Design and Evaluation of Energy Management using Map-Based ECMS for the PHEV Benchmark

— Plug-in Hybrid Electric Vehicles (PHEV) provide a promising way of achieving the beneﬁts of the electric vehicle without being limited by the electric range, but they increase the importance of the supervisory control to fully utilize the potential of the powertrain. The winning contribution in the PHEV Benchmark organized by IFP Energies nouvelles is described and evaluated. The control is an adaptive strategy based on a map-based Equivalent Consumption Minimization Strategy (ECMS) approach, developed and implemented in the simulator provided for the PHEV Benchmark. The implemented control strives to be as blended as possible, whilst still ensuring that all electric energy is used in the driving mission. The controller is adaptive to reduce the importance of correct initial values, but since the initial values affect the consumption, a method is developed to estimate the optimal initial value for the controller based on driving cycle information. This works well for most driving cycles with promising consumption results. The controller performs well in the benchmark; however, the driving cycles used show potential for improvement. A robustness built into the controller affects the consumption more than necessary, and in the case of altitude variations the control does not make use of all the energy available. The control is therefore extended to also make use of topography information that could be provided by a GPS which shows a potential further decrease in fuel consumption.

Cela fonctionne bien pour la plupart des cycles de conduite et les re´sultats sont prometteurs en matie`re de consommation. Le controˆleur fonctionne bien dans le benchmark ; toutefois, les cycles de conduite utilise´s montrent qu'un potentiel d'ame´lioration existe. La robustesse inte´gre´e au controˆleur affecte la consommation plus que ne´cessaire et en cas de variations d'altitude, le controˆle n'utilise pas toute l'e´nergie disponible. Le controˆle est donc e´tendu pour utiliser e´galement les informations topographiques qui pourraient eˆtre fournies par un GPS, ce qui conduit a`un potentiel de diminution ulte´rieure de la consommation de carburant. Gear ratio (-) D tot Estimated driving cycle distance (km) D real Actual distance traveled (km) n on Number of engine starts (-) Center of the k-control k c,init Initial k c k c,init,mod Modeled initial k c l l,s Shape parameters of the tan-function k p,i Gains for the k c control k [1][2][3][4][5] Parameters for the k c,init,mod estimation D x Corrected actual distance driven

INTRODUCTION
A Hybrid Electric Vehicle (HEV) utilizes both electric energy and energy from fuel to meet the demands set by the driver. This may lead to a reduction in the environmental impact and fuel consumption of the vehicle. A Plug-in Hybrid Electric Vehicle (PHEV) is a HEV with the possibility of recharging the battery from the grid. This adds the potential of using the vehicle as an electric vehicle, without the range limitations in a pure electric vehicle. The supervisory control algorithm for these more complex powertrains plays an important role in achieving the full potential of the powertrain. In order to evaluate different strategies, IFP Energies nouvelles (IFPEN) organized a benchmark for the energy management of a PHEV [1,2] held at the E-COSM'12 -IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling in Rueil-Malmaison near Paris, France. This paper describes the design, and evaluates the performance of the best-performing controller in the PHEV benchmark problem. As such, the paper describes and also contributes with discussions about several engineering trade-offs that were necessary to make, in order to provide a complete and efficient solution for the benchmark problem. This paper is an extension of [3] where the control strategy was outlined. The control is an extension of the adaptive map-based Equivalent Consumption Minimization Strategy (ECMS) developed in [4] for the PHEV problem and it is implemented for the simulator made available in the PHEV Benchmark.
The PHEV problem poses additional problems compared with HEV control since the control should no longer try to maintain the battery State of Charge (SOC) around a constant reference value. This is since it is desirable to make use of all the stored energy in the battery, the engine should only be started if the driving mission exceeds the electric range of the vehicle. Therefore the control strategy in [4] is extended to also handle a time-varying SOC reference as well as estimation of initial control values from driving cycle data provided in the simulator.
To achieve optimal results using ECMS the optimal value of an equivalence factor needs to be found [5]. However, this optimal value is driving cycle-specific and has to be approximated online. Two promising approaches are found in the literature. Both approaches use a cycle independent-equivalence factor and a correction based on the deviation of SOC from its reference value, denoted SOC error. In [5], the correction is a linear function in SOC error. In [6], the equivalence factor is corrected with a product of two terms, a cubic function of the SOC error and tanh of the low-pass filtered SOC error.
The contribution of the method proposed here is an efficient way of solving and implementing the ECMS control strategy for a PHEV that is also self-contained, using driving distance and average speed to estimate the initial equivalence factor and then adapting it continuously throughout the driving mission to ensure that it is robust to unknown driving missions and that the desired discharge profile is followed.
The main contributions of the paper are the evaluation of the performance in the benchmark, a discussion on the influence of some of the design choices, and finally, the extension of the control to incorporate topology information from GPS to improve the performance in the presence of altitude variations in the driving missions.

OUTLINE
In Section 2, the benchmark is presented and the models in the simulator are briefly described. In Section 3, the problem to be solved is formulated and in Section 4, the offline optimization is described. Section 5 describes the architecture of the controller, and the energy management is described in Section 6. Section 7 evaluates the controller's performance in the benchmark and the influence of some of the design choices is discussed in Section 8. Section 9 then suggests some improvements for the controller before the concluding remarks in Section 10.

IFPEN PHEV BENCHMARK
In the IFPEN PHEV Benchmark, a simulator is provided for which a supervisory control algorithm is to be designed. This simulator is a quasi-static model of the Chevrolet Volt with vehicle and battery dynamics and all energy converters modeled using stationary maps. The architecture of the vehicle and connections between components are shown in Figure 1. The Chevrolet Volt has three energy converters, an internal combustion engine (ENG), an Electric Motor (EM) and a generator (GEN), connected through a planetary gear set (GB). Both electric machines can work in both motoring and generating mode. The powertrain also incorporates three clutches that allow the vehicle to be driven in the following four modes: -Mode 1: one-motor pure electric vehicle. Only the EM is connected to the GB; -Mode 2: two-motor pure electric vehicle. Both the EM and GEN are connected to the GB; -Mode 3: series HEV. Only the EM is connected to the GB. The ENG and GEN work as an auxiliary power unit, producing electric power; M. Sivertsson and L. Eriksson / Design and Evaluation of Energy Management using Map-Based ECMS for the PHEV Benchmark -Mode 4: power-split HEV. All energy converters are connected to the GB. In the benchmark, the controller should output desired torque from the ENG, EM and mechanic brakes, the speed of the GEN, the position of the three clutches, and if the engine should be on or off. The inputs to the controller are the requested torque from the driver model, T req , minimum allowed regenerative torque, SOC, vehicle speed, average speed in the driving cycle, v avg , and approximate driving cycle length, D tot . The aim of the control is to minimize the criteria described in Table A1 in Appendix with a battery that is fully charged at the beginning of the driving cycle and may be depleted at the end of the driving cycle. There are also rules on how closely the controller has to follow the desired velocity profile [1].

Models
The model is provided as a Matlab/Simulink file. The key model equations in the simulator are briefly described below, while the interested reader is referred to [1] for more details.

Vehicle Model
The vehicle motion equation is implemented as (1) where T wh is the torque from the powertrain at the wheels, T b is the torque applied by the brakes, and v is the vehicle speed:

Battery Model
The battery model is of equivalent circuit type with a voltage source and internal resistance and implemented as:

Transmission
The transmission is a planetary gear set with three clutches, c 1 , c 2 and c 3 . The kinematic relations between the energy converters and the wheels given by the simulator are:

Consumption
There are two consumptions provided in the simulator and used in this paper; fuel consumption and a fuel equivalent of the electricity consumption. They are defined as: where _ m f is the fuel flow, q f is the density of the fuel, D real is the distance traveled, P ech is the electrochemical power, g f?ech is the average efficiency from fuel to electricity and q LHV is the lower heating value of the fuel.

PROBLEM FORMULATION
Looking at the scoring metrics and CO 2 data in Tables A1 and A2 the problem can be reformulated as delivering the torque requested by the driver, T req , or as close as possible if the requested torque is infeasible. This should be done in a fuel and computationally efficient way. The performance criteria are actually different measures on torque-tracking ability, therefore they need no further attention than that the controller should follow T req as closely as possible. Even though the specific CO 2 emissions are higher for electricity production, the higher efficiencies of the electric energy converters compared with the efficiency of the combustion engine result in the fact that the minimization of the well-to-wheel CO 2 emissions can be interpreted as fuel consumption minimization. So, the aim is to minimize the energy use, with emphasis on the fuel consumption, while fulfilling the driver's requests. This problem is well accommodated by the ECMS, where the sum of fuel and battery power is minimized. However, battery and fuel power are not directly comparable and therefore an equivalence factor k relating the two is needed; for more information on ECMS [7][8][9]. The problem is formulated as: Subject to: where x is the rotational speed of the energy converter, and P b is the power at the terminal of the battery. The torque and speed limits are applied to each individual energy converter.

OFFLINE OPTIMIZATION
Since the kinematic relations change with the actuation of the clutches, the optimization problem to be solved differs between the modes. Due to the complex nature of the problem the optimal solution is not calculated online. For a given combination of required torque, wheel speed and equivalence factor (T req , x wh , and k), the cost for each mode can be computed. Therefore, in order to find which mode to use when, the minimum cost for each mode is calculated offline, through discretizing the problem and selecting the combination with the lowest cost. The resulting controls are then stored in tables for a given set of (T req , x wh , and k). Since the efficiency of the battery does not change much as a function of SOC in the desired operating region of the battery, the SOC is found to only have minor effects on the optimal solution, therefore that effect is ignored.
To ensure that Equation (17) are all fulfilled, or in the case of T req being infeasible, the produced torque is as close to that requested as possible for that mode, the cost function in Equation (15) is augmented so that the closest point, that fulfills all the inequalities is selected.
In order to find which mode is optimal for each combination of T req , x wh and k, the optimal torque and speed setpoints also have to be found. However, instead of just storing all the control variables in tables a few insights can be gained from the kinematic relations in Equations (5-11) to reduce the amount of memory used: -Mode 1: T EM can be calculated from T req in all modes.
Therefore, Mode 1 requires no tables; -Mode 2: only x GEN has to be stored and since P f = 0 it is independent of k; -Mode 3: T EM , x EM , and therefore P EM are given by T req and x wh . The optimal output power from the generator should be on the optimal operating line of the engine-generator combination (GENSET). Therefore, only the optimal output power for each P EM , k combination has to be stored together with the optimal operating line of the GENSET; -Mode 4: both x GEN and T GEN or T ENG need to be stored as functions of T req , x wh and k.

Stored Data and Complexity
With the insight from above the following seven tables are stored for the different modes. An example of the resulting tables is also shown in Figure 2. This results in 7 tables to be stored, shown in The optimization is performed for a dense grid in T req , x wh and k. In order to minimize the amount of memory  Structure of the stored data, illustrating the complexity of each mode.
implementation and to reduce the memory consumption Mode 4 is only used when T req >0.

CONTROLLER
The basic structure of the controller is shown in a block diagram in Figure 3. The controller consists of three main subsystems. The first subsystem calculates the value of the equivalence factor, k, using the SOC and driving cycle data, discussed in Section 6. The second subsystem controls which mode to engage and the third calculates the torque and speed setpoints for the energy converters, both briefly described below.
The mode block consists of five subsystems, one for each mode and one for engine start. The mode controller outputs which mode to activate and if the engine should be started or not. In order to avoid too frequent engine starts/stops, two thresholds are used, t on and t off . The controller has to request engine on/off for a duration longer than t on /t off = 1/4 s before it is turned on/off. These values are found heuristically, iterating through several values and driving cycles and selecting the values giving the best performance qualitatively. In the simulator, the transition between modes is instantaneous, except for engine start, which is why no extra penalty or delay on mode switching is implemented. The torques and speed are then calculated using the tables calculated offline and the kinematic relations for that mode defined in Equation (5)(6)(7)(8)(9)(10)(11). Care is also taken not to exceed any of the constraints in Equation (17).

ENERGY MANAGEMENT
Since the optimal solution is calculated offline and T req and x wh are outputs from the driver model only k needs to be decided; k thus controls the energy management. The energy management of a PHEV is often divided into two categories. The first is to make use of all the stored energy in the battery, that is run as an electric vehicle until the SOC is under a certain limit, and then operates as a hybrid in charge-sustaining mode. This strategy is commonly denoted Charge Deplete-Charge Sustain strategy (CDCS). The main advantage of this strategy is that it is guaranteed to make use of the stored electric energy and does not need information about the future driving mission. The second strategy is to mix usage of [SOC] [v_avg] [D_tot] [T_wh] [Distance] [w_wh] Structure of the controller. The controller consists of three main subsystems, one where the equivalence factor is calculated, one where the mode is selected, and one where the torque and speed setpoints are calculated.
M. Sivertsson and L. Eriksson / Design and Evaluation of Energy Management using Map-Based ECMS for the PHEV Benchmark fuel and electricity throughout the driving cycle, a strategy known as blended strategy. It is well established in the literature that a blended strategy may result in lower fuel consumption than CDCS [10]. However, in order for a blended strategy to make use of all the energy in the battery the length of the driving cycle has to be known.
In the driving cycles provided by the PHEV Benchmark organizers only the approximate distance as well as the mean speed is known. In the provided driving cycles, this approximate distance can deviate from the actual distance of the driving cycle by up to almost 10%.

Reference SOC
In order to make use of all the stored energy in the battery, a mix between the blended and CDCS strategies is implemented. The strategy is to underestimate the approximate distance by 10%, and use that as a horizon for the blended strategy, then switch to charge-sustaining mode. This is achieved by setting a SOC reference, SOC c , that is linear in the ratio of traveled distance versus expected distance according to Equation (18), a method also used in [6]. The minimum SOC c , SOC f , is set to 0.315 in order to ensure that SOC(end) ! 0.3. The shape of SOC c is shown in Figure 4:

Equivalence Factor Adaptation
A common strategy when using ECMS is to adapt the equivalence factor according to an affine function of the SOC error [2,5]. Here, for robustness reasons, another approach is used. The strategy used in [4] is extended to fit the PHEV problem. The strategy is to adapt the equivalence factor according to a tangent function in SOC. The idea is that as long as the SOC is near the desired SOC the control should remain rather constant; but when the SOC approaches the limits the control needs to adapt. In [4], this is used in a HEV where the aim is to maintain the SOC around a constant level.
Here, since it is a PHEV, it is desirable to use the energy stored in the battery, therefore the center of the tanfunction is SOC c . The SOC window used is also decreased linearly with distance traveled. This is to allow larger deviations early in the driving mission, and then make the control follow the SOC c on a narrower band towards the end of the driving cycle. The k-adaptation is given by Equation (19), where l 1 and l s are constants that control the slope and range of the tangent function, and dSOC is the allowed deviation from SOC c : A benefit with this formulation is that the smaller the dSOC, the steeper the slope around SOC c becomes and the faster the control reacts to deviations. In Figure 4, the shape of the control is shown for the case when the approximate distance is correct. That is, the SOC c undershoots the distance traveled, and thus results in the control going over to charge-sustaining mode. Also shown is that the allowed SOC deviation gets smaller with distance.
The variable k c still has to be decided. In Table 1, the change in consumptions compared with the consumptions with optimal k c and end SOC are shown for different values of k c and different driving cycles. A k c is considered optimal if the k trajectory follows the desired discharge profile, SOC c . However, since SOC c is based on undershooting the approximate driving cycle length, there are k c values that result in lower consumptions; this is, however, hard to predict. Instead, the optimality of k c is qualitatively assessed and the parameter is found in an iterative manner. It is seen that the optimal value changes with the driving cycle. The control ensures SOC(end) ! 0.3 for all k c but it might come with a substantial increase in consumption if the k c value is wrong.
In Figure 5, the k and SOC trajectories for the different values of k c on 109US06 driving cycle are shown, as well as the mode selection for the final repetition of the cycle. Due to the driving mission length provided only being approximate, the control undershoots the length in order to make sure all electric energy is used. The outline of the basic control shape, k-function for D x % 0.2 (left), SOC c and dSOC (center) and k-function for D x ! 0.9 (right).
The US06 cycle is, however, 7% longer than the length provided, resulting in an undershoot of roughly 16% for the controller. It is seen that the control for k c 6 ¼ k c,opt does not follow the SOC c ; instead it follows SOC c ± dSOC. For k c = 2 this results in a control that switches rapidly between k % 2.5 and k % 5, something that comes with a large consumption penalty. It also affects the number of engine starts, seen in Table 1.

Adaptive Control of k c
In order to avoid the switching nature of the k-control seen in Figure 5 the idea is to adapt k c if the SOC deviates too much from SOC c . This is done with a PI controller according to: where K p and K i control how fast the controller adapts, but a faster controller comes with a slight consumption penalty. In Table 2, the consumption change compared with k c,opt for adaptive k c is shown for different driving cycles and k c,int . The number of engine starts is also shown. A k c,init is considered optimal if it roughly produces a SOC trajectory that follows the desired trajectory without k c deviating too far from k c,init , i.e. producing a roughly constant k trajectory. This value is, as with k c,opt , qualitatively assessed and found in an iterative manner. It is seen that the adaptive k c performs as well as k c,opt , better in some cases, worse in some cases, but most of all it reduces the effect of poor initial values. This is also confirmed in Figure 6, where the SOC and k trajectories are shown for 109US06 driving cycle, as well as the mode selection for the final repetition of the cycle.  The SOC and k-trajectories for different k c values on 109US06 driving cycle as well as the modes used for the last repetition of US06. Mode = 5 represents engine start. A poor k c may lead to a switching characteristic of the control, which is also visible in the number of engine starts.

M. Sivertsson and L. Eriksson / Design and Evaluation of Energy Management using Map-Based ECMS for the PHEV Benchmark
The switching nature is almost completely removed, resulting in a nearly constant k value during the entire blended phase.

Estimating k c,init
Although the developed control has been seen to perform well for all reasonable initial k c , the consumption is still affected by it. Therefore, it is desirable to achieve an estimate as close as possible to the optimal k c . In Figure 7, the optimal k c,init is plotted against approximate distance for the driving cycles used. It is seen that the shape of the profiles is similar for all driving cycles. The all-electric range, seen in Figure 7 as k c,init ! 2, differs up to almost 100% for the different driving cycles.  The SOC and k trajectories with adaptive k c for different values on k c,init on 109US06 driving cycle as well as the modes used for the last repetition of US06. Mode = 5 represents engine start. The adaptive k c reduces the effect of poor initial values.  The optimal k c,init as a function of approximate distance for different driving cycles. The general shape of the curves are similar; however, the all-electric range differs among the cycles.
In Figure 8, the approximate distance required to exceed the all-electric range is plotted against mean speed. Even if the mean speed is not enough to describe the driving cycle, since neither the slope nor how transient it is are captured by the mean speed, the all-electric range is approximated by a linear function, shown in Figure 8. Artemis Urban is plotted in magenta to mark that it is considered an outlier and is not included when the line is fitted. Since the losses in the vehicle motion Equation (1) are quadratic in speed, a straightforward assumption would be that the all-electric range decreases with mean speed, an assumption that is also used here. The approximate distance is then corrected with the proposed linear correction, in order to compensate for the different allelectric ranges. The result is shown in Figure 9. It is seen that the correction shifts the points to the same region, a trend that is well captured by an exponential function. The final scheme to estimate k c,init is of the form: In Table 3, the results for the full controller with k c,init,mod are compared with the results for k c,init,opt . Even if the estimated k c,init is not too far from the optimal, the consumption can differ substantially. Interesting to note is that the driving cycle with the largest k c,init error shows the best result. Looking at Figure 10, this appears to be due to the k c,init,mod -control that has a higher k value when entering charge-sustaining mode which results in less switching behavior and lower consumption.
Another important property of the k c,init estimation is that it should be such that it avoids unnecessary engine starts if the driving mission is within the allelectric range. This is achieved for all tested driving cycles except FHDS (1 unnecessary start) and Artemis Extra-Urban (2 unnecessary starts), which is deemed acceptable.

BENCHMARK EVALUATION
In the PHEV Benchmark, the controller is tested on two unknown driving cycles, hence not used in the design of  k c,init,opt versus corrected approximate distance and how it is modeled. Artemis urban is considered an outlier and is not included when the curve is fitted. The approximate distance required to exceed the all-electric range for different driving cycles and a linear model to capture the behavior. Artemis urban is considered an outlier and is not included when the line is fitted. the controller (Fig. 11). Both cycles are rather transient and the first cycle, Arco-Merano, has substantial altitude variations, whereas the second, Aachen, is on flat road. The results for the benchmark tests are shown in Table 4. For both tested cycles the controller performs relatively well and is close to the solution predicted by HOT, described in [5]. The results are within 3.6% in fuel consumption. This is despite the fact that the controller is implemented without knowledge of the future driving profile and road slope and with a memory usage of just 154 kB. For a closer comparison between the resulting controls and the solution predicted by HOT see [2].
The resulting SOC and k trajectories for the tested cycles are shown in Figure 12. For both cycles D tot is accurate and therefore the SOC c reference has both a blended and a charge sustaining phase. For Aachen, it is seen that the controller performs well, the k c,init is fairly close to the desired k-region and the control manages to maintain SOC near SOC c during the entire blended phase without large variations in k. During the chargesustaining phase the control becomes a bit switching to maintain SOC within the desired window.
For Arco-Merano, it is apparent that a linear discharge profile is not optimal. This is since the altitude SOC and k trajectories for the full controller, with k c,init,mod , compared with k c,init,opt . The modeled k c,init is quite far from the optimal but still SOC(end) ! 0.3. The two driving cycles used in the benchmark. a) Arco-Merano, b) Aachen. variations, or more accurately the road slope, acts as a disturbance and is unknown to the controller. During the first uphill the control works as expected, maintaining the SOC near SOC c , but during the subsequent downhill phase the recuperation moves SOC outside the desired SOC window. In the second uphill phase the control then brings the SOC back into the SOC window, but the final downhill yet again brings the SOC outside of the SOC window.

DISCUSSION
The main objective of the controller is to minimize fuel, and one of the basic ideas to accomplish this is to make sure that all the energy in the battery is used. However, since one of the requirements is that SOC(end) ! 0.3 for the entry not to be disqualified, this needs to be taken into account. This is accomplished by underestimating the total distance, setting a SOC target higher than SOC min , and decreasing the allowed deviation from the desired SOC the closer to the end of the cycle the vehicle gets. Using a tan-function can also be considered a safety measure since it is seen in Figure 5 that the tan-function does not make the control follow the desired discharge profile; instead it makes sure that the control stays within the desired SOC window. All these safety measures affect the consumption, but how much and in what way depends on the driving cycle. For instance, for Arco-Merano, setting k = k c , that is, removing the tan part, improves the fuel economy by 2.9%, but instead for Aachen SOC(end) < 0.3. In a real vehicle the lower SOC limit would be more of a soft constraint and this might not be critical. Without perfect The SOC and k trajectories for the two cycles used in the benchmark.
M. Sivertsson and L. Eriksson / Design and Evaluation of Energy Management using Map-Based ECMS for the PHEV Benchmark look-ahead the control will potentially end up in chargesustaining operation and this is something that needs to be handled. One way could be with gain scheduling of the gains in Equation (20), or as here with a tanfunction. This is also true for SOC f . For some cycles, especially with downhill phases, it would be beneficial to set SOC f < 0.3, forcing the controller to follow a steeper discharge profile but then for other cycles SOC(end) < 0.3. Removing the underestimation of driving cycle length is not as trivial since the design of k c,init,mod depends on it. However, since the aim is to minimize fuel consumption, a reasonable assumption is that the fuel penalty of ending with energy left in the battery is larger than the fuel penalty of the strategy not being completely blended, which supports the under-estimation as long as the driving cycle length is not exactly known.

CONTROLLER EXTENSIONS
Up until now the focus has been on the controller implementation and design trade-offs that were made for the benchmark. This section describes some extensions that were implemented after the benchmark was completed. Both cycles used in the benchmark evaluation highlight different aspects of potential improvement for the controller. Two suggested improvements for the controller are increasing the allowed SOC window and incorporating topology information, both described in the following subsections.

Increasing the Allowed SOC Window
For Aachen the control during the charge-sustaining phase switches between k % 3 and k % 6, something that The SOC and k trajectories for the case with increased dSOC min (left) and with topology taken into account (right), Arco-Merano.
is also visible to a lesser extent in Arco-Merano around 9 000 s, which increases the consumption. This is almost completely removed if dSOC min is increased from 1% to 2.5%, with a corresponding fuel consumption decrease of 2.7% (Aachen) and 0.9% (Arco-Merano). Even with this larger SOC window SOC(end) > 0.3 for both cycles, something that also holds for all other tested cycles except 109FUDS, where SOC(end) = 0.298, but in a real application such small deviations might be acceptable.

Including Topography Information
In Arco-Merano during the downhill segments braking is needed and energy can be recuperated, energy that could be used in the uphill phases. However, to be able to make use of this potential energy some look-ahead is necessary. If the topography is known beforehand and provided to the controller from map and GPS data this could be used in the controller. Vehicle potential energy recuperated in the downhill phases is not taken into account when setting the SOC reference; if estimates of this can be used this could offer potential for improvement. A suggested extension to the control strategy, given that this information is available, is to relate the potential energy to SOC and decrease the target SOC, SOC f , with the amount of energy that can be expected to be recuperated. The requirement is still that SOC(end) ! 0.3 and therefore SOC f is increased as a function of the traveled distance. The new SOC f strategy used together with equation (18) thus becomes: In Equation (23), SOC f,o = 0.315, h reg is the sum of altitude difference in the downhill phases in the driving cycle, g avg is an estimate of the average efficiency from the wheels to the battery, set to 0.8, and Q tot is the energy capacity of the battery. In the presence of altitude variations this evaluates to a quadratic expression in distance traveled, but on flat road it is equivalent to Equation (18). The results for Arco-Merano with this strategy, as well as the results when just increasing dSOC min , are shown in Figure 13.
The resulting trajectories are similar, but as expected the control with varying SOC f increases the battery usage during the first uphill and therefore ends at a lower SOC, SOC(end) = 0.5036 versus SOC(end) = 0.5454. When dSOC min is increased the switching nature of k disappears but with the addition of varying SOC f the switching returns. This is, however, deemed acceptable since the controller still needs to be robust to the other driving cycles. The extra depletion of the battery results in an additional fuel consumption reduction of 4.9%, results that also hold for the other driving cycle with altitude variations provided by the organizers (VAIL2N-REL, 12.4% decrease).

CONCLUSIONS
The design and development of the winning control strategy in the IFPEN PHEV Benchmark is described. The strategy is an adaptive map-based implementation of ECMS striving to be as blended as possible, but still ensuring that all electric energy is used. The controller tries to follow a SOC reference that is linear in traveled distance, but to ensure that all electric energy is used this distance is underestimated. The equivalence factor is adapted according to a function in SOC, a function whose center adapts according to how well the SOC reference is followed. Finally, a method for estimating the initial value for the controller from driving cycle data is developed.
In the benchmark, the controller is seen to perform well, close to the results predicted by HOT. This is despite being implemented just using the approximate driving distance and average velocity. In the case of altitude variations the assumed linear discharge profile is not followed, due to the fact that the slope of the road is unknown to the controller. Also, the allowed SOC window, kept narrow to ensure complete use of the battery energy whilst still ensuring that the final SOC is within the limits prescribed in the benchmark, affects the consumption more than necessary.
The controller is therefore extended, first to be allowed to make use of more of the battery, and finally to incorporate topology if available, a strategy that is seen to perform well with promising consumption results.