter), up to the output of the engine.
The Drivetrain Model
The Engine model includes the various sub-models related to the calculation of the speed, power, temperature and fuel consumption, starting from the engine's output speed and power towards the drivetrain.
In order to calculate the cold start effect, along with the fuel consumption, the engine coolant temperature is required. Here two options are available:
- Run the whole calculation in a loop, performing the calculation for each time step,
- Keep a (semi-)vectorial approach (--> double check that no loops are present), and use the perturbations method, starting from a constant temperature profile.
The second method is chosen in order to optimize calculation time and the overall performance.
The Perturbations Model: Starting from a constant temperature profile, and respecting the drivetrain model constraints in terms of speed and power required, a first estimation for the engine power, engine speed, and fuel consumption, is calculated. Using the estimated fuel consumption as an input, the thermal model provides a new temperature profile, and then the whole calculation is repeated. It has been demonstrated that over three perturbation steps a good estimation of the final temperature is achieved, which is then used for the calculation of the final engine speed, engine power and fuel consumtpion. More details on the methodology and the results of this method are provided here (--> Build a page explaining better and providing results for the various steps of the perturbation method).
The Engine Model / The Perturbations Model
Note: As it can be seen in the figure above, the Electrics Model is included in the engine model, as it is not a direct part of the drivetrain. It affects the engine power via the power demand from the vehicle's electrics system, and mainly the operation of the alternator which is presumed to be mechanically connected to the engine. More details on the reasoning behind the operation of the electrics model can be found bellow, in the relative section.
As a reference, the main structure of the official CO2MPAS tool can be found here, whereas it has to be noted that the Parametric CO2MPAS is focusing on the prediction parts, neglecting mainly the calibration and inputs "combination" steps.
Parametric CO2MPAS main inputs are provided in the table bellow.
| Name | Units | Values / Comments |
|---|---|---|
| Aspiration Method | - | Turbo or Natural Aspiration / Turbo concerns all charging technologies |
| Dynamic Rolling Radius | mm | Dynamic rolling radius of the wheel |
| Engine Capacity | cc | Engine's capacity |
| Final Drive Ratio | - | Final drive ratio |
| Fuel | - | Fuel can be gasoline, diesel, etc. |
| Gear Box Ratios | - | A dictionary with the gearbox ratios |
| Gear Box Type | - | manual or automatic |
| Mass in Running Order | kg | As defined in ... |
| Nominal Power | kW | Nominal power of the ICE |
| Nominal Speed | RPM | Nominal speed of the ICE |
| Nominal Torque | Nm | Nominal torque of the ICE |
| Reference Mass | kg | As defined in ... |
| Start Stop Technology | - | Declaring the presence of a S/S system |
| Stroke | mm | Cylinder's stroke |
| Unladen Mass | kg | As defined in ... |
| Velocity Profile | km/hr, sec, - | Velocity, Time, Gears |
| Wheel Drive | - | 2WD or 4WD |
A full list including all input data required is provided here, while the calculation of the unknown parameters and some discussion is provided here.
The description of the work performed for the definition of the Road Loads is available in the Road Loads section.
The main two models of the CO2MPAS tool concern the fuel consumption / co2 emissions calculation and the temperature calculation. The basics of the two models, along with a list of the additional models, can be found bellow.
The Fuel Consumption Model of the Parametric CO2MPAS is based on the Extended Willans Lines Model and is physically represented as follows:
, where:
A more detailed description is available here.
The temperature calculation of the Parametric CO2MPAS model is based on the energy equilibrium between the heat produced by the combustion of fuel and the various thermal losses, e.g. exhaust gases, temperature increase of engine body, cooling, etc.
The main function is separated on the cold and hot phases of the cycle and it is physically expressed as:
Cold Phase
Hot Phase
, where
and the different constants are provided either as an input to the model or calculated by empirical functions.
A more detailed description of the temperature calculation model used in the Parametric CO2MPAS, is available here.
- Engine Speed Model
- Engine Power Model
- Gearbox Model
- Start / Stop Model
- Cold Start Model
- Electrics Model
- Final Drive Model
- Vehicle Model
- Wheels Model
A pool of 26 measured vehicles is used for the calibration / validation of the tool. The main characteristics of those cars are provided in the table bellow, while several additional data required are provided by the various calibration steps using the Official CO2MPAS tool.
Pool of measured vehicles
Bellow the various calibration / validation steps of the tool are described. Here, only the key results are presented, while a complete analysis can be found in the relevant GIST. The tool's version used for the results provided bellow is given in the commit: e6d40f49.
The target of this step is to evaluate the error / the accuracy of the tool when the different submodels & functions - as compared with the Official Tool - are used.
In order to achieve that the complete set of parameters used by the tool are provided as an input - those parameters are defined after the simulation, calibration and prediction, of the pool of vehicles with the Official CO2MPAS Tool.
At a second step, Road Loads are excluded from the inputs, in order to assess the error introduced by the Road Loads calculation - which consists one of the keys parts of the tool and thus it is an important source of the tool's overall innacuracy.
The third step of the validation targets the evaluation of the full error introduced when all additional parameters of the Parametric Model are calculated as defined in the relative section.
This step constitutes also the main validation of the new Parametric Tool as a complete and independent tool.
The two figures bellow provide the simulation errors of the various steps on the NEDC and WLTP, while the table presents the aggregated results of the validation.
NEDC Simulation Error
WLTP Simulation Error
Summary Results
Discussion
As expected both the average and the standard deviation of the error increase when the "unknowns* of the model increase. We see that in Step 1 an overall absolute mean error of approx. 3% is achieved, representing a "benchmark" of the various models' error when all parameters of the tool are provided as inputs. This figure approximately doubles for NEDC, with a lower effect for WLTP, when the road loads are calculated from the tool (Step 2). In Step 3, we obserce a lower increase of the mean absolute error over NEDC, and a higher increase over WLTP, while for both cycles the effect on the standard deviation of the error increases.
The previous results confirm the fact that a big part of the error comes from the Road Loads calculation, while it is evident that this error is more important in NEDC. This can be explained from the "unrealistic" nature - or even the "extreme optimization" - of the NEDC Road Loads, as compared to the ones of WLTP. Since the empirical formulas used in the calculation of the Road Loads come from "real" values, and not "officially reported" values, this result is both expected and justified.
On the other hand, the error introduced on Step 3 - the calculation of the additional parameters of CO2MPAS Parametric - is as eplected minor for NEDC, but more important for WLTP. The latest could be justified by ..., but still needs to be further examined. Additionally, as expected this step has a higher effect on the startard deviation of the error, given that average values and linear interpolations are used. For vehicles close to the "average" vehicle measured, the error should be low, while when "extreme" cases / cars different than the average are studied the error should be increased.
As a conclusion for this validation exercise, it is noted that, overall, the accuracy of the results are within the expected limits, close to the various benchmarks of other simulation tools. As a next step, the tool is used to simulate a larger pool of cars, more accurately representing a complete fleet, and it's error, as compared to the reported CO2 emission values, is evaluated.
A first approach towards validating Parametric CO2MPAS on real world emissions is described in the section Parametric Validation Real Trips, while the ipython / gist with the detailed description of the work is provided here (Link not available, confidential data!).