Propulsion system for a vehicle, vehicle and method for predicting a pressure drop in a liquid hydrogen tank used therein during operation

Abstract

The invention relates to a drive system for a vehicle which is at least partially powered by hydrogen (H2), with a tank (1) for liquid hydrogen (H2) which has a tank heater (6), with an operating and consumption prediction module (10) which is configured to determine the required mass (consump vor ) to determine the amount of hydrogen (H2) needed to reach a driving destination, and with a control unit (12) for the tank heating (6). The drive system according to the invention is characterized in that a pressure prediction module (11) is provided and configured to determine a sampling mass (comsup). ges ) of hydrogen (H2) to achieve a desired target pressure (p End ) in the tank (1) upon reaching the destination, wherein the control unit (12) is configured to determine the required quantity (consump vor ) and the withdrawal quantity (comsup ges ) to compare with each other and in the event that the withdrawal quantity (comsupges ) greater than or equal to the quantity required (consumption) vor ) is to deactivate the tank heater (6) and in the event that the required quantity (consump vor ) greater than the withdrawal amount (comsup) ges The tank heater (6) is to be activated. Furthermore, the invention relates to a method for model-based calculation of the consumption quantity. ges ) in the pressure prediction module (11). The drive system can be used in a vehicle.

Description

[0001] The invention relates to a drive system for a vehicle according to the type defined in the preamble of claim 1. Furthermore, the invention relates to a method for predicting a pressure drop in a tank for liquid hydrogen used in such a drive system. Furthermore, the invention also relates to a vehicle with such a drive system.

[0002] DE 10 2020 004 202 A1 describes a method and a device for refueling a vehicle with liquid hydrogen. The core idea behind this application is to have the lowest possible residual pressure and, accordingly, the lowest possible residual amount of hydrogen in a liquid hydrogen tank upon reaching a filling station, in order to be able to fill the tank with the maximum amount of hydrogen as quickly as possible. WO 2023 / 025 566 A1 is similarly structured, emptying the tank in such a case by generating energy from the tank that can be used for other purposes and stored temporarily using hydrogen. Similar to the aforementioned document, a model-based approach is used here.

[0003] Determining and influencing consumption for such cases is also described in IN 2021 11 053 220 A and similarly in US 10 746 109 B2. For further prior art, reference can also be made to US 2019 / 0 203 886 A1 and US 2018 / 0 135 994 A1.

[0004] What all prior art documents have in common is that they predict a required quantity and, if necessary, adjust it to maintain a specific fill level in a liquid hydrogen tank at a specific time. None of these documents utilizes a prediction or verification of the actual pressure reduction. Thus, a specific target pressure cannot truly be controlled by estimating the potential consumption, for example, until a vehicle reaches its destination; rather, it can only be achieved randomly.

[0005] For further information on the state of the art, please refer to DE 10 2021 004 308 A1. This describes a method for planning vehicle usage in which a vehicle component is preconditioned.

[0006] Furthermore, DE 10 2022 114 781 A1 of the applicant describes a method for operating a fuel cell system.

[0007] The object of the present invention is therefore to provide an improved drive system that avoids the aforementioned disadvantages. Furthermore, the object of the invention is to provide a method suitable for a pressure prediction module in such a drive system for determining the required withdrawal quantity to achieve a target pressure.

[0008] According to the invention, this object is achieved by a drive system having the features of claim 1, and in particular in the characterizing part of claim 1. Advantageous embodiments and further developments emerge from the dependent subclaims. A method according to the invention is specified in claim 6. Here, too, an advantageous embodiment emerges from the dependent subclaim. Claims 8 and 9 also claim vehicles as a preferred application for such a drive system.

[0009] The drive system according to the invention is structured similarly to the drive system from the two prior art documents mentioned above. Essentially, it comprises an operation and consumption prediction module, which estimates the expected hydrogen demand for reaching a destination. This operation and consumption prediction module thus provides the required amount of hydrogen needed to reach the destination in the specified manner, for example, with a desired power trajectory, taking into account traffic conditions, geographical conditions, and weather conditions.

[0010] The drive system according to the invention further comprises a pressure prediction module which is configured and capable of precisely calculating the withdrawal quantity necessary to achieve a predetermined target pressure in the tank upon arrival at the destination, based on a detected current pressure in the tank and the fill level of the tank.

[0011] This pressure prediction module therefore makes a corresponding prediction of the required withdrawal quantity to reach the target pressure. Analogous to the already known designs from the prior art mentioned above, the target pressure should be as low as possible upon reaching the target location, for example, at a pressure of 4 bar. This is because such a pressure in conventional tanks, such as those used for storing liquid hydrogen in heavy commercial vehicles, is typically the pressure up to which corresponding consumers, such as a fuel cell system, can still be supplied with hydrogen from the tank.

[0012] This minimum pressure is ideal when parking the vehicle, as it allows the longest possible time until a so-called boil-off pressure is reached during a complete standstill. This boil-off pressure, which in the scenario described above is typically 15 bar, is the pressure at which hydrogen must be drained from the tank for safety reasons. The pressure increase in the tank is typically unavoidable when storing cryogenic liquid hydrogen, as heat flows through the walls and insulation of the tank over a longer period of several hours inevitably lead to heating and thus evaporation of the liquid hydrogen, which triggers the corresponding pressure increase.However, by using a minimum pressure when shutting down the drive system, it is possible to ensure that the time until the boil-off pressure is reached is as long as possible, so that in the drive system according to the invention, the hydrogen losses due to the boil-off can be avoided or at least greatly reduced.

[0013] Using a control unit configured to activate or deactivate the tank heater, the required quantity and the withdrawal quantity can now be adjusted to match each other. This allows the target pressure at the destination to be reliably achieved, thus ensuring maximum filling volume during a refueling or maximum downtime without boil-off. For this purpose, the control unit can deactivate the tank heater, for example, when the required quantity corresponds to the withdrawal quantity, to prevent further hydrogen from being unnecessarily evaporated. If the required quantity is higher, the tank heater can be reactivated – briefly – to adjust the quantities again.

[0014] Furthermore, according to a very advantageous embodiment, the control unit can be configured to increase the hydrogen consumption of the drive as needed, namely whenever the withdrawal quantity is greater than the required quantity. Such an increase in the hydrogen consumption of the drive is known in principle from the prior art mentioned above. In this case, the excess electrical power generated can, for example, be temporarily stored in a battery, used to generate compressed air, which is then temporarily stored in a compressed air tank, or the like.

[0015] According to an advantageous embodiment of the drive system according to the invention, the control unit is further configured to repeat the comparison of the required quantity and the withdrawn quantity and the resulting control of the tank heater at predetermined intervals from time to time or, more preferably, continuously. This enables continuous adjustment in order to achieve the target pressure at the end of the route, i.e., at the destination, as precisely as possible, which can ensure the longest possible downtime without boil-off.

[0016] According to an advantageous embodiment, the pressure prediction module itself can be configured to determine the withdrawal quantity up to the target pressure based on a model-based approach based on the current pressure and the current fill level. Such a model-based calculation offers the advantage that various scenarios that can occur in the tank and influence the withdrawal quantity up to the target pressure can be easily and efficiently considered.

[0017] The drive system according to the invention can comprise any type of drive that generates drive power from hydrogen. This can be, for example, an internal combustion engine, a gas turbine, or the like. The drive system should particularly preferably comprise a fuel cell system for converting the hydrogen into electrical drive power and a coupled high-voltage battery for temporarily storing electrical power. The high-voltage battery, where the term "high voltage" is defined in accordance with ECE 100R, can, for example, absorb excess power from the fuel cell system and buffer dynamic power peaks, which are difficult to implement in a fuel cell system with high dynamics and which would place extreme strain on the fuel cell system in terms of its service life. In addition, recuperation energy generated in the vehicle can be temporarily stored.This design is common in fuel cell systems, so it needn't be discussed further here. However, reference can be made to the two publications mentioned above.

[0018] The method according to the invention serves for the model-based calculation of a required withdrawal quantity from the tank for liquid hydrogen in the pressure prediction module in order to achieve a target pressure based on a current pressure and a current fill level at the destination or destination of a vehicle equipped and driven by the drive system. The drive system can be designed in one of the variants described above. The model-based calculation uses a transition function which, depending on the pressure and fill level, distinguishes a transition between a single-phase and a two-phase state of the hydrogen in the tank. This transition is crucial for the subsequent calculation because in a two-phase state there is greater compressibility due to the existing gas phase and the pressure reduction rates behave differently than in the single-phase state.Accordingly, the method according to the invention provides that, based on the current fill level, a transition pressure is determined from this transition function, which is present during the change of state. The current pressure is then compared with this transition pressure to determine whether a single-phase or two-phase state exists at the beginning of the pressure reduction. Accordingly, in the two-phase state, a single linear function is used, which, with a corresponding pressure reduction rate, can determine the pressure reduction and thus the withdrawal quantity up to the target pressure.Since the pressure reduction rate differs from that in the two-phase state due to the missing compressible phase in the single-phase state, in the event that the process starts in a single-phase state and later a two-phase state is present, a combination of a first linear function in a first sub-area and a second linear function in a subsequent second sub-area is used, wherein this second linear function has a different pressure reduction rate or gradient compared to the first linear function.

[0019] A very advantageous further development can provide that, in the case of a single-phase state at the beginning of the pressure reduction, an intersection point is first determined between the transition function and a linear function that depends on the current pressure, the current fill level, and a first pressure reduction rate. This intersection point then divides the first sub-range into the second sub-range and can simultaneously serve to determine the corresponding transition pressure in the sense described above and to determine the conditions occurring at the beginning based on the comparison of the transition pressure with the current pressure.

[0020] As already mentioned, such a drive system can now be used in particular in a vehicle, particularly preferably in a commercial vehicle, preferably a heavy commercial vehicle, and here again in a commercial vehicle or heavy commercial vehicle powered by a fuel cell system.

[0021] Further advantageous embodiments of the drive system and the method also emerge from the exemplary embodiment, which is described in more detail below with reference to the figures.

[0022] Showing: Fig. 1 a side view of a tank for liquid hydrogen; Fig. 2 a pressure drop above the withdrawal quantity; Fig. 3 a pressure drop when hydrogen is withdrawn above the filling level; Fig. 4 a curve of the transition of the contents of the tank from a two-phase to a single-phase state of the tank contents in a pressure-level diagram; Fig. 5 a flow diagram of the model for predicting the withdrawal quantity up to a target pressure in a two-phase or single-phase state of the tank contents; and Fig. 6 a schematic representation of the most important components of a drive system according to the invention.

[0023] Fig. 1 shows the schematic structure of a tank 1 for liquid hydrogen H2 with a sampling line 2 and a capacitive level probe 3. In the tank 1 there is an internal tank pressure p Tank The contents of tank 1 consist of cryogenic hydrogen, which at a given time is in thermodynamic equilibrium as a liquid and gas phase, separated by the surface 4 of the liquid phase, shown schematically here. Fig. The setup shown in Figure 1 is intended to represent a test setup on a test bench, but its design is modeled after a tank 1 intended for heavy goods vehicles. In addition to a capacitive level probe 3, it also has a pressure measuring probe indicated by 5. Furthermore, a heating element 6 and a vibrating device 7 are provided. This serves to simulate the operation of the tank 1 on a road vehicle on the test bench. The vibrating device 7 sets the tank 1 and its contents in motion to prevent temperature stratification of the tank contents, similar to that in a moving vehicle.

[0024] Tank 1 is filled to a desired level Ivl and internal tank pressure p before each measurement run. TankThe pressure drop during hydrogen withdrawal should be measured over the widest possible pressure spectrum with as many different initial fill levels as possible. Therefore, 15 bar is chosen as the starting pressure and 4 bar as the target pressure. 15 bar is the boil-off pressure, i.e., the pressure at which gaseous hydrogen is released if the pressure continues to rise, and 4 bar is the lower limit of the tank's internal pressure p Tank , in which the extraction of hydrogen, for example, to power a fuel cell system, still functions relatively unrestrictedly. During continuous hydrogen extraction, the mass flow dm / dt and the pressure p must be continuously measured. In addition to the experimentally obtained data, data acquisition could also be carried out using AI. For this purpose, the pressure increase in the tanks 1 of vehicles in a test fleet could be independently monitored and systematized by the AI ​​or a neural network.

[0025] The mass flow is summed for the period in which a withdrawal from tank 1 occurs. The pressure drop Δp is then represented by the withdrawn mass, as shown in Fig. 2. The diagram of the Fig. Figure 2 shows the pressure drop Δp from a pressure p of 13 bar to 5 bar. A sudden change in the pressure drop rate x can also be seen, which is denoted by SP. At this intersection point SP, a gas phase forms in the upper area of ​​tank 1, which, due to its higher compressibility, has a direct influence on the pressure change behavior. At the same time, part of the liquid phase evaporates. The pressure drop rates x vary depending on the fill level and must therefore be systematized. Fig. The diagram shown in Figure 3 shows such a systematization in the two-phase area.

[0026] Similar systematizations must also be performed for the pressure drop rates x for single-phase tank contents. Since the drop rates are approximately linear, the average of the initial fill level and final fill level can be used for systematization during withdrawal. The pressure drop rates for each fill level Ivl and pressure p can then be stored in a 3D map. Consequently, with each gram of hydrogen withdrawn, the fill level Ivl, the pressure p, and also the pressure drop rate x change.

[0027] This results in a prediction approach for the pressure reduction. To predict the pressure reduction, the pressures p SP and fill levels IvI SPin tank 1, which require a transition from the two-phase to the single-phase state in tank 1. These points can be determined via the total density of the tank contents using the material properties of (para-) hydrogen and plotted in a diagram as a quadratic - hereinafter referred to as the transition function f Phase This is shown in Fig. 4 shown.

[0028] Since temperature stratification does not occur in tank 1 during vehicle travel due to the movements, these values ​​can be used in practice. In the next step, the intersection point of a pressure drop line f1 with the transition function f Phasebe determined. Here, too, the pressure curves determined by measurements are presented as functions in a matrix. A distinction is also made according to the number of phases occurring in tank 1 at the current time. Since a high fill level Ivl and high pressure p can prevail in tank 1 even at the beginning of the pressure reduction, a transition of the cryogenic liquid hydrogen (H2) from its state as a single-phase cryogen to a state in the two-phase region with mass withdrawal can be observed here as well. This transition must be determined by a specific internal tank pressure p Tank at a specific fill level Ivl. Unlike a pressure increase, which is represented by functions with quadratic components, the decreases in the curves during pressure reduction are always approximately linear. Thus, there is a sudden transition without the formation of a curve.

[0029] Parallel to the pressure curves, data on the transition pressure p SP corresponding to the fill level Ivl in the system. These are located on the Fig. 4 shown transition function f Phase can be retrieved via their function and the current fill level Ivl in the scenario. In real operation, the fill level Ivl in tank 1 and the pressure p are retrieved and the data are compared with those on the transition function f Phase For the transition function f Phase used fill level IvI SP then a pressure value p fPhase (IvI akt ) is output. Depending on whether the output pressure value p fPhase (IvI akt ) below or above a measured current pressure p akt in the tank, the cryogen is in a single-phase or two-phase state. If the current pressure p akt below that determined via the transition function f Phase certain pressure p fPhase(IvI akt ), then the hydrogen H2 in tank 1 is in the two-phase region. If the current pressure p akt above the pressure p fPhase (IvI akt ), the hydrogen H2 is in a single-phase state and a separate data set must be used to determine the pressure drop rate x. Based on the current pressure value p akt , the current fill level IvI akt and the negative slope, a function f1 is generated. The negative slope is converted from the value in bar per kg to the unit grams per % fill level in order to subsequently determine the intersection point SP with the transition function f Phase From this transition onwards, the pressure reduction to the target pressure will occur at a lower pressure reduction rate x2 rate while maintaining the same withdrawal rate. If the cryogen is in a two-phase state at the initial time, the calculation starts at this point. As can be seen from the flow chart / logic plan of the Fig. 5. This contains the basic calculations and the case differentiation. Depending on the fill level Ivl, the corresponding pressure reduction rate x2 is taken from the database, which is used to determine the mass or quantity of hydrogen to be withdrawn (consump2) via the pressure difference dp2 required to reach the target pressure. Depending on the initial state, based on the number of phases in tank 1, the masses to be withdrawn (consump1 and consump2) are added.

[0030] The final result of the withdrawal quantity or total quantity consump ges of hydrogen H2 to be extracted is now compared with the quantity required for the remaining distance to be driven vor of hydrogen H2 from time to time or preferably continuously. If the two values ​​approach the consumption quantity ges and the required quantity consump vorto each other, the pressure can be raised to a level by targeted heating intervention, which allows the precise reduction of the internal tank pressure p Tank until the end of the journey without further operation of the tank heater 6. This essential function is explained in the last section of the description using the Fig. 6 will be described in detail.

[0031] When implementing pressure drop prediction, a case distinction should first be made. The two cases relate to the number of phases in the tank: Case distinction: Calculation of H2 extraction:{Case1:pact>pfPhase(|v|act),H2 at the beginning single-phaseCase2:pact <pfPhase(|v|akt),H2 zu Beginn zweiphasig Case 1: p akt >p fPhase (IvI akt )

[0032] If the current pressure p akt greater than the transition pressure p fPhase (IvI akt), which at the current fill level marks the transition to the single-phase state of the cryogen, the hydrogen is in a single-phase state. At the current fill level IvI akt The pressure drop rate x1 in bar per % of the fill level Ivl removed is known. This results in the starting pressure or current pressure p akt a linear function f1. We are looking for a function of the form: y=a*x+b

[0033] Where y is the pressure p, x is the level Ivl, and the constant a is given by the positive pressure drop rate x1. The desired constant b and the function f1 are given by: b=pact / (x1*|v|act) f1(|v|=p=x1*|v|+(pact / (x1*|v|act)))

[0034] It is now the intersection point SP of f1 and f Phase to determine the point in the diagram of the Fig. 4, which the function f1 is the curve of the transition function f Phase intersects. The function f Phasewas previously determined using material properties of (para-) hydrogen and is represented here for mathematical illustration by a quadratic function opening downwards: fPhase=−a*|v|2+b*|v|+c

[0035] The two functions f Phase and f1(IvI) are to be set equal to the intersection point SP and the level IvI present at this point SP to determine x1*|v|+(pact / (x1*|v|act))=−a*|v|2+b+|v|+c |v|SP=(√[4*a*(c−(pact / (x1*|v|akt)))+(b−x1)2]+b−x1) / (2*a)

[0036] Since f Phase Since it is a quadratic function, there are two intersection points. Due to the constant positive slope of f1(IvI), the intersection point with the higher level value should be used. The difference between the initial level IvI akt and the filling level at the transition to the two-phase state IvI SPis the amount of hydrogen removed in the single-phase state until a gas phase is formed consump1. consump1=|v|act−|v|SP

[0037] From the point of reaching IvI SP is calculated with a pressure reduction rate x2. The constant x2 was used for the level IvI SP experimentally determined in the two-phase region. From the new starting pressure p SP and the target pressure p End the pressure difference Δp2 results. pSP=x1*|v|+(pact / (x1*|v|act)) Δp2=pSP−pEnd

[0038] Based on the pressure reduction rate x2 and the pressure difference Δp2 up to the target pressure p End the mass to be removed consump2 is to be calculated as follows: consump2=Δp2 / x2

[0039] The total mass removed, which is also referred to here as the quantity removed, is: consumpges=consmp1+consump2 By substituting you get: consumpges=|v|akt−[(√[4*a*(c−(pakt / (x1*|v|akt)))+(b−x1)2]+b−x1) / (2*a)]+[x1*|v|SP+(pakt / (x1*|v|akt))−pEnd] / x2 Case 2: p akt < p fPhase (IVI akt )

[0040] In case 2, the tank contents are in a two-phase state at the beginning of the pressure reduction. Therefore, no intersection point determination with the transition function f Phase necessary and only one pressure reduction rate in bar per % fill level is used. The relevant pressure reduction rate was determined experimentally for the respective fill level IvI akt in a two-phase state and is denoted by x2, analogous to case 1. Starting from the current pressure p akt the pressure difference referred to as Δp2 up to the target pressure is determined as follows: Δp2=pact−pEnd

[0041] Furthermore, the calculation of the hydrogen consumption required for the pressure drop Δp2 is carried out analogously to case 1. ges : consumpges=(pact−pend) / x2 consumpges=(pact−pend) / x2

[0042] Fig. 6 now describes the actual prediction approach for controlling the pressure with the tank heater 6 and a power specification P vor to a fuel cell system 8.

[0043] A predictive operating strategy for a fuel cell vehicle, as described, for example, in the aforementioned DE 10 2020 004 102 A1, calculates an assumed energy requirement and an optimized power trajectory for the fuel cell system 8 in an operating and consumption prediction module 10 based on a forecast horizon 9. This can be converted into hydrogen consumption and integrated along the remaining distance to the destination, where either refueling or a longer downtime is planned. This hydrogen quantity is referred to here as the specified required quantity. vor It is required to achieve the performance target Pvor by the fuel cell system 8, as is known, for example, from the aforementioned document.

[0044] In addition to the basically known operation and consumption prediction module 10, the described structure also includes a pressure prediction module designated 11, which in the previously described sense calculates the withdrawal quantity consump ges to achieve the desired target pressure p End based on the current pressure p akt and fill level IvI akt This withdrawal quantity consump determined by the pressure prediction module 11 is then sent to a control unit 12 for the tank heater 6, indicated here outside the tank 1. ges supplied and also the required quantity consump determined by the operation and consumption prediction module 10 vor . The control unit 12 now controls the tank heater 6 of the tank 1 based on a comparison of these two quantities in order to, on the one hand, set the power P vorthrough the fuel cell system 8 and on the other hand to increase the internal pressure p Tank of tank 1.

[0045] If the predicted demand quantity consump vor with the calculated withdrawal quantity consump ges from the pressure prediction module 11, the tank heater 6 can be switched off. With the already evaporated hydrogen in the tank 1, the desired lower target pressure p End reached. If there are deviations, action can be taken. If the withdrawal quantity consump ges higher than the predicted demand quantity consump vor a slightly higher consumption of the fuel cell system 8 can be used for correction. The generated excess electrical power can be used for other purposes and / or stored in a known manner (see, for example, DE 10 2020 004 202 A1). However, if deviations occur where the consumption gessmaller than the predicted demand quantity consump vor If the hydrogen vaporized is insufficient to reach the destination, the control unit 12 must briefly activate the tank heater 6 to correct the problem.

[0046] Thus, the desired lower target pressure p End when parking or refueling the vehicle. This extends the time until boil-off and, with longer periods of inactivity, also the boil-off loss. In the case of refueling, the lower target pressure p End a larger filling quantity can be achieved in a shorter time with less H2 loss, as is already fundamentally known from DE 10 2020 004 202 A1.

Claims

[1] Drive system for a vehicle which is at least partially powered by hydrogen (H2), with a tank (1) for liquid hydrogen (H2), which has a tank heater (6), with an operation and consumption prediction module (10) which is designed to calculate a demand mass (consump vor ) of hydrogen (H2) to reach a destination, and with a control unit (12) for the tank heating (6), characterized by that a pressure prediction module (11) is provided and is designed to calculate a withdrawal mass (comsup ges ) of hydrogen (H2) to achieve a desired target pressure (p End ) in the tank (1) upon reaching the destination, wherein the control unit (12) is set up to determine the required quantity (consump vor ) and the withdrawal quantity (comsup ges ) and in case the withdrawal quantity (comsup ges ) greater than or equal to the required quantity (consump vor) is to deactivate the tank heating (6) and in case the required quantity (consump vor ) greater than the withdrawal quantity (comsup ges ) the tank heater (6) must be activated. [2] Drive system according to claim 1, characterized by that the control unit (12) is set up to compare the required quantity (consump vor ) and the withdrawal quantity (consump ges ) and the resulting control of the tank heater (6) at predetermined intervals from time to time or continuously. [3] Drive system according to claim 1 or 2, characterized by that the control unit (12) is further configured to, in the event that the withdrawal quantity (consump ges ) is greater than the required quantity (consump vor ) is to increase the hydrogen consumption of the drive. [4] Drive system according to one of the preceding claims, characterized bythat the pressure prediction module (11) is configured to determine the pressure reduction from the current pressure (p akt ) to the target pressure (p End ) model-based taking into account the filling level (Ivl) of the hydrogen (H2) in the tank (1). [5] Drive system according to one of the preceding claims, characterized by a fuel cell system (8) for converting hydrogen (H2) into electrical drive power and a high-voltage battery electrically coupled thereto for temporarily storing generated electrical power. [6] Method for model-based calculation of a required withdrawal quantity (consump ges ) from a tank (1) for liquid hydrogen (H2) in the pressure prediction module (11) in order to calculate, based on a current pressure (p akt ) and a current fill level (IvI akt) at a destination of a vehicle equipped and driven by a drive system according to claims 1 to 6, a pressure below the current pressure (p akt ) target pressure (p End ), for which a transition function (f Phase ) of the transition between a single-phase and a two-phase state in the tank (1) dependent on pressure (p) and fill level (Ivl), from which a value corresponding to the current fill level (IvI akt ) corresponding transition pressure (p fPhase (IvI akt ) is determined when the state changes, so that at a pressure above the transition pressure (p fPhase(IvIakt )) current pressure (p akt ) to a single-phase state at the beginning of the pressure reduction and at a pressure below the transition pressure (p fPhase(IvIakt )) current pressure (p akt) a two-phase state can be concluded at the beginning of the pressure reduction, according to which in the two-phase state the pressure reduction is set as a single linear function or in the two-phase state the pressure reduction is determined in a first partial area from a first linear function and in a second subsequent partial area from a second linear function with a different pressure reduction rate (x2). [7] Method according to claim 6, characterized by that in the case of the single-phase state at the beginning of the pressure reduction, an intersection point (SP) between the transition function (f Phase ) and a linear function (f1) depending on the current pressure (p akt ), current fill level (IvI akt ) and a first pressure reduction rate (x1), wherein the intersection point (SP) separates the sub-areas. [8] Vehicle with a drive system according to one of claims 1 to 5. [9] Vehicle according to claim 8 characterized by its training as a commercial vehicle, preferably as a heavy commercial vehicle.

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