Performance Analysis of Hybrid Electric Vehicle over Different Driving Cycles

Article aims to find the nature and response of a hybrid vehicle on various standard driving cycles. Road profile parameters play an important role in determining the fuel efficiency. Typical parameters of road profile can be reduced to a useful smaller set using principal component analysis and independent component analysis. Resultant data set obtained after size reduction may result in more appropriate and important parameter cluster. With reduced parameter set fuel economies over various driving cycles, are ranked using TOPSIS and VIKOR multi-criteria decision making methods. The ranking trend is then compared with the fuel economies achieved after driving the vehicle over respective roads. Control strategy responsible for power split is optimized using genetic algorithm. 1RC battery model and modified SOC estimation method are considered for the simulation and improved results compared with the default are obtained.


Introduction
Hybrid electric vehicle (HEV) has turned up as a promising solution for the automotive industries in terms of reduced toxic emissions. As two power sources, battery and engine are present, an intelligent power split energy management strategy should be implemented to split the power to achieve better fuel economy. HEV's performance will obviously vary over the type and conditions of road, driver's aggressiveness/behavior and weather conditions. Kuhlar and Karstens [1] and Fomunung [2] introduced few parameters which characterize the roads. These parameters have been used to model emissions or fuel economies by others. These parameters are able to describe a driving cycle (DC) behavior but can't clearly identify a DC which may result in the best fuel economy (FE). The aim of the study is to find parameters of DCs, which impacts the FE. Using size reduction techniques, few governing parameters are selected and with these parameters DCs are ranked using 'Technique for order preferences by similarity to an ideal solution' (TOPSIS) and 'The Vlse Kriterijum-ska Optimizacija Kompromisno Resenje' (VIKOR). The vehicle is then run over the different considered DCs to find out their FE using genetic algorithm (GA) based control strategy and then ranked accordingly. These two results are compared to get a sense that how the parameters are linked with FE.
In most of the literature ten parameters are generally considered to characterize a DC. These  [4] is a statistical procedure to un-correlate the variable and reduce the dimension of the data. PCA yields orthogonal vectors of high energy content in terms of covariance. ICA also decomposes the variables into smaller sets and extracts the independent variables from a multivariate dataset. ICA was developed by Jueten and Herault [5] and Comon [6] to solve cocktail party problems and for blind source separation. DC data sets are reduced here using ICA and PCA and some of these reduced parameters are maximized and others are minimized to compute FE. This requires multi-criterion decision making (MCDM) measures. Valuable MCDM methods like TOPSIS and VIKOR, are applied here to rank DCs in the order of their FE. Further, to support the analysis obtained by these methods, an intelligent power split control strategy is developed using GA. Engine on/off trend helps in achieving this. To control the engine on/off, threshold values of governing parameters (which are responsible for power split) are obtained using optimization techniques and FE is determined. Table 1 lists the parameters of DCs. To extract features of these DCs, PCA and ICA methods are used and explained in the subsequent sections. time. Identification of the variables of driving cycle through PCA will be useful in ranking a DC and while analyzing its fuel economy.

Independent Component Analysis
For the hidden feature extraction another popular technique, ICA is also used. ICA is a statistical and computational technique to identify the meaningful hidden features. In contrast to PCA, ICA extracts six parameters which are significant for analysis. These are trip time, average speed, maximum deceleration, average acceleration, idle time during the trip. The smaller data sets received by PCA and ICA do not have same parameters, so selecting one of them is important. Generally, PCA is applicable to Gaussian data and is restricted to the first and second moments of the data, whereas ICA is applicable to non-Gaussian data and explores higher order moments. Thus, it is important to identify the nature of DC data on which these techniques are applied.

Nature Identification of driving Cycles
To analyze the nature of DCs, probability distribution functions are determined. The mean and standard deviations (SD) of the distributions are recorded and listed in table 2. It can be observed that no DC follows a normal distribution with mean=0 and SD=1. This enables us to choose ICA for feature extraction as ICA fits for non-Gaussian data set.

Analysis of fuel economy over different driving cycles
The FE of Prius over considered DCs is measured using GA in ADVISOR. GA is a robust and feasible approach and solves complex optimization problems. The available battery power is governed by state of charge (SOC). ADVISOR uses Ampere Hour Counting method for SOC estimation. But, the importance of open circuit voltage for SOC estimation is also emphasized in literature. Thus, SOC estimation algorithm is accordingly modified and incorporated in ADVISOR library. In this paper, 1RC (parallel combination of 1 RC components in series with internal resistance) model along with modified SOC estimation method is used to perform the simulations. Threshold values of governing parameters responsible to turn on/off the engine are estimated using GA and corresponding FEs are recorded [9]. Table 4 records the threshold values of these parameters, namely cs_eng_on_soc, cs_min_off_time, cs_min_pwr, cs_electric_launch_spd and cs_eng_min_spd for considered DCs.    Table 6 performs the comparison between default SOC estimation method with R int battery model and modified SOC estimation method with 1RC battery model. Modified SOC estimation algorithm in table 6 is either improving FE or speed traces or both. In general cases, idling is allowed at the stops. But if, idle stopping is implemented, the significant amount of fuel can be saved. The comparative study of the FEs in case of idle stopping with zero engine speed and engine on is tabulated here. Table 7 shows noteworthy improvement in FEs for all DCs but Indian DC is dominating. Two major reasons idle time and number of stops may play momentous functionality. Idle time is considerable, but a greater no. of stops will recuperate more kinetic energy which will motivate the vehicle to run more on electrical energy, hence improves FE. Further, lower acceleration rate and lower speed of Indian DC make it in favor of HEVs. Indian DC also provides highest regenerative efficiency.

Conclusion
The efficiency of an HEV obviously depends on the road profiles. A profile is a composition of various parameters. In this paper, few vital parameters are identified using size reduction techniques and based on these DC are ranked in order of their fuel economy using multi criterion optimization methods. The results are further validated using GA based intelligent power split control strategy. It is concluded that the Indian urban DC is promising and provides higher fuel efficiency for an HEV as compared to other countries. The favorable Indian road profile will attract more people to use HEVs, thus boom in the automobile manufacturing market is expected. This will further reduce toxic emissions and will contribute to the Indian economy. It is also recommended that ICA should be applied rather than PCA for extracting DC parameters to analyze the performance as they follow non-Gaussian distribution. Engine idling should be considered as a powerful feature for improving fuel economy on city roads.