EP2822803A2 - Method and apparatus for power source control - Google Patents

Abstract

Method and Apparatus for Power Source Control A method for generating an efficiency control map for controlling a power source of a hybrid electric vehicle is disclosed. The power source comprises a primary source of power and a secondary source of power. The method comprises determining, for a plurality of operating powers of the power source, power source efficiencies associated with a plurality of different operating conditions of the power source; selecting, in accordance with the determined power source efficiencies, for each of the plurality of operating powers, an operating condition of the plurality of operating conditions providing an optimum power source efficiency; and producing, in accordance with the selected optimum operating conditions, an efficiency control map designating the optimum operating condition for each of the plurality of operating powers.

Description

Method and Apparatus for Power Source Control

The present invention relates to a method, apparatus, and computer readable medium for control of a power source of a vehicle. More specifically, embodiments are disclosed that relate to methods for improving the performance of a vehicle's power source.

Background to the Invention

An increasing awareness of climate change from manufacturers, consumers as well as regulators, coupled with an increasing demand for a finite supply of fossil fuels, is seeing the automotive industry in a historical transition. It is projected that by 2020 about 18% of all new vehicles sold in Europe (7% in US) will be hybrid electric vehicles (HEVs).

This offers many interesting technological challenges for researchers to address, including the control of the HEVs. The utilization of multiple power sources requires supervisory control systems (SCS) to make intelligent decisions on how to power the HEV. A vast range of SCSs have been proposed in the literature over the past decade, ranging from rule-based controllers to optimization-based solutions. However, many SCSs of the latter nature are not implementable due to computational burden. Furthermore, SCSs in the past have often been developed and tested through simulations on vehicle models based on steady-state characteristics. This results in the loss of important transient behaviours, in particular during switching of power sources.

Additional challenges relate to the improvement of the efficiency of the combustion process used in both standard combustion engine vehicles and HEVs.

Summary of Invention

According to a first aspect of the invention there is provided a method for generating an efficiency control map for controlling a power source of a hybrid electric vehicle. The power source comprises a primary source of power and a secondary source of power. The method comprises determining, for a plurality of operating powers of the power source, power source efficiencies associated with a plurality of different operating conditions of the power source. The method also comprises selecting, in accordance with the determined power source efficiencies, for each of the plurality of operating powers, an operating condition of the plurality of operating conditions providing an optimum power source efficiency. In addition the method comprises producing, in accordance with the selected optimum operating conditions, an efficiency control map designating the optimum operating condition for each of the plurality of operating powers.

This method for producing an efficiency control map can be used by a HEV to control which power sources are used, or what ratio of each power source is used, for each output power.

The different operating conditions may comprise different power share factors between the primary source of power and the secondary source of power. Furthermore, the optimum operating condition may comprise an optimum power share factor. The power share factor may be indicative of one of the primary or secondary source of power providing all of the required power and the other power source not providing any of the required power.

The different operating conditions may also comprise different power source speeds. In addition, the optimum operating condition may comprise an optimum power source speed. The power source speed may correspond to the speed of an engine associated with the primary source of power. The engine associated with the primary source of power may be a combustion engine. The secondary source of power may be an electrical battery.

The power source efficiency may be determined in accordance with the following equation: η_ίοί = ( 1 -U)'1]_SS(P_SS(M), SO V) + u-i)ps(P_PS(u), ω,_α:) wherein η_ίοί is the total power source efficiency, u is the power share factor, r|_ss is the efficiency of the secondary source of power, P_ss is the power demand of the secondary source of power, SOC is the state of charge of the secondary source of power, v is the average efficiency of the charging of the secondary source of power, r|p_S is the efficiency of the primary source of power, P_PS is the power demand of the primary source of power and ( is the speed of the primary source of power.

The SOC may be set at 65%. The average efficiency of the charging of the secondary source of power, v, may be updated in real-time. The average efficiency of the charging of the secondary source of power v may be set at 0.5.

The efficiency of the primary source of power may be determined in accordance with the following equation: T}ps - Ep_S/ (mf_uei^■ L) wherein E_PS is the total energy generated by the primary source of power for a time period in steady-state operation, m_&ei is the total mass of fuel consumed for the same period, and L is the specific latent heat of the fuel.

The efficiency of the secondary source of power may be determined in accordance with the following equation: wherein the r|ss-charge-discharge is the efficiency of the charge-discharge cycle of the secondary source of power determined in accordance with the energy ratio across the charge-discharge cycle.

The power source efficiencies may be determined separately for a charging state and a discharging state of the power source. Such a procedure provides a more accurate calculation.

The power source efficiencies may be determined for a discharging state in accordance with the following equation:

The power source efficiencies may be determined for a charging state in accordance with the following equation:

Vtat-c arge

wherein P_M is an operating power of the plurality of operating powers, Pss is the power demand of the secondary source of power, P_PS is the power demand of the primary source of power, SOC is the state of charge of the secondary source of power, COKE is the speed of the primary source of power, P_Ps-m is the power used by the primary source of power, Pss-m is the power used by the secondary source of power and v is the average efficiency of the charging of the secondary source of power. The optimum power source efficiency may be determined in accordance with a minimisation algorithm. The minimisation algorithm may be:

EMM: {u_opt, _lCE -opt \ = f (P_M, SOC, v) Alternatively, the minimisation algorithm may be:

wherein u is the power share factor, u_opt is the optimum power share factor, P_M is an operating power of the plurality of operating powers, P_ss is the power demand of the secondary source of power, P_PS is the power demand of the primary source of power, SOC is the state of charge of the secondary source of power, COKE is the speed of the primary source of power, C0i_CE-o_Pt is the optimum speed of the primary source of power, P_Ps-m is the power used by the primary source of power, Pss-m is the power used by the secondary source of power, v is the average efficiency of the charging of the secondary source of power, k is the charge sustaining factor.

Such a minimisation algorithm may help to provide a charge sustaining operation.

The power share factor, u, may be determined in accordance with the following equation:

wherein P_PS is the power of the primary source of power, and P_M is an operating power of the plurality of operating powers. The efficiency control map may be generated off-line or in real-time on-board the hybrid electric vehicle.

The plurality of operating powers may cover a range of operating powers of the power source. The range of operating powers may be the full range of operating powers provided by the power source. Alternatively, the range may be a limited range of operating powers.

The method may further comprise operating the power source of the hybrid electric vehicle in accordance with the efficiency control map. The hybrid electric vehicle may determine what power share factor between a plurality of power sources to use, and at what engine speed to run a combustion engine of one of the plurality of power sources, for each of the required power output for driving a motor of the hybrid electric vehicle.

According to another aspect of the invention there is provided an apparatus for generating an efficiency control map for use in a hybrid electric vehicle, the apparatus operable, in use, to perform any of the various method steps described above. The apparatus may comprise a processor for performing the method steps. Furthermore, the apparatus may comprise a memory for storing information necessary for implementation of the method steps. The apparatus may be a supervisory control unit. The apparatus may be an apparatus separate from a vehicle, arranged to generate the efficiency control map. The apparatus may be arranged to provide the efficiency control map to one or more vehicles.

According to yet another aspect of the invention a hybrid electric vehicle is provided comprising a power source having a primary source of power and a secondary source of power. The hybrid electric vehicle also comprises a supervisory control unit arranged, in use, to perform any of the various method steps described above.

The primary source of power may comprise an internal combustion engine. The secondary source of power may comprise a battery. The primary source of power may comprise a generator to convert the energy produced by the internal combustion engine into electrical energy. The power sources may comprise an electrical converter, which connects the power source to a DC link, which then powers the motor. For an internal combustion engine the electrical converter is an AC to DC converter. For a battery the converter is a DC to DC converter. The generation of the efficiency map may take into account the losses in the power conversion. The primary and secondary power sources may comprise at least one of an internal combustion engine, a battery, a supercapacitor, a fuel cell, and a flywheel. The primary and secondary power sources may be arranged in a series hybrid combination.

The hybrid electric vehicle may further comprise an electric motor for driving the vehicle. The motor may be powered by the power source.

According to another aspect of the invention a method for air- fuel ratio correction in a combustion engine is provided. The method comprises determining if a current ratio of air to fuel is less than a saturation threshold. The method also comprises increasing the ratio of air to fuel if the current ratio of air to fuel is less than the saturation threshold.

The ratio of air to fuel may be increased by reducing an injected fuel mass flow rate.

The method may further comprise determining if the increase in the ratio of air to fuel has resulted in the current ratio of air to fuel being greater than the saturation threshold. In addition, the method may also comprise stabilising the injected fuel mass flow rate when the current ratio of air to fuel is determined to be greater than the saturation threshold.

The ratio of air to fuel may be determined in accordance with the following equation:

W- λ =— 1 14.22

^Wfuel

wherein λ is the ratio of air to fuel, w_ie is the injected air mass flow rate, and Wf _ei is the fuel- mass flow rate.

The saturation threshold may be between 1.25 and 1.3. 1.25 may be the minimum value for the saturation threshold. However, it will be appreciated that other saturation values could be provided, which are outside the aforementioned range.

The method may further comprise measuring a current amount of fuel and a current amount of air being input into the combustion chamber prior to determining if the current ratio of air to fuel is less than the saturation threshold.

Also, the method may further comprise receiving information relating to a current amount of fuel and a current amount of air being input into the combustion chamber prior to determining if the current ratio of air to fuel is less than the saturation threshold. In addition, the method may further comprise determining the current ratio of air to fuel being input into the combustion chamber in accordance with the current amount of fuel and the current amount of air being input into the combustion chamber.

According to a further aspect of the invention a combustion controller is provided. The combustion controller is arranged to perform, in use, any of the various method steps disclosed above.

According to yet a further aspect of the invention an engine system is provided. The engine system comprises a combustion chamber. The engine system also comprises a fuel injector for inputting fuel into a combustion chamber. In addition, the engine system comprises an inlet manifold for inputting air into the combustion chamber. Furthermore, the engine system comprises the combustion controller disclosed above. The combustion controller may be arranged to control the fuel injector to increase the ratio of air to fuel being input into the combustion chamber.

A feedback loop may be provided to enable the fuel injection controller to monitor the amount of fuel injected.

The air- fuel ratio may be the ratio of air to fuel input into a combustion chamber. The fuel may be injected into the combustion chamber. The combustion chamber may be a combustion chamber of a diesel engine.

According to another aspect of the invention a computer readable medium is provided. The computer readable medium comprises a computer readable code operable, in use, to instruct a computer to perform any of the various method steps disclosed above.

Embodiments of the invention provide a SCS which performs an off-line optimization to maximize the efficiency of the powertrain and which is stored as a map to be accessed at low computational cost during driving without the need of further processing.

Embodiments of the invention provide an SCS that has been developed and tested on a dynamic vehicle model which allows the analysis of operation during complex transient behaviour. This platform is utilized to achieve more robust design as well as to assess stability. Embodiments of the invention provide an SCS developed for a dynamic model of a series hybrid electric vehicle. The powertrain steady-state behaviour may be analyzed to produce a control map offline which maximizes the vehicle energy efficiency for any driving condition. This map can be accessed on a real-time basis during driving at low computational cost to locally optimize efficiency. The vehicle transient response may be considered to ensure efficient, stable and healthy operation. Simulations using standard drive cycles verify that the designed Efficiency Maximizing Map (EMM) control allows smoother operation of the powertrain and it brings reductions in fuel consumption as compared to a Thermostat control scheme.

Embodiments of the invention provide a comprehensive model of a series hybrid electric vehicle which is used to develop and test a SCS. An off-line optimization can be performed to produce a control map which allows the EMM control system to perform local maximization of efficiency of the powertrain on a real-time basis without the need of any further processing during driving. This optimization relies on analysis of the individual efficiency maps of the PS and SS.

Embodiments of the invention help to reduce exhaust emissions.

Aspects of the invention provide a means for optimising the efficiency of a vehicle, and more specifically a HEV. Such optimisation may be achieved by determining the most efficient ratio of usage of a primary and a secondary power source, in addition to a most efficient speed for an engine of the primary power source. The optimisation may be repeated across a range of powers associated with the power source. From this optimisation process, a map providing information indicative of an optimum power share factor between the primary and secondary power source and the engine speed of the primary power source may be provided. This optimisation map can then be used by a HEV to determine what power source operating characteristics to use at different required output powers. The optimisation map is therefore a means for controlling the operation of the power source.

Other aspects of the invention provide a means for optimising the efficiency of a vehicle, and more specifically a HEV, but achieve this optimisation in a different way to the previously described aspect. In particular, a determination may be made as to the amount of fuel being injected into a combustion chamber relative to the amount of air being injected in the combustion chamber. If the amount of fuel being injected is too high, due to, for example, the ratio of air-fuel being below a threshold, then the amount of fuel being injected may be reduced. In respect of such other aspects, reference to "a power source" may refer to a power source of a HEV, which comprises a primary and secondary source of power, or may refer to a power source of another type of vehicle, such as a combustion engine of a car or such like.

It will be appreciated that the two different aspects of the invention described above may be utilised separately, or in combination.

Brief Description of the Drawings

Embodiments of the invention shall hereinafter be described with reference to the corresponding Figures, in which:

Figure 1 provides an overview of the architecture of a modelled series HEV;

Figure 2 illustrates Primary Source efficiency T|PS variation with power demand P_Ps and engine speed (%_¾ wherein data at unfeasible operating conditions is omitted;

Figure 3 illustrates Secondary Source efficiency r|_s as a function of power requested P_ss, for two different SOC values and v is chosen to be 1 ;

Figure 4 illustrates optimal total efficiency η_ίοί, given an optimal power share factor u_opt and engine speed ω_ΚΕ-ο_Ρί, as a function of power demanded by the motor-set P_M;

Figure 5 illustrates optimal power share factor u_opt and optimal engine speed (Oi_CE-_opt as a function of power demanded by the motor-set P_M;

Figure 6 illustrates speed profiles for the NEDC and FTP-75 drive cycles;

Figure 7 illustrates power time histories for PS, SS and motor-set using the Thermostat control for the EUDC drive cycle, wherein a velocity profile is also shown;

Figure 8 illustrates power time histories for PS, SS and motor-set using the EMM control for the EUDC drive cycle, wherein a velocity profile is also shown;

Figure 9 illustrates power transitions for SS and PS to meet power requirements of the motor-set for the EUDC drive cycle, wherein the velocity profile is also shown;

Figure 10 provides a comparison of total equivalent fuel consumption m_eq for FTP- 75, EUDC and NEDC using Thermostat control and EMM control;

Figure 11 illustrates efficiencies of a Primary Source at different operating conditions;

Figure 12 illustrates Secondary Source efficiencies for varying operating conditions, left side corresponds to ⁷1ss-charg* and right with Vss-charg* ;

Figure 13 illustrates a power share factor for varying power requirement and correction factor v, wherein the SOC level is constant at 65%;

Figure 14 illustrates a total efficiency as a function of power requirement and correction factor v, wherein the SOC-levels are fixed at 65%;

Figure 15 illustrates an engine speed as a function of power requirement and correction factor v, wherein the SOC-levels are constant at 65%;

Figure 16 illustrates a power share factor for varying power requirement and SOC level, wherein the correction factor v is constant at 0.45;

Figure 17 illustrates a total efficiency as a function of power requirement and SOC- levels, wherein the correction factor v is fixed at 0.45;

Figure 18 illustrates a charge sustaining factor, as a function of SOC, to ensure charge is sustained around 65%, but most importantly, is constrained within the range 50 to 80%;

Figure 19 illustrates a power share factor for varying power requirement and SOC level, wherein the Correction factor v is constant at 0.45;

Figure 20 illustrates a total efficiency as a function of power requirement and SOC- levels, wherein the correction factor v is fixed at 0.45;

Figure 21 illustrates an integration of turbocharged diesel engine subsystems and speed control scheme; and

Figure 22 illustrates a fuel amount control unit with implementation of the non-linear saturation feedback control for the relative air-fuel ratio λ. Specific Description

A first exemplary embodiment of the invention shall now be described.

HYBRID VEHICLE MODEL

The SCSs are designed and simulated based on a novel dynamic vehicle model, of which the details can be found in S. A. Evangelou and A. Shukla, "Advances in the modelling and control of series hybrid electric vehicles", Amer. Control Conf, June 2012. Its overall architecture is presented in Fig. 1. The model provides an accurate description of a series HEV in Simulink, including consideration for transient behaviour. For the purposes of the presented work, a start-stop system has been introduced, allowing a reduction of idling losses for the HEV engine.

The powertrain contains a Permanent Magnet Synchronous Motor (PMSM) connected to a three-phase inverter which is driven by a Primary Source of energy (PS) and a Secondary Source of energy (SS). The PS consists of a turbocharged 2.0L diesel engine and a Permanent Magnet Synchronous Generator (PMSG) connected to a three-phase rectifier. The SS consists of a lithium-ion battery connected to a bi-directional DC-DC converter. The motor-set (PMSM and inverter), the PS and the SS are all connected to a DC bus where the power transfer occurs. In the case of regenerative braking, the PMSM behaves as a PMSG to capture the energy from the wheels and convert it to electric energy, and store it into the SS.

POWERTRAIN EFFICIENCY ANALYSIS

The aim of the SCS is to provide the motor-set with the required power at all times in the most efficient way. To this end, we need to understand the performance of the available energy sources in order for the SCS to determine the optimal mode of operation for the powertrain.

Performance of Primary Source of Energy

From an operation point of view, the key variables of the PS are the speed and torque of the internal combustion engine (ICE). To investigate the impact of these variables on the PS efficiency for any given power demand, a test-model is prepared. The function of the model is to load the PS with a varying amount of power (and corresponding torque) for a certain engine speed and measure the generated energy as well as the fuel consumed. The efficiency can then be expressed as in equation 1 , where E_PS is the total energy generated by the PS for a time period in steady-state operation; wif_uei is the total mass of fuel consumed for the same time -period; and L is the specific latent heat of the fuel.

Equation 1

The series of tests are performed over the range of power demands from 5 kW to 70 kW in 5 kW increments and engine speeds from 1200 rpm to 2400 rpm in 200 rpm increments, giving a total of 98 tests. The results are shown in Fig. 2. The region of investigation has been limited to this range of engine speeds due to the fact that the engine model has only been validated for such a limited range. Furthermore, within this range of operation there are points (low engine speeds but high power demands) which are not operationally feasible, and have thus been omitted as well.

The data shows that the PS operates at its optimal efficiency at an engine speed of 1600 rpm and power demand of 25 kW. It is also worth noting that the optimum engine speed is approximately constant at 1600 rpm for power demands in the range of 15 kW to 35 kW, which covers most of the commonly used range of the PS for standard drive cycles.

Consequently, it is expected that the SCS developed based on this data will tend to operate quite often at this engine speed, while other engines might have a more varying optimal engine speed.

Performance of Secondary Source of Energy

Strictly speaking, the SS is not used as an energy source, but rather as an energy buffer. All the energy supplied by the SS, ultimately originates from either the PS having charged the battery directly or through regenerative braking. It is therefore not possible to express the efficiency as an instantaneous function given by a ratio of power input and output as in the case of the PS. The efficiency can instead be defined according to the energy ratio across a charge-discharge cycle, as shown in equation 2. However the resultant efficiency is dependent on the nature of the chosen charge-discharge cycle. ^"^SS-charge-discharge ~ ^discharge ' charge

Equation 2

To obtain an efficiency map for the SS a test-model is developed to charge the SS with constant power (Ragone test) until the state of charge (SOC) has increased by 5%. Thereafter the flow of constant power is reversed, so the SS is loaded until the SOC reaches its initial value. Upon completion the total discharging energy and charging energy are measured, to obtain the efficiency as defined in equation 2.

This procedure is repeated for a range of initial SOC values from 50% to 75% in 5% increments and for power demands from 2 kW to 20 kW in 2 kW increments. The data of these 60 tests are then processed to obtain the efficiency at each operating point. The results are presented in Fig. 3. The main variable affecting the efficiency of the SS is its power output, while the effect of SOC is quite marginal in this range. It is also clear that the SS performs best at lower loads.

The fact that the SS is more of a buffer than an actual energy source raises the question of the associated cost of SS usage. The energy of the SS always originates from either direct charging from the PS or through regenerative braking. To consider these different scenarios we introduce a new variable v, which corresponds to the average efficiency of the charging of the SS. In the case of only regenerative braking we have v=\ as the energy received by the SS is essentially free. However, if all the energy of the SS was charged by the PS at its optimum point, we would have v=0.36 (obtained from Fig. 2). The overall efficiency of the SS, in its useful form, can therefore be expressed as follows in equation 3.

Equation 3

Efficiency Maximizing Map (EMM) Generation

The operating conditions at any time of driving are defined by the engine speed ICE and the power share factor u, as defined in equation 4 and related to Pss by equation 5, where P_M is the power required by the motor-set. With the possession of efficiency maps r ss and r_Ps, the total efficiency rj_tot can be formulated as shown by equation 6. u = P ps I P, M

Equation 4

Equation 5

= (l-u)-i]ss(Pss(u), SOC, v) + u-T)p_S(Pps(u), ω_1€Ε)

Equation 6

Consequently, the optimal operating conditions u_opt and ω icE-_opt can now be found such that r|_tot is maximized. However, this optimization is computationally intensive, and would require significant processing capabilities on the vehicle to implement on a real-time basis. It is preferable to perform offline processing of the efficiency maps of the two energy sources to obtain a single efficiency maximizing control map, such as shown in equation 7.

[⁽i)lCL-opr, Uoptl = EMM(P , SOC, v)

Equation 7

Since off-line computational time is not an obstacle, a simple iterative algorithm is compiled to compute the total efficiency η_ίοί at all feasible operating points, for all possible power share factors u. The efficiency maps for all u values are combined, selecting the highest efficiency points and noting the associated u_opt and ω icE-_opt to produce the optimal efficiency map shown in Fig. 4.

The implementation presented in this paper has made a few simplifications. The dependence on SOC is negligible in our particular model (as shown in Fig. 3), so for the purposes of the control it is considered to be 65% constantly. Also, the correction variable v has been assumed to be constant at 0.5. It has very slow dynamics, and it isn't worthwhile to vary it over short durations, such as the standard drive cycles. However, for real-life driving, a realtime estimation at low computational cost will be required for this variable. Hence, using the control map, the optimal power share factor u and the optimal engine speed can be directly obtained as a function of P_M, as is illustrated in Fig. 5. As mentioned above, the optimal engine speed remains 1600 rpm for a majority of the operating region. SUPERVISORY CONTROL SYSTEMS

The concept and foundation of the EMM control has been established already, but this section describes its implementation and introduces the Thermostat control which will function as a benchmark SCS against which the performance of this aspect of the invention can be compared.

Efficiency Maximizing Map Control

The control map which has been presented above is integrated into the SCS to operate in realtime. It is able to choose the optimal power share factor u_opt and optimal engine speed ω icE-_opt for any given power demand. This control map is implemented into the Simulink model using an embedded Matlab function, and thus a real-time local maximization of efficiency is attained throughout the drive cycles tested. Some minor additions are made to accommodate regenerative braking. Also, the rate of change of the power share factor u is limited to avoid sudden surges putting engine stability at risk.

Thermostat Control

The Thermostat control strategy (also called On-off control) is a simple, robust SCS which achieves a good fuel economy. It is thus a suitable benchmark for the EMM control. The basic principle is to run the PS at its optimal point and have the SS act as an equalizer, as specified in equation 8.

Equation 8

The ability of the SS to absorb energy is limited to -Pss-Max- For our particular vehicle PSS-M_OX is smaller than Pps-_opt and the SS risks being overcharged by the PS during operation at low loads of PM. For this reason, an additional rule is included to have the SS power the motor-set for P_M < (P PS-opt - PsS-Max)-

This mode of operation is valid while the battery SOC is within set limits. The upper limit of SOC in this case has been chosen to be 80% to allow a buffer for regenerative braking, as well as avoid very high SOC that accelerates degradation of the battery. Similarly a lower limit of 50% is chosen to limit the depth of discharge to 30%>, as it is exponentially related to battery degradation. Also, delays have been introduced to avoid oscillations and ensure stable transitions. If operation reaches these limits, the SCS switches into PS-only mode or SS-only mode, for minimum- and maximum-limit respectively.

RESULTS

Power Profiles

Simulations are run for three different drive cycles. The FTP-75 is an American high-speed urban drive cycle, the EUDC is a European highway drive cycle and finally the NEDC offers a combination of European urban and highway driving. The speed profiles of FTP-75 and NEDC are shown in Fig. 6. Note that the period from 780 seconds to the end of the

NEDC drive cycle corresponds to a EUDC drive cycle. This range of drive cycles are chosen to test the SCSs under varying conditions of driving.

The EUDC drive cycle shows most clearly the fundamental mode of operation of the SCS, so only results of this drive cycle are presented here. Fig. 7 and Fig. 8 illustrate the power time histories for the PS, SS and motor-set together with the vehicle velocity for the Thermostat and EMM control respectively.

The key characteristic of the Thermostat control is the sharp transition profile for the PS power, which is persistently operated at its optimum point. The SS power on the other hand varies from negative to positive to balance the difference between the motor-set power and the PS power. It is also worth noting the early switching in the drive cycle, due to the additional rule discussed above. The EMM control on the other hand has a smoother profile in general where the power is typically split between both the PS and the SS. The extent to which the PS powers the motor is determined by the control map which clearly varies throughout the cycle.

Transient Behaviour

It is evident from Fig. 7 and Fig. 8 that there is a significant difference in the nature of the two control strategies. The Thermostat control involves a significant number of sudden spikes and drops in both P_PS and P_ss. This behaviour of extreme loading is strenuous on the engine as well as the battery.

Whenever the PS is switched on it is required to suddenly boost its power output while increasing its engine speed. Equally, when the load is suddenly removed from the PS it will cause the engine speed to spike which is undesirable from an efficiency, stability and health point of view. A comparison of the engine speed profiles for the PS for both of the control strategies reveals indeed up to 1.5% deviations from steady-state in the case of the Thermostat control compared to around 0.1 % deviations for the EMM control. Similarly, it is not healthy or efficient for the battery either to have a sudden onrush of power demand or supply. The stability of the DC-bus of the vehicle has also been studied, and similar improvements of transient operation have been observed.

The transient issues for the vehicle model used to be more severe, causing the PS to occasionally fall out of operation under tough but plausible conditions. However, these were addressed through the implementation of predefined limits on rates of change of PS power. So, as power demand spikes, the SS temporarily takes on the load (as it has significantly faster dynamics) to allow the PS the time it needs to meet the demand without risking stability of operation. This is shown in Fig. 9 and is one example of where the transient dynamics of the vehicle model allows the design of more robust SCSs.

Fuel Economy

Simulation results for fuel consumption nif_uei and final SOC are presented in Table 1 for the FTP-75, EUDC and NEDC drive cycles. However, it is not apparent which of the two SCS has the better fuel economy. To perform a useful comparison it is necessary to unify the two variables under the same domain, and the Equivalent Fuel Consumption (EFC) methodology is an established one. The fundamental principle is that the shortage/surplus SOC (any deviation from initial value) is expressed in terms of an equivalent mass of fuel m_eq. The developed EFC is based on the efficiency analysis presented above, but is not critical to the principle or design of the SCSs. The resulting m_eq values for each drive cycle are presented in Fig. 10.

TABLE I. FUEL ECONOMY COMPARISON

It is evident from the comparison in Fig. 10 that the EMM control offers lower fuel consumption (reductions in the range of 8.5-14.7% for chosen drive cycles) as compared to the Thermostat control. As the highest improvement is seen for the NEDC drive cycle (both urban and highway) it can't be asserted that the EMM control is more suitable for a particular type of driving.

It should be noted however, that for this set of drive cycles the Thermostat control always finishes on surplus SOC, while the EMM control always finishes on a shortage of SOC with respect to the initial value. As such, the fuel economy data is susceptible to bias from the precision of the EFC calculations. To reduce this effect, simulations are also run for consecutive drive cycles, to capture long-term impact of the control strategies when the net change in SOC becomes close to negligible, relative to total fuel consumption. Thus, the present results are sufficient to indicate an improvement in fuel economy.

A further aspect of the invention shall now be described. The further aspect shares many similarities with the previously described aspect, and as such only the differing features shall be described in detail.

The basic principle of this aspect of the invention is as follows: generating efficiency maps for the power sources to perform offline computation to obtain optimal power share between the power sources. Key additions to the previously described aspect include: consideration of idling losses for engine; alternative approach to model battery efficiencies; new equation for total efficiency to be maximized; capability for optimisation algorithm to consider cases of engine producing surplus power to charge the battery; and a charge sustainer or charge sustaining factor to ensure that battery SOC levels are maintained within desired limits. These features shall therefore now be described in detail.

PRIMARY SOURCE EFFICIENCY MAP

New results which are more detailed have been obtained for the Primary Source. In addition to providing an improved data resolution, there are two key differences from the previously described aspect of the invention.

Firstly, the engine -model is changed to include a constraint on the air-to-fuel ratio, to limit the amount of emissions. This constraint becomes active, and limits the power output of the engine, explaining the large gap of data on the upper left corner of Figure 11. Secondly, data has been included for zero output power, corresponding to idling losses. While the previous work relied on a Start-Stop system to avoid consideration of idling losses, the following work is capable of considering these losses. The loss is defined by the power loss associated with the fuel consumed to overcome frictional losses while idling, as specified in equation 9:

Equation 9 where ^ηι 'α*ϊ is the fuel rate consumed by the engine and LHV is the Low Heating Value of fuel.

Equation 9 is used to obtain the efficiency for the PS, as shown in Figure 1 1 (Pps-m is mapped as well but not shown).

SECONDARY SOURCE EFFICIENCY MAP

The battery model used is still based on the model from the Simulink library. The characteristics are almost identical as in the previous aspect, but a previously included saturation limit has been removed. The purpose of the past constraint was to avoid overloading the battery. In this embodiment of the invention the removal of the saturation limit means that the battery can now deliver power up to around 50 kW (although at a reduced efficiency) compared to the previous 20 kW.

As discussed in respect of the previous aspect, it is not straightforward to define the efficiency of the battery as it is really an energy buffer rather than an energy source. Consequently, the approach of performing Ragone tests to obtain cycle-efficiencies for the battery was used.

In the present aspect of the invention, a new approach has been adopted. It has not been assumed that any discharge of X kW is associated with a charging of X kW. The battery can be charged at 1 OkW and later be used at 20kW. It is in fact very unlikely that charging and discharging levels are matched during driving. Rather than attempting to express the full efficiency of the battery at once, the problem is separated into obtaining charging and discharging efficiencies separately. The cause of the losses is the deviation of voltage level of battery. The State of Charge (indicator for how "full" the battery is) measures current flowing in and out of the battery. Thus, if there is a discharge of 1 OA for 1 second and then a charge of 10A for 1 second there will be a net change of zero in SOC. The important question is what the voltage level was. If the charge is carried out at 300V but discharged at 200V then 3 kW has been charged but 2kW has been discharged, without any gain in SOC. So the losses can be quantified according to the deviation in voltage relative to the open circuit voltage of the battery, as shown in equation 10:

Equation 10

Note that the efficiency above only considers the battery. To obtain the full efficiency of the SS, also considering the losses in the DC-DC converter, equation 11 is used:

bat

Equation 11

Similarly, the efficiency can be obtained for the charging of the battery (voltage increase beyond the open circuit voltage for negative current flow) as shown in equations 12 and 13:

_ Pss-in (Pss> SOC) _ Vbat-OC ' hat _ Vbat-OC

Vbat— charge _D 1/ r 1/

vv ^vbat ^" ' bat ^vbat

Equation 12

_ P SS-in (¾> SOC) _ Vbat -PC ^' hat

ss— charge ~ _D ^— _τ/ τ

SS ^v DC-link 'DC-link

Equation 13

Based on above definitions (Pss-m is mapped as well but not shown here), simulations are run to obtain the data presented in Figure 12.

This approach brings three particular benefits:

1. As mentioned, it avoids the artificial connection between charging and discharging power levels, by not needing to measure cycling energies; 2. It allows more appropriate real-time estimation of the correction factor v, which was assumed to be 0.5 for the previously; and

3. It allows the optimisation map to instruct the PS to charge the SS.

The second point is discussed in respect of the previous aspect, and some further details will be presented later in the discussion of this aspect of the invention.

In respect of the third point, optimisation in the past has (implicitly or explicitly) constrained the optimisation for only positive values of power delivered by the SS. However, with the efficiency map of this aspect, the optimisation map can take into consideration cases where we deliver 15 kW by the PS, even though the motor only requires 10 kW, to let 5 kW be stored in the SS. Such operation could be beneficial as operating PS at 15 kW could be significantly more efficient than 10 kW. This is particularly relevant now when we are also considering the idling losses of the PS.

EFFICIENCY MAXIMISING MAP GENERATION

The basic principle and expressions remain the same as in the previous aspect of the invention (see Equations 4 and 5). However, there is a need to redefine the total efficiency of the system, as we now have to also consider the idling losses of the engine, when operating the SS alone. In terms of the PS and SS-efficiencies, the overall efficiency can be expressed as specified in equation 14:

Equation 14

However, as we will obtain efficiencies of zero, information about input power in the above expression is lost, which is why it is more appropriate to implement it as specified in equation

15:

Equation 15 When implemented, however, the discharging efficiency has to be modified to account for the correction factor v. So during the optimisation, it is checked whether Pss-_m is positive or negative to choose the discharging or charging efficiencies respectively, according to equations 16 and 17:

¾

rPS-in \^rPS> ^ωΐ€ε) 7,

Equation 16

hot c^harge P_ps__in(P_ps, ω_ΚΕ) + SOC)

Equation 17

Note that the Pss-_m (Pss, SOC) is a negative quantity in the case of charging. To

these efficiencies the minimisation problem shown by equation 18 is utilised: for P_ss≥ 0

for P_ss < 0

Equation 18

To perform the above optimisation, the following variables are influential: P_PS, ^ωιοε, P_Ss, SOC and v. From these, P_Ps and Pss can both be jointly defined by the power share factor u and the motor power P_M as defined by equation 4 and 5. From these five variables, three are given (P_M, SOC and v) and two are decision variables (u and ^ωπε ). Thus, the solution obtained by solving the optimisation defined in equation 18, is a set of u and ^ωκε such that efficiency is maximised, given the values of P_M, SOC and v. This can be expressed as shown in equation 19:

EMM: {u_opt, ω_ΚΕ→ρί] = f(P_M, SOC, v)

Equation 19

Preliminary results have been obtained for the control map, based on above data and calculations. Figure 13 shows varying SOC-levels and their impact on the optimal power share factor u. Note that the control chooses a power share factor larger than one for low power levels. This allows the PS to operate at a more efficient region rather than simply wasting fuel on idling losses. A closer look on the efficiency levels realised through the above control is presented in Figure 14.

The selection of the optimal engine speed selection can also be considered. Figure 15 shows the engine speeds corresponding to above results.

Similarly, plots are obtained for varying SOC-levels. Power share factor variations are shown in Figure 16 and efficiency values are shown in Figure 17.

CHARGE SUSTAINING FACTOR

The EMM control has no inherent constraints in terms of SOC, so the battery could end up depleted or overcharged and permanently damaged. To address this, a charge sustaining factor k is included, which encourages the battery to be charged at low SOC values and encourages it to be discharged at high SOC values. This bias is introduced, by attaching a weight with the PSS-in as shown below in equation 20:

for P_ss > 0 for P_ss < 0

Equation 20

For k values larger than one, the SS discharging power (2nd term, 1st equation) becomes heavier, causing it to be less attractive to the optimisation algorithm. Simultaneously the SS charging power (2nd term, 2nd equation) becomes heavier, but since it is a negative quantity, it actually encourages further charging of battery (as we are aiming to minimise the function). Thus, a charge sustaining factor map can be produced, as shown in Figure 18.

It is clear from the map of Figure 18 that the lower values of SOC are associated with a value, encouraging the supervisory control to charge the battery, as discussed above.

Similarly, at high SOC values, the k value is low and thus encourages the battery to be discharged. There is a quite flat region around 65% where no modification is desired. The nature of the function can easily be adapted and tuned.

This charge sustaining factor is implemented and new maps are produced for optimal power share factor and efficiency in Figures 19 and 20 respectively. Clearly the power share factor is consistently higher for lower SOC (often larger than one) and quite low (often zero) for higher SOC. This charge sustaining factor is thus successful in maintaining the SOC within these thresholds. However it is clear from the efficiency plot that it comes at the expense of a decrease in efficiency in the case of extreme SOC values. However, arguably, it is better to suffer some reduced efficiency immediately rather than damaging battery or for that matter suffer heavy inefficiency later on.

Another aspect of the invention shall now be described. This aspect of the invention aims to improve the efficiency of a vehicle's power source, and in particular a combustion engine forming a part or whole of a vehicles power source.

TUBROCHARGED DIESEL ENGINE MODEL AND SPEED CONTROL STRATEGY

Figure 21 shows the subsystems of the engine and how they are connected together. In particular, Figure 21 shows the integration of turbocharged diesel engine subsystems and a speed control scheme. co_desired and co_eng are the desired and actual speed of the engine. w_&ei and w_ie are the mass flow rate of the fuel and air injected into the engine cylinder for burning, λ is the relative air-fuel ratio. T_ex and w_ex are the temperature and mass flow rate of the cylinder- out gasses. We; and w_xt are the mass flow rate of the gasses into the inlet and exhaust manifolds after leaving the compressor and turbine respectively, p;, T_;, p_x and T_x are the pressure and temperature of the inlet and exhaust manifold respectively. T_eng, T_fric,_eng, T_fric;gen, and T_ei_ec;gen is the indicative torque of the engine, engine friction torque, PMSG friction torque and electromagnetic torque of the PMSG, respectively. T_c and T_t are the torques applied on the turbo-shaft by the compressor and turbine, respectively. co_te is the rotational speed of the turboshaft. T_ci is the temperature of gasses at the output of the compressor. p_atm and T_atm are the atmospheric pressure and temperature. u_vgt is the vane angle for the turbine.

The engine shaft is mechanically connected to the rotor of a permanent magnet synchronous generator (PMSG) and their combined inertia is rotated by the action of the engine torque (T_eng) and opposed by T_fric,_eng, T _C,_gea, and T_elec,_gen. The engine torque is continuously adjusted so that the actual engine speed (co_eng) follows the desired engine speed (co_desired)- In a diesel engine, there are two parameters available for control of the generated torque: the injected fuel amount and the fuel injection timings. In the current mean-value modelling approach of the engine, all the in-cylinder effects are assumed to be evenly spread over the whole thermodynamic cycle and over all the cylinders without any discontinuity. Therefore, discrete fuel-injections are not considered and fuel injection timings are ignored. The only variable used here to influence the amount of torque generated by the engine is the air- fuel ratio λ which is given by λ =—— / 14.22 in which w_ie is the injected air mass flow rate and

^Wfuel

Wfuei is the fuel-mass flow rate. The turbocharger model calculates w;_e and the fuel amount control unit calculates Wf _ei (the "fuel injection" block in Figures 21 and 22 is a first order lag which represents the delay between the commanded value of Wf ei by the control unit, and the actual value of Wf _ei injected by the fuel injector valve). Therefore the only control variable used here to control the engine torque is Wf_uei. The control unit adjusts Wf_uei continuously so that the error between the desired (co_desi_red) and actual (co_eng) engine speeds becomes zero, codesired is set externally from the supervisory controller.

FUEL AMOUNT CONTROL UNIT

The fuel amount control unit is a proportional-integral-derivative (PID) controller with fixed saturation limits; it has a maximum positive value of 0.0026 and a minimum value of 5 x 10^"5 (ideally the minimum value should be zero but a small positive value is chosen to avoid numerical instability in our model in the torque calculation). The presence of a saturation in a closed loop in which an integrator is also present can cause integrator windup. In order to avoid this an integrator anti-windup scheme is included in the fuel controller as shown in Figure 22; the difference between the calculated fuel amount (before saturation) and the actual fuel amount (after saturation) is multiplied by a gain (Ka) and added to the integrator of the controller. The gain Ka is a tuning parameter of the controller. In the context of the present application the integrator windup problem can occur for example when the engine speed error becomes negative because of a sudden reduction in the engine load, as in the case of car deceleration. In that situation the PID controller will calculate a negative fuel amount, which is not physically possible, and the saturation will become active and limit the fuel amount to 5 x 10^"5. As a result the negative speed error will not be corrected and the integrator will start integrating a persistent negative speed error thus winding up. Once conditions are restored, for example when the engine speed error becomes positive again, for which the fuel amount should normally not be saturated, the value of the integrator state is large from the previous winding up and keeps the fuel amount saturated for an unnecessarily large amount of time.

CONTROL OF THE RELATIVE AIR-FUEL RATIO (λ)

When there is a sudden increase in the load on the engine, for example during hard acceleration the speed of the engine is switched by the supervisory controller from 800 rpm to 1600 rpm, the PID controller tries to burn a significant positive amount of fuel almost instantaneously. Diesel engines are mostly operated at lean conditions, otherwise there can be excess emissions leading to violation of emission constraints. When the temperature is high and the air-fuel mixture is too rich in fuel content, it leads to the formation of soot and visible smoke. To avoid such critical conditions, generally the fuel-air equivalence ratio is kept bellow a certain number (cpeq < 0.8). The fuel-equivalence (cpeq) ratio is the inverse of the relative air- fuel ratio as shown by equation 21.

1

λ = —

Since $_Eq < 0.8 then λ > 1.25

Equation 21

To enforce this condition on λ, a feedback control loop is designed similar to the anti-windup loop, as shown in Figure 22. The current value of λ is measured and compared with the minimum allowed value (although λ > 1.25 is sufficient, a more strict limit λ min = 1.3 is chosen); essentially the output of a one sided saturation is subtracted from the actual value of λ, then multiplied by a gain (KL) and finally added to the amount of fuel calculated by the PID controller. The idea is that if the constraint on λ is violated, the amount of fuel will be reduced to bring the value of λ back up to acceptable levels. The gain KL is a tuning parameter of the controller. This control scheme successfully maintains the value of λ > 1.3.

The various methods described above may be implemented by a computer program. The computer program may include computer code arranged to instruct a computer to perform the functions of one or more of the various methods described above. The computer may be arranged away from the vehicle for off-line computation, or integrated within the vehicle for real-time computation. The computer program and/or the code for performing such methods may be supplied to an apparatus, such as a computer, on a computer readable medium. The computer readable medium could be, for example, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, or a propagation medium for data transmission, for example for downloading the code over the Internet. Non-limiting examples of a physical computer readable medium include semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disc, and an optical disk, such as a CD-ROM, CD-R/W or DVD.

An apparatus such as a computer may be configured in accordance with such computer code to perform one or more processes in accordance with the various methods discussed above.

The aspects and embodiments of the invention discussed above are provided as examples only. Furthermore, the various aspects of the invention may be implemented separately, or in combination, where appropriate. It will be appreciated that the invention may be

implemented in various other ways and the scope of the invention is only limited by the scope of appended claims.

Claims

Claims:

1. A method for generating an efficiency control map for controlling a power source of a hybrid electric vehicle, the power source comprising a primary source of power and a secondary source of power, the method comprising: determining, for a plurality of operating powers of the power source, power source efficiencies associated with a plurality of different operating conditions of the power source; selecting, in accordance with the determined power source efficiencies, for each of the plurality of operating powers, an operating condition of the plurality of operating conditions providing an optimum power source efficiency; and producing, in accordance with the selected optimum operating conditions, an efficiency control map designating the optimum operating condition for each of the plurality of operating powers.

2. The method according to claim 1, wherein the different operating conditions comprise different power share factors between the primary source of power and the secondary source of power, and the optimum operating condition comprises an optimum power share factor.

3. The method according to claim 1 or claim 2, wherein the different operating conditions comprise different power source speeds, and the optimum operating condition comprises an optimum power source speed.

4. The method according to claim 1, wherein the power source efficiency is determined in accordance with the following equation: r _tot = (i~u)-r[_Ss(Ps,M, SOC, v) + u-i)ps(P_Ps(u), (£>_ICE) wherein η_ίοί is the total power source efficiency, u is the power share factor, r|_ss is the efficiency of the secondary source of power, P_ss is the power demand of the secondary source of power, SOC is the state of charge of the secondary source of power, v is the average efficiency of the charging of the secondary source of power, rj_PS is the efficiency of the primary source of power, P_PS is the power demand of the primary source of power and ( is the speed of the primary source of power.

5. The method according to claim 4, wherein the SOC is set at 65%.

6. The method according to claim 4 or claim 5, wherein the average efficiency of the charging of the secondary source of power, v, is updated in real-time.

7. The method according to claim 4 or claim 5, wherein the average efficiency of the charging of the secondary source of power v is set at 0.5.

8. The method according to any one of claims 4 to 7, wherein the efficiency of the primary source of power is determined in accordance with the following equation: wherein E_PS is the total energy generated by the primary source of power for a time period in steady-state operation, m_&el is the total mass of fuel consumed for the same period, and L is the specific latent heat of the fuel.

9. The method according to any one of claims 4 to 8, wherein the efficiency of the secondary source of power is determined in accordance with the following equation: ~ T sS-charge-discharge " V wherein the r|ss-charge-discharge is the efficiency of the charge-discharge cycle of the secondary source of power determined in accordance with the energy ratio across the charge- discharge cycle.

10. The method according to any one of claims 1 to 3, wherein the power source efficiencies are determined separately for a charging state and a discharging state of the power source.

11. The method according to claim 10, wherein the power source efficiencies are determined for a discharging state in accordance with the following equation: and for a charging state in accordance with the following equation: ¾

tot— charge - _Pps__{m (Pps}, + _Pss__{m (Pss}, SOC) wherein P_M is an operating power of the plurality of operating powers, P_ss is the power demand of the secondary source of power, P_PS is the power demand of the primary source of power, SOC is the state of charge of the secondary source of power, COKE is the speed of the primary source of power, P_Ps-m is the power used by the primary source of power, Pss-in is the power used by the secondary source of power and v is the average efficiency of the charging of the secondary source of power.

12. The method according to any preceding claim, wherein the optimum power source efficiency is determined in accordance with a minimisation algorithm.

13. The method according to claim 12, wherein the minimisation algorithm is:

mm P_PS__in(Pp_S, w_[CE) + - for P_ss≥ 0 u, V

mi" Pps-in iPps- ω/cfi) + P_SS-in (Pss> SOC) for P_ss < 0

P_PS≥ 0

Pl'S + $S ⁼ P M

50 < SOC ≤ 80

EMM: {u_opt, )_{IC →pt} ] = f(P_M, SOC, v) wherein u is the power share factor, u_opt is the optimum power share factor, P_M is an operating power of the plurality of operating powers, Pss is the power demand of the secondary source of power, P_PS is the power demand of the primary source of power, SOC is the state of charge of the secondary source of power, COKE is the speed of the primary source of power, (Oi_CE-_opt is the optimum speed of the primary source of power, P_Ps-m is the power used by the primary source of power, Pss-m is the power used by the secondary source of power and v is the average efficiency of the charging of the secondary source of power.

14. The method according to claim 12, wherein the minimisation algorithm is:

wherein u is the power share factor, u_opt is the optimum power share factor, P_M is an operating power of the plurality of operating powers, P_ss is the power demand of the secondary source of power, P_PS is the power demand of the primary source of power, SOC is the state of charge of the secondary source of power, COKE is the speed of the primary source of power, (OicE-_opt is the optimum speed of the primary source of power, P_Ps-m is the power used by the primary source of power, Pss-m is the power used by the secondary source of power, v is the average efficiency of the charging of the secondary source of power, k is the charge sustaining factor.

15. The method according to any preceding claim, wherein the power share factor, u, is determined in accordance with the following equation: wherein P_PS is the power of the primary source of power, and P_M is an operating power of the plurality of operating powers.

16. The method according to any preceding claim, wherein the efficiency control map is generated off-line.

17. The method according to any one of claims 1 to 15, wherein the efficiency control map is generated in real-time on-board the hybrid electric vehicle.

18. The method according to any preceding claim, wherein the plurality of operating powers covers a range of operating powers of the power source.

19. The method according to any preceding claim, further comprising operating the power source of the hybrid electric vehicle in accordance with the efficiency control map.

20. Apparatus for generating an efficiency control map for use in a hybrid electric vehicle, the apparatus operable, in use, to perform the method of any preceding claim.

21. A hybrid electric vehicle, comprising: a power source having a primary source of power and a secondary source of power; and a supervisory control unit arranged, in use, to perform the apparatus of any one of claims 1 to 19.

22. The hybrid electric vehicle according to claim 21, wherein the primary source of power comprises an internal combustion engine; and the secondary source of power comprises a battery.

23. The hybrid electric vehicle according to claim 21 or claim 22, further comprising an electric motor for driving the vehicle, the motor powered by the power source.

24. A method for air-fuel ratio correction in a combustion engine, the method comprising: determining if a current ratio of air to fuel is less than a saturation threshold; and increasing the ratio of air to fuel if the current ratio of air to fuel is less than the saturation threshold.

25. The method according to claim 24, wherein the ratio of air to fuel is increased by reducing an injected fuel mass flow rate.

26. The method according to claim 25 wherein the method further comprises: determining if the increase in the ratio of air to fuel has resulted in the current ratio of air to fuel being greater than the saturation threshold; and stabilising the injected fuel mass flow rate when the current ratio air to fuel is determined to be greater than the saturation threshold.

27. The method according to any one of claims 24 to 26, wherein the ratio of air to fuel is defined in accordance with the following equation:

W- λ =—^- 1 14.22

^Wfuel wherein λ is the ratio of air to fuel, w_ie is the injected air mass flow rate, and Wf _ei is the fuel-mass flow rate.

28. The method according to any one of claims 24 to 27, wherein the saturation threshold is between 1.25 and 1.3.

29. The method according to any one of claims 24 to 28, further comprising measuring a current amount of fuel and a current amount of air being input into a combustion chamber prior to determining if the current ratio of air to fuel is less than the saturation threshold.

30. The method according to any one of claims 24 to 28, further comprising receiving information relating to a current amount of fuel and a current amount of air being input into a combustion chamber prior to determining if the current ratio of air to fuel is less than the saturation threshold.

31. The method according to claim 29 or 30, further comprising determining the current ratio of air to fuel being input into the combustion chamber in accordance with the current amount of fuel and the current amount of air being input into the combustion chamber.

32. A combustion controller arranged to perform, in use, the method of any one of claims 24 to 31.

33. An engine system, comprising: a combustion chamber; a fuel injector for inputting fuel into the combustion chamber; an inlet manifold for inputting air into the combustion chamber; and the combustion controller of claim 32, wherein the combustion controller is arranged to control the fuel injector to increase the ratio of air to fuel input into the combustion chamber.

34. A computer readable medium comprising computer readable code operable, in use, to instruct a computer to perform the method of any one of claims 1-19 and claims 24 to 31.