DE102017201061A1 - Method for operating a hybrid energy storage system - Google Patents

Abstract

The present invention relates to a method for determining an optimized system behavior of a hybrid energy storage system (1) having at least a first energy store (2) and a second energy store (3) by determining an optimal adjuster (λ *), and an associated method for controlling a hybrid Energy storage system (1) comprising at least the first energy storage (2) and the second energy storage (3). In this case, based on a Hamilton function (H) associated with the energy storage system (1), the optimal adjoint (λ *) is calculated by solving an optimization problem. This is provided for controlling the hybrid energy storage system (1), whereby it can be dispensed with solving the optimization problem in this.

Description

State of the art

The present invention relates to a method for operating a hybrid energy storage system.

Technical systems, whose energy requirements are supplied by electrical energy storage devices, place different power requirements and energy requirements on the energy storage devices. Energy storage can be, for example, primary batteries, secondary batteries, fuel cells or double-layer capacitors.

In fuel cell vehicles, another electrical storage is often used to operate the fuel cell in an efficient workspace and to facilitate recuperation as well as to enable higher efficiency. For example, passive interconnections of batteries of different energy and power characteristics are known for increasing the performance. Furthermore, systems are known in which two electrical memories are coupled together via a DC / DC converter and thus enable different voltage levels and a more independent operation.

Here, these systems, when they couple, for example, fuel cell and battery or battery and double-layer capacitor together, called hybrid energy storage systems. For the special case that the system couples two secondary batteries together, the system is also called a hybrid battery storage system.

Current systems with a hybrid energy storage system usually use a simple control whose real-time implementation can be made with little effort. However, this control leads to suboptimal results in terms of possible goals over the operating time, such as in terms of energy efficiency.

For example, systems are known in which two memories are connected to a DC / DC converter and a simple current controller is used for load sharing. Also, hybrid battery control systems for use in plug-in hybrid vehicles are known, which are controlled with a rule-based controller or a filter.

For hybrid vehicles, approaches have already been presented which, using optimization methods, aim to minimize fuel consumption in a vehicle while driving. These are based on the mimimum principle of pontryagin and are often derived today in use in the vehicle by simplification and assumptions to the so-called Equivalent Consumption Minimization Strategy (ECMS).

Furthermore, an approach is known which also leads on the basis of the minimum principle of Pontryagin to a control of a hybrid energy storage system of a vehicle consisting of fuel cell and double-layer capacitor bank. The strategy minimizes hydrogen consumption and a double layer capacitor state of charge is maintained within a defined range.

In the DE102013014667A1 a control for a hybrid vehicle is disclosed. It is described a coupling of internal combustion engine and electric machine, wherein the electric machine is powered from the battery. It is based on the minimum principle of Pontryagin.

Disclosure of the invention

The method according to the invention for determining an optimized system behavior of a hybrid energy storage system having at least one first energy store and a second energy store by determining an optimal adjuster comprises executing a first iteration loop in a plurality of passes, wherein successive passes each have a possible adjoint associated therewith first iteration loop a second iteration loop is executed. The second iteration loop comprises determining each an optimal control variable for successive times of a predetermined period of time, the optimal control variable being a quantity describing an energy received or delivered by the second energy store and being determined based on a minimum of a Hamiltonian function , wherein the Hamilton function is associated with the energy storage system and depending on a modeled system parameter, the possible adjoint and a memory state of the second energy store, wherein the modeled system parameter is a parameter of the hybrid energy storage system to be optimized, and is determined according to a predetermined power profile, which is traversed by the energy storage system in the predetermined time period, and calculating a final storage state of the second energy storage, the second energy store after the predetermined period of time, if the energy absorbed or emitted by the second energy store was controlled in the predetermined period according to the respective optimum control variable. The method further comprises detecting whether the final storage state of the second energy storage calculated by the second iteration loops is within a predetermined interval and providing an optimal adjoint corresponding to the possible adjoint of the first iteration loop for which the final one has been detected Memory state is within the specified interval.

The method according to the invention for controlling a hybrid energy storage system comprising at least a first energy store and a second energy store comprises detecting a first input value and a second input value, wherein the first input value describes a precalculated value of an optimal adjoint and the second input value describes a deviation of a memory state of the second energy store from a reference memory state describes adapting the optimal adjuncts for a current memory state of the second energy store based on the first and second input values to determine an adapted adjoint, providing an energy target value describing an energy that is from the first energy storage and the second energy storage is to be provided together, and determining an optimal control variable based on the adjusted adjoint and the energy target value i the optimal control quantity is a quantity describing an energy received or delivered by the second energy store, and the optimal control variable is determined according to a Hamilton function associated with the energy storage system, the Hamilton function being dependent on a calculated system parameter, the adjusted Adjoint and the current memory state of the second energy storage is.

Thus, by the method according to the invention for determining an optimized system behavior of a hybrid energy storage system, a value of an adjoint optimized for a specific energy storage system is determined. The inventive method for controlling a hybrid energy storage system, this value is used to control this particular energy storage system. Although each of these methods is advantageous in itself, optimal control is achieved only by cooperating with these methods. By combining the method according to the invention, optimal control is provided. A mathematical term for an adjoint is Lagrange multiplier. A memory state is a state of the memory and thus describes a property of the respective energy store, which in particular has an influence on the system parameter to be optimized if it changes.

The optimal control serves the energy-optimal power distribution in a hybrid energy storage system, in particular a hybrid battery control system. In addition, the functionality is also given that the controller responds to a constantly emptying high energy storage part, which is formed by one of the energy storage, and can hold in the high-performance storage part performance.

Even if the real-time capable optimal control according to the invention is particularly advantageous for battery systems, it can be applied to any type of hybrid energy storage systems. So it is not absolutely necessary that one or both of the energy storage are electrical or electrochemical energy storage. An energy store may likewise be a mechanical energy store, for example a flywheel. Another conceivable energy storage as part of a hybrid energy storage system is a fuel cell.

The operation of a hybrid energy storage system requires a stored control. The method according to the invention enables energy-efficient control without being based on simple filter or control approaches. The determination according to the invention of a control value, that is to say of a control parameter, also enables a broad power maintenance of the hybrid energy storage system during operation.

The inventive method allow optimization of the energy storage system according to any system parameters. For example, the system parameter can describe a system loss, ie an energy loss, and the energy storage system can be operated particularly energy-efficiently become. In another example, the system parameter may describe system aging, and the energy storage system may be operated for a particularly long service life.

The inventive method for controlling a hybrid energy storage system is particularly advantageous because it can be performed in real time with low processing power. The inventive method for determining an optimized system behavior of a hybrid energy storage system is particularly advantageous because it can be performed without a physical presence of a corresponding energy storage system.

The dependent claims show preferred developments of the invention.

It is advantageous if the optimal control variable describes a current to be delivered by the second energy store, and / or the modeled system parameter is a modeled system loss, and / or the store state is a state of charge, the final store state being a final state of charge and / or the interval is a charging interval. Such a selection makes it possible to adapt the method for determining an optimized system behavior of a hybrid energy storage system to a battery system, the method being particularly suitable for minimizing a power loss of the battery system. Especially for battery cells with high internal resistance is a strategy that can minimize the energy losses in conjunction with a system solution, advantage. As a side effect, the process can lead to aging advantages in a hybrid energy storage system by the current rate relief of the high energy part. The minimization of the electrical losses, as they can be achieved by the method according to the invention, also leads to a reduced temperature development in the energy storage, which is caused, inter alia, by ohmic losses.

It is advantageous if the first iteration loop performs a bisection method to determine the possible adjoint. Thus, a number of passes of the first iteration loop can be minimized. In this case, the possible adjoint is determined in particular based on an interval bisection method or interval division method.

It is advantageous if, in determining an optimized system behavior of a hybrid energy storage system, the optimum control variable is determined in each pass of the second iteration loop by executing a third iteration loop, wherein successive passes in the third iteration loop each have a possible control value associated with it For each iteration of the third iteration loop, a value of the Hamiltonian function is calculated according to the possible control variable associated with the respective iteration of the third iteration loop and the possible control variable is determined to be the optimal control variable at which the value of the Hamiltonian function has a minimum value. In this way, the determination may be limited to a number of possible control values that can actually be processed and applied by a controller of the energy storage system. Such determination of the optimal control variable is also easy to implement and requires little computing power in one embodiment. Alternatively, it is advantageous if the determination of the optimal control variable takes place in each run of the second iteration loop by analytical calculation. As a result, a particularly accurate value for the optimal control variable can be determined.

Furthermore, it is advantageous if, in determining an optimized system behavior of a hybrid energy storage system, the predetermined interval is an interval around an initial storage state of the second energy store, which the second energy store has at the beginning of the predetermined period. In particular, the interval is a percentage deviation from the initial state of charge of the second energy store. In this way it can be defined which accuracy is sufficient in determining the adjoint.

It is also advantageous if, in determining an optimized system behavior of a hybrid energy storage system, the modeled system parameter is based on a DC resistance of the first energy store, a DC resistance of the second energy store, a power to be output by the energy storage system for the respective time according to the predetermined power profile and an efficiency of DC / DC converter, via which the first energy storage and the second energy storage are connected in the energy storage system, is determined. In this way, the modeled system loss can be approximated to an actual system loss of the energy storage system. Thus, a particularly precise determination of the optimal adjoint is made possible. In particular, the system parameter is a system loss of the energy storage system.

It is equally advantageous if, in determining an optimized system behavior of a hybrid energy storage system when calculating the value of the Hamiltonian function, an addition of the modeled system parameter takes place with a derivation of the storage state of the second energy store which has been multiplied by the possible adjoint. Such a formulated Hamilton function describes the system behavior of the hybrid energy storage system in a particularly precise manner.

It is advantageous if the memory state is a state of charge, and / or the energy target value is a current target value, and / or the optimal control variable describes a current to be delivered by the second energy store, and / or the calculated system parameter is a system loss of the hybrid energy storage system. Such a selection makes it possible to adapt the method for determining an optimized system behavior of a hybrid energy storage system to a battery system, the method being particularly suitable for minimizing a power loss of the battery system.

It is advantageous if, in the method for controlling a hybrid energy storage system, the calculated system parameter is dependent on a power loss of the first energy store and a power loss of the second energy store. In particular, it is advantageous if the calculated system parameter is further dependent on a power loss of an energy converter, via which the first energy store and the second energy store are connected in the energy storage system. The energy converter is preferably a DC / DC converter. The calculated system parameter can thus be calculated particularly accurately, which leads to a particularly efficient control of the hybrid energy storage system. The method can thus be optimized for minimizing the power loss. The system parameter is in particular a system loss of the energy storage system.

It is also advantageous if, in the method for controlling a hybrid energy storage system, the optimum control variable is determined by calculation. In this way, a value for the optimal control quantity is calculated and does not need to be provided in advance. Thus, no precalculated values need to be provided.

It is equally advantageous if in the method for controlling a hybrid energy storage system the optimal control variable is determined in a tabular manner, wherein a table is queried in which different combinations of values of the adjusted adjuncts and values of the current target value are each assigned an optimal control variable. In this way, a particularly responsive control of the hybrid energy storage system can be achieved.

In addition, it is advantageous if, in the method for controlling a hybrid energy storage system, the adaptation of the optimal adjacents takes place by means of a PI controller. Such a device is available at low cost and allows rapid execution of the method in real time.

It is particularly advantageous if the optimal adjoint, which is received as the first input value in the method for controlling a hybrid energy storage system, has been determined by the inventive method for determining a system behavior of a hybrid energy storage system. Thus, an optimal adjuvant, for example, can be determined at the factory and transmitted to a control device, by which the method for controlling a hybrid energy storage system is performed. This can be installed, for example, in a vehicle.

An apparatus for generating an optimal adjoint, which comprises a computing unit which is set up to carry out the method according to the invention for determining an optimized system behavior of a hybrid energy storage system, has all the advantages of the method.

A device for controlling a hybrid energy storage system, which comprises a control unit which is set up to carry out the method according to the invention for controlling a hybrid energy storage system, has all the advantages of the method.

list of figures

• 1 ein Schaltbild eines beispielhaften hybriden Energiespeichersystems,
• 2 ein Ablaufdiagram eines erfindungsgemäßen Verfahrens zum Bestimmen eines optimierten Systemverhaltens eines hybriden Energiespeichersystems gemäß einer bevorzugten Ausführungsform der Erfindung,
• 3 ein Blockdiagramm einer erfindungsgemäßen Vorrichtung zur Steuerung eines hybriden Energiespeichersystems gemäß einer bevorzugten Ausführungsform der Erfindung, und
• 4 eine erfindungsgemäße Vorrichtung zum Erzeugen einer optimalen Adjungierten.

Hereinafter, embodiments of the invention will be described in detail with reference to the accompanying drawings. In the drawing is:

• 1 a circuit diagram of an exemplary hybrid energy storage system,
• 2 1 is a flow chart of a method according to the invention for determining an optimized system behavior of a hybrid energy storage system according to a preferred embodiment of the invention,
• 3 a block diagram of a device according to the invention for controlling a hybrid energy storage system according to a preferred embodiment of the invention, and
• 4 a device according to the invention for generating an optimal adjoint.

Embodiments of the invention

1 shows a circuit diagram of an exemplary hybrid energy storage system. The energy storage system is a battery storage system 1 , The battery storage system 1 includes as a first energy storage a first battery 2 , The battery storage system 1 includes as a second energy storage a second battery 3 ,

A positive pole of the first battery 2 is with an input of a DC / DC converter 4 coupled. A positive pole of the second battery 3 is with an output of the DC / DC converter 4 coupled. A negative pole of the first battery 2 is connected via a circuit ground to a negative pole of the second battery 3 coupled. The DC / DC converter 4 is an energy converter.

The first and the second battery 2 . 3 are of different design. That's the first battery 2 For example, a battery that is capable of providing high performance in the short term. The second battery 3 For example, a battery that is capable of providing a constant power in the long term. In alternative hybrid energy storage systems, at least one of the batteries 2 . 3 replaced by another energy storage, such as a capacitor.

At the output of the DC / DC converter 4 Furthermore, a contact terminal is arranged, via which the battery storage system 1 can be contacted to remove from this one total current I _ges . The total current I _ges is composed of one of the DC / DC converter 4 output transducer current I _1d and one of the second battery 3 provided second current I ₂ together. When unloading the first battery 3 becomes the DC / DC converter 4 from the first battery 2 supplied with a first current I ₁ . When charging the first battery 3 becomes the first battery 3 from the DC / DC converter 4 supplied with the first current I ₁ . In this case, a flow direction of the first current I _{1 changes} .

For an efficient and gentle discharge of the battery storage system 1 To achieve this is operated by the inventive method. In this case, the second current I _{2 is} regulated according to an optimal control variable I ₂ ^* , which defines an amount of the second current I ₂ . The second current I ₂ is, for example, via the DC / DC converter 4 regulated. The first battery 2 has a first battery voltage U ₁ . The second battery 3 has a second battery voltage U ₂ .

The invention and the underlying mathematical principles are explained in more detail below.

The methods according to the invention enable energy-efficient control of a hybrid energy storage system, for example the battery storage system 1 , and each define one of two steps. In the first step, an optimal adjoint λ * or a Lagrangian multiplier is found and provided offline, that is to say under the calculation of a priori known case examples. This can optionally be done for different case studies. In the second step, an associated adaptive control is disclosed, which enables the energy storage system, for example the battery storage system 1 to operate in real time and to regulate an amount of the first current I ₁ and the second current I ₂ .

The method of determining optimized system performance of a hybrid energy storage system solves an optimal control problem for the hybrid battery storage system.

First, a general optimization problem for optimal control problems will be described. Following is in the specially for the hybrid battery storage system 1 occurring optimum control problem and its solution using the minimum principle of Pontryagin presented. It is described how, by means of the method according to the invention, the optimal adjoint λ * can be determined iteratively by means of a so-called bisection method.

In a optimal control problem, a cost function J should be minimized under given constraints. An example of such a problem is given below. The Lagrangian quality measure L indicates the costs as a function of the state variables x (t) and the control variables u (t) for each point in time.

$$\begin{array}{l}J:={\displaystyle {\int }_{t_a}^{t_e}L\left(\underset{\_}{x}\left(t\right),\underset{\_}{u}\left(t\right)\right)dt}\\ \text{ s}\text{.t}\end{array}$$

$$\underset{\_}{x}\left(t\right)\in \mathcal{X}\left(t\right)\subseteq {ℝ}^n$$

$$\underset{\_}{u}\left(t\right)\in \mathcal{U}\left(t\right)\subseteq {ℝ}^m$$

$$\underset{\_}{x}\left(t_a\right)={\underset{\_}{x}}_0$$

$$\underset{\_}{x}\left(t_e\right)\in \left[{\underset{\_}{x}}_{t_e,min},{\underset{\_}{x}}_{t_e,max}\right]$$

The optimal control problem can be formulated as follows: $$\underset{\left\{\forall k:\underset{\_}{x}\left(t\right)\in \mathcal{X}\left(t\right).\underset{\_}{u}\left(t\right)\in \mathcal{U}\left(t\right)\right\}}{{\displaystyle \text{min}}}J$$

$$\begin{array}{l}J:={\displaystyle {\int }_{t_a}^{t_e}L\left(\underset{\_}{x}\left(t\right).\underset{\_}{u}\left(t\right)\right)dt}\\ \text{s}\text{.t}\end{array}$$

$$\underset{\_}{x}\left(t\right)\in \mathcal{X}\left(t\right)\subseteq {ℝ}^n$$

$$\underset{\_}{u}\left(t\right)\in \mathcal{U}\left(t\right)\subseteq {ℝ}^m$$

$$\underset{\_}{x}\left(t_a\right)={\underset{\_}{x}}_0$$

$$\underset{\_}{x}\left(t_e\right)\in \left[{\underset{\_}{x}}_{t_e.min}.{\underset{\_}{x}}_{t_e.max}\right]$$

An optimal control quantity u * then satisfies the following equation: $$u*=arG\underset{\left\{\forall t:x\left(t\right)\in \mathcal{X}\left(t\right).u\left(t\right)\in U\left(t\right)\right\}}{{\displaystyle min}}\left(J\left(\underset{\_}{x}\left(t\right).\underset{\_}{u}\left(t\right)\right)\right)$$

The optimization problem and its solution by means of the minimum principle of pontryagin will now be applied to the in 1 illustrated hybrid battery storage system 1 based. The goal of the method is to minimize the losses in the hybrid battery storage system 1 over a given period [t _a , t _e ]. With electrical losses in the first battery P _{v, 1} (t), electrical losses in the second battery P _{v, 2} (t) and electrical losses in the DC / DC converter P _{v, dcdc} (t), the cost function J for the hybrid battery storage system 1 out 1 be set up. When the cost function J is minimized over the period [t _a , t _e ], the electrical losses in the illustrated battery storage system become 1 minimized: $$J={\displaystyle {\int }_{t_a}^{t_e}\left[P_{v\mathrm{,1}}\left(t\right)+P_{v2}\left(t\right)+P_{v.dcdc}\left(t\right)\right]dt}$$

The total current I _tot is made up of the sum of the converter current I _1d at one of the second battery according to the following node equation 3 facing side of the DC / DC converter 4 and the second current I _{2 of} the second battery 3 together: $${{\rm I}}_{\text{ges}}={\mathrm{<figure-callout\; id="1d"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_{1\text{d}}+{\mathrm{<figure-callout\; id="2"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_2$$

On one side of the first battery 2 applies in the event that the first battery 2 is discharged (this is in the battery storage system shown 1 the case because the first current I _{1 is} greater than 0 (I ₁ > 0)) with a DC / DC wander efficiency η _dcdc : $${{\rm I}}_1=\frac{1}{{\eta }_{\text{dcdc}}}\cdot {\mathrm{<figure-callout\; id="1d"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_{1\text{d}}\cdot \raisebox{1ex}{$U_2$}\!\left/ \!\raisebox{-1ex}{$U_1$}\right.={\eta }_{\text{dcdc}}^z\cdot {\mathrm{<figure-callout\; id="1d"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_{1\text{d}}\cdot \raisebox{1ex}{$U_2$}\!\left/ \!\raisebox{-1ex}{$U_1$}\right.\text{With}z=-1\text{in the unloading case}$$

In the event that the first battery 2 is loaded accordingly: $${{\rm I}}_1={\eta }_{\text{dcdc}}\cdot {\mathrm{<figure-callout\; id="1d"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_{1\text{d}}\cdot \raisebox{1ex}{$U_2$}\!\left/ \!\raisebox{-1ex}{$U_1$}\right.={\eta }_{\text{dcdc}}^z\cdot {\mathrm{<figure-callout\; id="1d"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_{1\text{d}}\cdot \raisebox{1ex}{$U_2$}\!\left/ \!\raisebox{-1ex}{$U_1$}\right.\text{With}z=1\text{in loading case}$$

$$So{C}_2\left(t\right)=So{C}_{\text{init}\text{,2}|t=t_a}-{\displaystyle \underset{\tau =t_a}{\overset{t}{\int }}\frac{{{\rm I}}_2\left(\tau \right)}{Q_{\text{nom}\text{,2}}}d\tau }$$

A state of charge of the first battery SoC ₁ and a state of charge of the second battery SoC ₂ can be determined by the respective temporal integral of the current supplied by the respective battery 2 . 3 flows, the nominal charge (Q _{nom, 1} , or Q _{nom, 2} ) and an initial charge state (SoC _{init, 1} , SoC _{init, 2} ) are calculated. The calculations are shown in equations (12) and (13). Here, the convention was chosen that a positive current to the discharge of each battery 2 . 3 equivalent. $$SO{C}_1\left(t\right)=SO{C}_{\text{init}\text{,1}|t=t_a}-{\displaystyle \underset{\tau =t_a}{\overset{t}{\int }}\frac{{{\rm I}}_1\left(\tau \right)}{Q_{\text{nom}\text{,1}}}d\tau }$$

$$SO{C}_2\left(t\right)=S\mathrm{<figure-callout\; id="2"\; label="O\; C\; init"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">O\; </figure-callout>}{C}_{\text{init}}{\text{2}|t=t_a}_{}-{\displaystyle \underset{\tau =t_a}{\overset{t}{\int }}\frac{{{\rm I}}_2\left(\tau \right)}{Q_{\text{nom}\text{2}}}d\tau }$$

The foregoing general form of optimum control problem will now be directed to the hybrid battery storage system 1 based. The state of charge of the second battery SoC _{2 is selected} as state variable x (x = SoC ₂ ). The battery current of the second battery 3 represents the control variable, as shown in Equation (14). $$u={\mathrm{<figure-callout\; id="2"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_2$$

$$\begin{array}{c}So{C}_{\mathrm{2,}min}\le So{C}_2\left(t\right)\le So{C}_{\mathrm{2,}max}\\ {{\rm I}}_{\mathrm{2,}min}\le {{\rm I}}_2\left(t\right)\le {{\rm I}}_{\mathrm{2,}max}\end{array}$$

The mentioned constraints and constraints for the optimization quantities are for use in the hybrid battery storage system 1 in Equations (15) and (16). A starting state of charge SoC ₂ (t _a ) of the second battery 3 is a fixed value. A final state of charge SoC ₂ (t _e ) of the second battery 3 should be in the immediate vicinity of this starting value, ie the starting state of charge SoC ₂ (t _a ). For a battery whose state of charge is in the range 0% to 100%, values in the region of 50% are reasonable. The definition of the starting state of charge SoC2 (ta) can also depend on other factors, such as the system structure, voltage requirement, a choice of a connected inverter or a nature of the energy storage itself. $$\begin{array}{c}SO{C}_2\left(t_a\right)=\mathrm{<figure-callout\; id="2"\; label="S\; O\; C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">S\; </figure-callout>}O{C}_{}{}_{\mathrm{2,}{t}_a}\\ SO{C}_2\left(t_e\right)=\mathrm{<figure-callout\; id="2"\; label="S\; O\; C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">S\; </figure-callout>}O{C}_{}{}_{\mathrm{2,}{t}_e}\end{array}$$

$$\begin{array}{c}\mathrm{<figure-callout\; id="2"\; label="S\; O\; C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">S\; </figure-callout>}O{C}_{}{}_{\mathrm{2,}min}\le SO{C}_2\left(t\right)\le \mathrm{<figure-callout\; id="2"\; label="S\; O\; C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">S\; </figure-callout>}O{C}_{}{}_{\mathrm{2,}ma\mathrm{<figure-callout\; id="2"\; label="x\; {\rm I}"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">x\; </figure-callout>}}& \\ {{\rm I}}_{}{}_{\mathrm{2,}min}\le {{\rm I}}_2\left(t\right)\le {\mathrm{<figure-callout\; id="2"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_{\mathrm{2,}max}\end{array}$$

The solution of the optimization problem by the minimum principle of pontryagin is presented below. The Lagrangian quality measure (see equation (2)) corresponds here to the sum of the electrical loss components in the batteries integrated in equation (8) 2 . 3 and the DC / DC converter 4 as described by equation (17). $$L=P_{\text{v}\mathrm{,1}}+{\mathrm{<figure-callout\; id="2"\; label="P\; v"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">P\; </figure-callout>}}_{\text{v}}+P_{\text{v}\text{, dcdc}}$$

Equation (18) shows the defined Hamiltonian H. In addition to the Lagrangian quality measure L, this includes another term, the product of a time-variant adjoint λ (t) ^T and a state differential equation f (x (t), u (t), t). $$H\left(x\left(t\right).u\left(t\right).\mathrm{\lambda }\left(t\right).t\right)=L\left(x\left(t\right).u\left(t\right).t\right)+\mathrm{\lambda }{\left(t\right)}^T\cdot f\left(x\left(t\right).u\left(t\right).t\right)$$

$$\stackrel{.}{\mathrm{\lambda }}*\left(t\right)={\nabla }_x{H|}_{*}\text{ siehe nachfolgende Erläuterungen}$$

$$x\left(t_a\right)=x_a$$

$$x\left(t_e\right)=x_e$$

The minimum principle of Pontryagin specifies a set of necessary conditions that must be met for optimality to apply. This is formulated in equations (19) to (23). Optimal trajectories and sizes are indicated here by the mark (·) *. $$\dot{x}*\left(t\right)={\nabla }_{\mathrm{\lambda }}{H|}_{*}\stackrel{Hier}{=}{\dot{x}}_2^{*}\left(t\right)=-\frac{u*}{{\mathrm{<figure-callout\; id="2"\; label="Q\; nom"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">Q\; </figure-callout>}}_{\text{nom}}}=f\left(x_2^{*}\left(t\right).u*\left(t\right)\right)$$

$$\stackrel{,}{\mathrm{\lambda }}*\left(t\right)={\nabla }_x{H|}_{*}\text{see the following explanations}$$

$$x\left(t_a\right)=x_a$$

$$x\left(t_e\right)=x_e$$

The temporal changes of the state x and the Lagrange multiplier (also called adjuncts λ) are described by the canonical differential equations (19) and (20). By the choice of the optimal control quantity u *, the value of the Hamiltonian function H according to equation (23) which is to be minimized is always smaller than the value of the Hamiltonian H, which results from a control variable deviating from the optimal control variable u *. $$H\left(u\left(t\right).x*\left(t\right).\mathrm{\lambda }*\left(t\right).t\right)\geqq H\left(u*\left(t\right).x*\left(t\right).\mathrm{\lambda }*\left(t\right).t\right).\forall u\left(t\right)\in U\left(t\right).\forall t\in \left[t_0.t_e\right]$$

Now, over the period of t ∈ [t _a , t _e ], an optimal traktorector u * (t) from the range of the permissible control values u (t) is to be found which, while maintaining the boundary and secondary conditions of the control and state variables, the Hamilton function H minimizes. In this case, there does not always have to be an extreme value in the form dH / du = 0, since it may happen that a minimum of the Hamilton function H is present at the edge region of the permissible control variable range in which the derivative of the Hamiltonian function H is not yet 0 , Thus, generally, the requirement u * = arg min H applies, where values of the control quantity u are considered within the allowable control value range.

Solving the two-point boundary value problem, consisting of state differential equation (19) and adjoint differential equation (20), can be solved under the assumptions described below.

The losses of the DC / DC converter 4 are essentially dependent on the input and output voltage, ie the first and second battery voltage U ₁ , U ₂ , as well as a transferred power P _{v, dcdc} . Assuming that the battery voltage U1 of the second battery 3 During operation in a partial voltage range and thus in a small state of charge range x ₂ (t) = SoC ₂ (t) ≈ constant, the following simplification can be made in equation (24). $$\frac{\partial }{\partial SO{C}_2}{P}_{\text{v}\text{, dcdc}}\left(U_1.U_2\left(SO{C}_2\left(t\right)\right).{\mathrm{<figure-callout\; id="1d"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_{1\text{d}}\right)\stackrel{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">U</figure-callout>}}_2\approx kOnstant}{\approx }0$$

For the partial derivation of a power loss of the second battery P _{v, 2} applies with the assumption made equation (25). $$\frac{\partial }{\partial SO{C}_2}{P}_{\text{v}\text{2}}\left(R_{dc2}\left(SO{C}_2\left(t\right).{{\rm I}}_2\right)\right)=\frac{\partial }{\partial SO{C}_2}\left({\mathrm{<figure-callout\; id="2"\; label="R\; dc"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">R\; </figure-callout>}}_{\text{dc}}\cdot {\mathrm{<figure-callout\; id="2"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_2^2\right)\stackrel{\mathrm{<figure-callout\; id="2"\; label="S\; O\; C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">S\; </figure-callout>}O{C}_{}{}_2\approx kOnstant}{\approx }0$$

A power loss of the first battery P _{v, 1} is independent of the state of charge of the second battery SoC ₂ and thus applies to the partial derivative of this power loss equation (26). $$\frac{\partial }{\partial SO{C}_2}{P}_{\text{v}\text{,1}}\left(R_{\text{dc}\text{,1}}.{{\rm I}}_1\right)=0$$

In addition, Equation (27) holds for the state differential equation with SoC ₂ (t) ≈ constant. $$S\dot{O}{C}_2\left(t\right)\stackrel{\mathrm{<figure-callout\; id="2"\; label="S\; O\; C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">S\; </figure-callout>}O{C}_{}{}_2\approx kOnstant}{\approx }0$$

With the assumption made and the resulting partial differential equations (24) to (27), the necessary condition in equation (20) can be solved. It results in 0. It also follows that the adjoint λ is constant, as can be seen from equation (28). $$\begin{array}{c}\stackrel{,}{\mathrm{\lambda }}\left(t\right)=-\frac{\delta H\left(SO{C}_2\left(t\right).u\left(t\right).\mathrm{\lambda }\left(t\right).t\right)}{\delta SO{C}_{PB}}\\ \approx 0\\ \Rightarrow \mathrm{\lambda }\left(t\right)=\mathrm{\lambda \; =}kOnstant\end{array}$$

$$P_{\text{v}\text{,2}}=R_{\text{dc}\text{,2}}\cdot {{\rm I}}_2^2$$

The losses in the battery parts, ie in the first battery 2 and the second battery 3 , can be determined via the DC resistance of the respective battery part according to equations (29) and (30). $$P_{\text{v}\mathrm{,1}}=R_{\text{dc}\mathrm{,1}}\cdot {{\rm I}}_1^2$$

$${\mathrm{<figure-callout\; id="2"\; label="P\; v"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">P\; </figure-callout>}}_{\text{v}}={\mathrm{<figure-callout\; id="2"\; label="R\; dc"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">R\; </figure-callout>}}_{\text{dc}}\cdot {\mathrm{<figure-callout\; id="2"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_2^2$$

With equations (29) and (30), the node equation (9), the relationship u = I ₂ and the current efficiency equations (10) and (11) on the DC / DC converter 4 the calculation of the electrical losses of the first battery P _{v, 1 can be converted} and represented by equation (31). Here, z = -1 for the discharge case of the first battery 3 and z = +1 for the loading case. The current of the first battery I ₁ is formulated according to equations (10) and (11). $$\begin{array}{c}{P}_{v\mathrm{,1}}\left(u\right)=R_{dc\mathrm{,1}}\cdot {{\rm I}}_1^2\\ =R_{dc\text{,1}}\cdot {\left({\mathrm{<figure-callout\; id="1d"\; label="{\rm I}"\; filenames="DE102017201061A1\_0039.png"\; state="\{\{state\}\}">{\rm I}</figure-callout>}}_{1d}\cdot {\eta }_{dcdc}^z\cdot \frac{U_2}{U_1}\right)}^2\\ =R_{dc\text{,1}}\cdot {\left(\left({{\rm I}}_{Ges}-u\right)\cdot {\eta }_{dcdc}^z\cdot \frac{U_2}{U_1}\right)}^2\end{array}$$

The output power P _{out, dcdc of} the DC / DC converter 4 can be represented with a current direction dependent factor k as a function of a discharge power P _{1d of} the first battery when discharged, as also represented by equation (32). $$P_{\text{out}\text{, dcdc}}={\mathrm{<figure-callout\; id="1d"\; label="P"\; filenames="DE102017201061A1\_0039.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1\text{d}}\cdot k.\text{With}k=\{\begin{array}{l}\begin{array}{ccc}1& & \text{Discharge battery part}\mathrm{1,}{{\rm I}}_1>0\end{array}\\ \begin{array}{cc}\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${\eta }_{\text{dcdc}}^z$}\right.& \text{Charge battery part}\mathrm{1,}{{\rm I}}_1<0\end{array}\end{array}$$

Now, the power loss of the DC / DC converter can be 4 depending on the control quantity u according to equation (33). In this case, the discharge power P _1d in the discharge case of the first battery 3 P _1d = U ₂ · (I _ges - u). In the charging case of the first battery 3 applies: P _1d = U ₂ . (I _ges - u) · 1 / η _dcdc . With these relationships, the following equation (33) is obtained for the power dissipation of the DC / DC converter P _{v, dcdc} . $$P_{\text{v}\text{, dcdc}}={\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">U</figure-callout>}}_2\cdot \left({{\rm I}}_{\text{ges}}-u\right)\cdot k\cdot \left(1-{\eta }_{\text{dcdc}}\right)$$

With the equations (17), (19), (28), (32) and (33), the Hamiltonian function H can be represented as a function of the control variable u = I ₂ , as has been done in equation (34). $$\begin{array}{c}H=L+\mathrm{\lambda }\cdot S\dot{o}{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\\ ={\mathrm{<figure-callout\; id="2"\; label="P\; v"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">P\; </figure-callout>}}_v+P_{v\mathrm{,1}}+P_{v.dcdc}-\mathrm{\lambda }\cdot \frac{u}{Q_{\mathrm{<figure-callout\; id="2"\; label="n\; O\; m"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">n\; </figure-callout>}Om2}}\\ \begin{array}{l}=R_{dc2}\cdot {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">u</figure-callout>}}^2+R_{dc\mathrm{,1}}\cdot {\left(\left({{\rm I}}_{Ges}-u\right)\cdot {\eta }_{dcdc}^z\cdot \frac{U_2}{U_1}\right)}^2\\ +U_2\left({{\rm I}}_{Ges}-u\right)\cdot k\cdot \left(1-{\eta }_{dcdc}\right)-\mathrm{\lambda }\cdot \frac{u}{Q_{\mathrm{<figure-callout\; id="2"\; label="n\; O\; m"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">n\; </figure-callout>}Om2}}\end{array}\end{array}$$

The minimum principle of pontryagin implies that the Hamiltonian H has a global minimum at each time t ∈ [t _a , t _e ] of the given period. Finding the minimum is equivalent to solving an extreme value problem. By deriving the Hamilton function H according to the control variable u and zeroing, an extreme value can first be determined. This corresponds to a necessary condition for the validity of the extreme value. Whether it is at the time t at the control variable u in the control area u ∈ U (t) is a global extreme value must be checked. Equation (35) shows the Hamiltonian H derived from the control variable u, equated to zero (∂H / ∂u = 0) and resolved after the control variable u = I ₂ . The sizes of the batteries 2 . 3 (Voltages, DC internal resistances) can be calculated at any time depending on the state variable and currents, or they are, like the nominal charge, permanently storable. Similarly, the efficiency of the DC / DC converter 4 be determined for the respective operating point. Only the optimal adjoint λ * is to be determined. This is achieved in a corresponding manner by the method according to the invention for determining an optimized system behavior of a hybrid energy storage system. $$u=\frac{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">U</figure-callout>}}_2\cdot k\left(1-{\eta }_{dcdc}\right)+2\cdot {{\rm I}}_{Ges}\cdot R_{dc\mathrm{,1}}{\left({\eta }_{dcdc}^z\cdot \frac{U_2}{U_1}\right)}^2+\frac{\mathrm{\lambda }}{Q_{\mathrm{<figure-callout\; id="2"\; label="n\; O\; m"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">n\; </figure-callout>}Om2}}}{2\cdot \left(R_{dc2}+R_{dc\mathrm{,1}}{\left({\eta }_{dcdc}^z\cdot \frac{U_2}{U_1}\right)}^2\right)}$$

The method for determining an optimized system behavior of a hybrid energy storage system therefore describes a method for determining the optimum constant adjoint λ * by means of a bisection method.

With the given equation (35), it is possible depending on the battery storage system 1 demanded current I _tot the optimal control variable u *, or to calculate the optimal current I ₂ ^* . However, the calculation still lacks the optimal adjoint λ * for which the constraints and boundary conditions are met.

The method for determining an optimized system behavior of a hybrid energy storage system is an iterative loop method whose flowchart in FIG 2 is shown. By means of the method for determining an optimized system behavior of a hybrid energy storage system, the optimum (time-constant) adjoint λ * can be determined for a power profile P _ges (t) given a priori over the predetermined time period [t _a , t _e ]. Assuming the assumption made that in the second battery 3 the influence of the state of charge of the second battery SoC ₂ on the Hamilton function H is low.

At the beginning of the process are by an initialization 40 Initial values for a possible adjoint λ _m and model sizes of the hybrid battery storage system 1 , In particular, an initial state of charge of the first battery SoC ₁ (t _a ) at the beginning of the predetermined period, an initial state of charge of the second battery SoC ₂ (t _a ) at the beginning of the predetermined period and a zero current at the beginning of the predetermined period, given.

After initialization, a first iteration loop 10 started. This has several passes, wherein successive passes each have a possible adjoint λ _{m is} associated. Thus, when executing the first iteration loop, a number of passes are executed in which the respective same method steps are executed. In this case, the respective same method steps are carried out for changing values of the possible adjuncts λ _m . The optimal adjoint λ * is determined from the multiplicity of possible adjuvants λ _m . This is done by means of a so-called Bisektionsverfahrens. This is also called interval nesting. In the described embodiment, an interval bisection method is used by way of example.

For this purpose, a range of values is defined which describes values which the possible adjoint λ _m can assume. This value range starts with an initial value λ _u and extends up to a final value λ _o . This range of values initially has a lowest initial value λ _{u, 0} and a highest final value λ _{o, 0} .

At the first pass of the first iteration loop 10 becomes a value of the possible adjoint λ _m in a selection step 14 set to a value which is between the initial value λ _{u, 0} and the highest final value λ _{o, 0} . The value of the possible adjoint λ _{m of} the first iteration loop is referred to as the first possible adjoint λ _{m, 1} . The first possible adjoint λ _{m, 1} thus results from the lowest initial value λ _{u, 0} and the highest final value λ _{o, 0} to: λ _{m, 1} = (λ _{u, 0} + λ _{o, 0} ) / 2.

In the further iterations of the first iteration loop 10 the value of the possible adjoint λ _{m is} redefined. For this purpose, it is determined whether a value of the optimum adjoint λ * is higher or lower than the value of the possible adjoint λ _{m of} the current iteration of the first iteration loop 10 is. This is done after the first pass of the first iteration loop 10 for example, by checking that the following criterion is met: $$\left[{\text{SoC}}_2\left({\text{t}}_{\text{e}}.{\mathrm{\lambda }}_{\text{m}\text{,1}}\right)-{\text{<figure-callout id="2" label="SoC" filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png" state="{{state}}">SoC</figure-callout>}}_{\mathrm{2,}\text{Ref}}\right]*\left[{\text{SoC}}_2\left({\text{t}}_{\text{e}}.{\mathrm{\lambda }}_{\text{0}\text{,1}}\right)-{\text{<figure-callout id="2" label="SoC" filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png" state="{{state}}">SoC</figure-callout>}}_{\mathrm{2,}\text{Ref}}\right]<0$$

In this case, the variable SoC ₂ (t _e , λ _{m, 1} ) describes a state of charge which, when the possible adjunct λ _m associated with this passage is used, in the first pass of the first iteration loop 10 , ie when applying the first possible adjoint λ _{m, 1} , yields. This charge state is one of the respective possible adjuncts λ _m associated end state of charge SoC ₂ (t _e ), which results for a last time step t _e . Accordingly, the variable SoC ₂ (t _e , λ _0,1 ) describes a state of charge which, when the final value λ _{o, 0} associated with this pass is used _{, is} in the first pass of the first iteration loop 10 if its value is chosen as the value for the possible adjoint λ _m . This charge state is a final charge state SoC ₂ (t _e ) associated with the respective end value λ _{0, 0} , which results for the last time step t _e .

Depending on whether this condition is met, the initial value λ _u and the final value λ _o for the next iteration of the first iteration loop 10 established. If the condition is fulfilled, then after the first pass of the first iteration loop 10 the initial value λ _u for the second pass of the first iteration loop 10 fixed at λ _{u, 1} = λ _{m, 1} . The final value λ _{o, 0} remains for the second pass of the first iteration loop 10 unchanged and thus results in: λ _{o, 1} = λ _{o, 0} . If the condition is not fulfilled, then the final value λ _{o, 0} for the second pass of the first iteration loop 10 fixed to: λ _{o, 0} = λ _{m, 1} . The initial value λ _{u, 0} remains in this case for the second pass of the first iteration loop 10 unchanged and thus results in: λ _{u, 1} = λ _{u, 0} .

On each subsequent pass of the first iteration loop 10 the possible adjoint λ _{m is set} to a new value. In this case, the initial value λ _u and the final value λ _{o are} chosen to be the value to which they were added during the previous iteration loop pass 10 were determined. Accordingly, the possible adjoint λ _m for the respective run of the first iteration loop 10 is determined from the associated initial value λ _u and the associated final value λ _o . For the second pass of the first iteration loop 10 the possible adjoint λ _m thus results as follows: λ _{m, 2} = (λ _{u, 1} + λ _{o, 1} ) / 2.

Corresponding to the second pass of the first iteration loop 10 Checked that the following criterion is met: $$\left[{\text{SoC}}_2\left({\text{t}}_{\text{e}}.{\mathrm{\lambda }}_{\text{m}\text{2}}\right)-{\text{<figure-callout id="2" label="SoC" filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png" state="{{state}}">SoC</figure-callout>}}_{\mathrm{2,}\text{Ref}}\right]*\left[{\text{SoC}}_2\left({\text{t}}_{\text{e}}.{\mathrm{\lambda }}_{0.2}\right)-{\text{<figure-callout id="2" label="SoC" filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png" state="{{state}}">SoC</figure-callout>}}_{\mathrm{2,}\text{Ref}}\right]<0$$

Thus, for each pass of the first iteration loop 10 an initial value λ _u , a final value λ _o and an associated possible adjoint λ _m .

The first iteration loop 10 is run through until a termination criterion is met, which is in a test step 13 is detected, which is also executed each time the first iteration loop passes.

Each time the first iteration loop ( 10 ), a second iteration loop ( 20 ). It turns out that the second iteration loop ( 20 ) is carried out a number of times, wherein in the second iteration loop ( 20 ) are different values for the possible adjoint λ _m underlying.

The second iteration loop 20 has several passes, wherein successive passes each have a time value t from a predetermined period [t _a , t _e ] is assigned. Thus, when executing the second iteration loop, a number of passes are executed in which the respective same method steps are executed. In this case, the respective same method steps are carried out for changing values of the time value t.

For this purpose, the predetermined period [t _a , t _e ] is defined by an initial time t _a and an end time t _e . At the first pass of the second iteration loop 20 a value of the time value t is set equal to the starting time t _a . At the beginning of each further pass of the second iteration loop 20 this value will be in a time value increment step 21 elevated. The second iteration loop 20 is passed through until the value of the time value t is equal to the end time t _e . Through the second iteration loop 20 becomes a behavior of the battery storage system 1 simulated over the given period [t _a , t _e ]. The time value t describes one in the respective run of the second iteration loop 20 currently considered time from the given period [t _a , t _e] .

In each pass of the second iteration loop 20 a determination is made in each case of an optimal control variable u * for successive points in time of the predetermined period. It thus becomes for each pass of the second iteration loop 20 an associated optimal control quantity u * determined. This will be for each pass of the second iteration loop 20 determined from a variety of possible control variables u _m .

The optimal control variable u * describes one of the second battery 3 current to be delivered I ₂ . The optimal control quantity thus describes one of the second battery 3 absorbed or released energy. For example, a value of the optimal control quantity u * is equal to a value to which the second current I ₂ for that in the respective iteration of the second iteration loop 20 Considered time t is to be regulated in the given period [t _a , t _e ] to the lowest possible energy-efficient operation of the battery storage system 1 to allow with the DC / DC converter.

The optimal control quantity u * becomes in each pass of the second iteration loop 20 determined and saved. The optimal control quantity u * is determined based on a minimum of the Hamilton function H. The determination of the optimal control variable u * takes place in each pass of the second iteration loop 20 by adding a third iteration loop 30 is performed.

The third iteration loop 30 has several passes, successive passes each having a possible control value u _{m is} associated. This will be the case when executing the third iteration loop 30 executed a number of passes in which the same process steps are processed. In this case, the respective same method steps are carried out for changing values of the possible control value u _m .

For this purpose, a control value range is defined which describes values which values the possible control value u _m can assume. This control value range has a lowest u-start value and a highest u-end value. At the first pass of the third iteration loop 30 at each pass of the second iteration loop 20 a value of the possible control value u _{m is set} to the u-initial value. At the beginning of each further pass of the third iteration loop 10 this value is incremented in a u-increment step 31. The third iteration loop 30 is passed through until the value of the possible control value u _{m is} equal to the u-end value. The third iteration loop 30 is thus traversed for a number of possible control values u _m , which results from the increase of the value of the possible control value u _m in the u-increment step 31.

In each pass of the third iteration loop 30 is in a calculation step 11 a value of the Hamiltonian H, as shown in formula (34), according to the respective iteration of the third iteration loop 30 associated value of the possible control variable u _m calculated. When calculating the value of the Hamiltonian function H, therefore, an addition of a modeled system loss L _m with a derivation of the state of charge SoC _{2 of} the second battery takes place 3 , which has been multiplied by the possible adjoint λ _m . The modeled system loss L _m is a parameter, which is a behavior of the energy storage system, ie the battery storage system 1 , describes and is thus a modeled system parameter. In The Hamilton function H thus formed is thus the modeled system loss L _{m of} the parameters to be optimized of the hybrid battery storage system 1 which should be minimized. At the same time, the state of charge SoC _{2 of} the second battery 3 a state of the second energy storage, and thus is a storage state.

The derivation of the state of charge SoC _{2 of} the second battery 3 is doing by means of the current iteration of the first iteration loop 10 chosen value of the possible adjoint λ _m , that of the present iteration of the third iteration loop 30 selected value of the possible control variable u _m and the nominal charge Q _{nom, 2 of} the second battery 3 calculated for the currently considered time.

The modeled system loss L _m and the nominal charge Q _{nom, 2 of} the second battery 3 for the currently considered time are in a modeling step 32 determined, which before the calculation step 11 in the third iteration loop 30 is performed.

In the modeling step 32 is calculated the modeled system loss L _m . This is referred to as "modeled" in the context of this method, since the described method for determining an optimized system behavior of a hybrid energy storage system can be performed by software, without the battery storage system 1 physically available. In formula (34) this is represented by the system loss L. The modeled system loss L _m results from the electrical loss in the first battery P _{v, 1} (t), the electrical losses in the second battery P _{v, 2} (t) and the electrical losses in the DC / DC converter P _{v, dcdc} (t). To calculate these electrical losses, it is necessary that the battery storage system 1 required total current I _{ges is} known, which is required for the currently considered time. Therefore, in the modeling step 32 that of the battery storage system 1 required total current I _{ges determined} according to a predetermined power _profile P _ges (t). In the power _profile P _ges (t) is for each time of the predetermined period [t _a , t _e ] a required power deposited by the battery storage system 1 is to provide. This required performance is determined by a query 22 , which in the context of the second iteration loop 20 takes place for in the respective run of the second iteration loop 20 currently selected time and for the calculation step 11 provided. Based on the required power, the required total current I _{tot is} calculated for the currently considered time. The remaining values required for this are at initialization 40 deposited. The modeled system loss L _m is thus determined according to a predetermined power _profile P _ges (t), which is derived from the battery storage system 1 in the given period of time [t _a , t _e ]. The modeled system loss L _m is based on the DC _resistance R _{dc, 1 of} the first battery 2 , the DC _resistance R _{dc, 2 of} the second battery 3 , one of the battery storage system 1 for the respective time to be delivered power P according to the predetermined power profile P _ges (t) and the efficiency η _{dcdc of} the DC / DC converter 4 determined.

Further, in the modeling step 32 the nominal charge Q _{nom, 2 of} the second battery 3 calculated for the currently considered time. For this purpose, the state of charge SoC _{2 of} the second battery 3 which is at a previous pass of the second iteration loop 20 was saved. This state of charge of the second battery SoC ₂ is updated according to the formula (13) and for the calculation step 11 provided. In addition, this state of charge of the second battery SoC _{2 is} stored, so that on this in a subsequent pass of the second iteration loop 20 can be accessed. On a first pass of the second iteration loop 20 , if still no state of charge of the second battery SoC ₂ from a previous pass of the second iteration loop 20 is present at the initialization 40 provided initial state of charge of the second battery SoC ₂ (t _a ) accessed.

For the calculation of the Hamiltonian H in the calculation step 11 Furthermore, as shown in formula (34), an adjoint λ is required. As adjoint λ, the possible adjoint λ _m , which is the respective pass of the first iteration loop 10 is associated, used for calculation. From formula (34) it follows that the Hamiltonian function H is dependent on a modeled system loss L _m , the possible adjoint λ _m and the state of charge of the second battery SoC ₂ . The Hamilton function H is the battery storage system 1 as this is formulated by value which the battery storage system 1 describe.

For each iteration of the third iteration loop, 30 becomes the value of the Hamiltonian H, which is in the calculation of the Hamiltonian H in the calculation step 11 results, saved. It will be in the calculation step 11 a smallest value of the stored values is determined. The smallest of the stored values, which occurs on a last pass of the third iteration loop 30 in each case, the minimum of the Hamiltonian function is H. The possible control variable u _m in its passage through the third iteration loop 30 the smallest of the stored values has been generated is determined as the optimal control quantity u *. Thus, the possible control variable u _{m is determined} as an optimal control quantity u *, at which the value of the Hamiltonian H has a minimum value.

Each time the second iteration loop is executed 20 a final state of charge of the second battery SoC _2E (also referred to as SoC ₂ (t _e )) is calculated by the second battery 3 after a lapse of the predetermined period [t _a , t _e ] when that of the second battery 3 delivered second current I ₂ in the predetermined period [t _a , t _e ] was controlled in accordance with the respective optimal control variable u *. This is done in the last run of the second iteration loop 20 in the modeling step 32 stored stored state of charge of the second battery SoC ₂ , which results when in the third iteration loop 30 the possible control quantity u _{m is} equal to the optimal control quantity u *.

Is the second iteration loop 20 done, so all the passes are the second iteration loop 20 Completely executed, so in the first iteration loop 10 detecting whether the second iteration loop 20 calculated final state of charge of the second battery SOC _{2E is} within a predetermined charging interval and providing an optimal adjoint λ *, which of the possible adjoint λ the passage of the first iteration loop 10 for which it has been detected that the final state of charge SoC _{2E is} within the predetermined charging interval. The predetermined charging interval is an interval around an initial charging state of the second energy storage SOC _2A , that is, the initial state of charge of the second battery SoC ₂ (t _a ). Thus, in this embodiment, it is checked whether the final state of charge SoC _{2E of} the second battery 3 at an interval around that at initialization 40 Selected initial state of charge of the second battery SoC ₂ (t _a ) is located. Thus, it is checked whether the final state of charge SoC _{2E of} the second battery 3 for the respective run of the first iteration loop 10 less than 1% from the initial state of charge of the second battery SoC ₂ (t _a ) is different. If this is the case, the value of the possible adjoint λ _m associated with the respective run of the first iteration loop 10 is determined as the value for the optimum adjoint λ *.

In the method for determining an optimized system behavior of a hybrid energy storage system, an iterative method is used to solve an optimization problem both in terms of time and model dynamics. After the initialization in the first time step, the state can be updated for the subsequent time step, the development of the model variables (states of charge in the batteries). It then becomes u = I ₂ in the "u = I ₂ loop", ie the third iteration loop, for a given set of control values 30 , for the given adjoint λ, each associated value of the Hamiltonian H is calculated by equation (34). The amount of control values corresponds to the possible current values of the first battery 3 ,

Subsequently, in the block "min (H)", the current value for the second current I ₂ and thus the optimum control quantity u * is determined, which minimizes the Hamiltonian function H while maintaining the secondary conditions.

Then takes place in a test step 12 Checking whether the entire performance profile L (t) has been run through to the end time step t _e . If not, then this computation of the optimal current setpoint for the entire problem and the possible adjoint λ given in the step is performed.

If the calculation has arrived at the last time step t _e , it is checked whether the boundary condition that the final state of charge SoC ₂ (t _e ) from the second battery 3 corresponds to the initial state of charge SoC ₂ (t _a ) for which given possible adjoint λ _{m has been} maintained. Since the model is discretized, a barrier of, for example, SoC ₂ (t ₂ ) +/- 1% can be selected. If this is not the case, proceed as described below.

The method now selects the first iteration loop in a further loop pass 10 , by iteratively approximating to an optimal value for the optimal adjoint λ *, further possible adjuncts λ _m , which according to the scheme described in the selection step 14 be entered in the calculation cycle.

It will, as in 2 to see the sequence repeated until the test step 13 the criterion SoC ₂ (t _a ) ≈ SoC ₂ (t ₂ ) is fulfilled. Then the optimal adjoint λ * is determined. This criterion is the termination criterion. The optimal adjoint λ * is the possible adjoint λ _m , which is the passage of the first iteration loop 10 underlying the abort criterion.

In alternative embodiments of the method for determining an optimized system behavior of a hybrid energy storage system ( 1 ), the optimum control variable (u *) is determined in each pass of the second iteration loop ( 20 ) by an analytical calculation. In this case, there is a mathematical minimization of the Hamilton function given in equation (34). This can be done using algorithms that, for example, can also run in a control unit. In this case, the general optimization task u * = arg min H applies. There is thus a change from dH / du = 0 to the more general requirement u * = arg min H. This is therefore advantageous since it may happen that the minimum the Hamilton function within the limited-valid value range of the control variable u, takes a minimum at the edge of this value range. In this case, the condition dH / du = 0 is not. Therefore, the more general form is advantageous.

The following is with reference to 3 the inventive method for controlling a hybrid energy storage system 1 explained. In this, an adaptation of the optimal adjoint λ * for a real-time capable adaptive control.

The off-line determinable solution described in the above method for determining an optimized system behavior of a hybrid energy storage system is now converted to real-time capable control. The goal is therefore for any time-dependent current request I _ges (t) over a period of time to enable optimal control. This creates a causal energy management, which manages without information from a prediction time horizon. Here, an adaptive method is thus enabled which operates on the basis of the off-line solutions predetermined by the method for determining an optimized system behavior.

The optimal adjoint λ * calculated for a known problem can now be used in conjunction with the relationships defined in equation (35) to control or divide the current between the current of the first battery I _1d (t) and to be determined in each time step to realize the current of the second battery I ₂ (t). At each time step, the current of the second battery I ₂ (t) is calculated, which corresponds to a control quantity u (t). The following therefore holds: I ₂ (t) = u (t).

Now, if a control problem is solved, which is similar to that of the off-line solution process, but does not exactly correspond, the final value criterion of a fixed state of charge will not be met in every case.

Similarly, the end time t _{e is} not known. In order to cope with this problem, an adaptive control is introduced which deviates from a reference state of charge SoC _{2, setpoint of} the second battery 3 counteracts. This is done with a PI controller 51 realized on the difference between the target and actual state of charge of the second battery 3 responding. The reference state of charge SoC _{2, target in} this case corresponds in particular to the reference state of charge SoC _{2, Ref} , which was selected in determining the optimum first adjoint λ *.

The equation of the PI controller 51 is shown in formula (36). Depending on the control difference between the nominal and actual state of charge of the second battery 3 This avoids too fast unloading or loading. The state of charge is maintained as a function of the regulator quantities provided to the regulator, a proportional value Kp and an integral value Ki in the region of the reference state of charge SoC _{2, target} . The magnitudes of the proportional value Kp and the integral value Ki can be found by a parameter study. $$\tilde{\mathrm{\lambda }}\left(t\right)=\mathrm{\lambda }*+K_p\left(\mathrm{<figure-callout\; id="2"\; label="S\; O\; C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">S\; </figure-callout>}O{C}_{}{}_{\mathrm{2,}SOll}-SO{C}_2\left(t\right)\right)+K_i{\displaystyle \underset{t_a}{\overset{t}{\int }}\left(\mathrm{<figure-callout\; id="2"\; label="S\; O\; C"\; filenames="DE102017201061A1\_0039.png,DE102017201061A1\_0040.png"\; state="\{\{state\}\}">S\; </figure-callout>}O{C}_{}{}_{\mathrm{2,}SOll}-SO{C}_2\left(\tau \right)\right)d\tau }$$

In 3 becomes the controller structure of the hybrid battery storage system embedded in the energy management 1 shown. This starts from a control difference between the setpoint and actual state of charge of the second battery 3 , with the given optimal adjoint λ * and with the controller parameters.

So shows 3 a device 50 for controlling the hybrid battery storage system 1 comprising a control unit 54 , which is adapted to the method for controlling the hybrid battery storage system 1 perform.

The device 50 includes the PI controller 51 which has two inputs. A first input value and a second input value are detected via the two inputs, wherein the first input value describes a precalculated value of the optimum adjoint λ * and the second input value describes a deviation of a state of charge SoC _{2 of} the second battery 3 , So a memory state of the second battery 3 Describes from a reference state of charge SOC _{2, intended.} The value for the optimal adjoint λ * is provided, for example, by a memory module in which the optimum adjoint λ * determined according to the method for determining an optimized system behavior of a hybrid energy storage system has been stored. The reference state of charge SOC _{2, setpoint is also} stored in this memory module and is detected by the PI controller 51 provided as a second input value. For example, the reference state of charge SOC ₂ , _target is equal to a value of the initial state of charge of the first battery SoC ₁ (t _a ) at the beginning of the predetermined period [t _a , t _e ] selected in the method for determining an optimized system behavior of a hybrid energy storage system. was chosen.

Through the PI controller 51 an adaptation of the optimal adjuncts λ * for a current state of charge of the second battery SoC ₂ based on the first and the second input value, ie based on the optimal adjoint λ * and the reference state of charge SOC _{2, Soll} , is performed by an adapted adjoint λ _a to investigate. For this purpose, a current state of charge of the second battery SOC ₂ is first determined. This is done by means of at least one measured value, which at the second battery 2 is detected. The adjusted adjoint λ _a is determined according to formula (36) and at an output of the PI controller 51 provided.

The value determined for the adjusted adjoint λ _{a is} determined by the PI controller 51 to a control unit 52 transfer. The control unit 52 also has an input to which a current target value describing a current coming from the first battery is provided 2 and the second battery 3 is to provide together. Thus, the current target value is an energy target because it describes an energy of the first battery and the second battery 3 is to provide. This current target value is provided, for example, by an external electronics, which determines a current, which flows from one to the battery storage system 1 connected consumer is needed. The current target value describes the required total current I _ges .

Through the control unit 52 According to formula (35), a value of an optimal control quantity I ₂ ^{* is} determined (u = I ₂ ^* ) corresponding to that of the second battery 3 to be given stream. The optimal control variable I ₂ ^* thus describes one of the second battery 3 absorbed or released energy. In this case, the adjusted adjoint λ _{a is used} as adjoint A for the calculation of the optimal control variable I ₂ ^* according to formula (35). The optimal control quantity I ₂ ^* is determined by the formula (35) in the control unit 52 is stored and is solved by calculation. This can be done for example by means of a digital processing unit. Alternatively, it is advantageous that the optimal control variable I ₂ ^* from the control unit 52 is determined in tabular form, wherein a table is queried in which different combinations of values of the adjusted adjoint λ _a and values of the current target value I _ges each have an optimal control variable I ₂ ^{* is} assigned. This means that an associated optimal control variable I ₂ ^{* has} already been calculated for all possible value combinations for the adjusted adjoint λ _a and the current target value, and this in the control unit 52 were deposited.

Determining an optimum control variable I ₂ ^* in both cases based on the adjusted adjoint λ _a and the current target value I _ges. Regardless of whether the values of the optimal control quantity I ₂ ^{* have} been pre-calculated and are now selected, or whether they are calculated in real time, the optimal control quantity I ₂ ^* becomes according to a battery storage system 1 Hamilton's function H, since this is determined based on formula (35), which results from solving the Hamiltonian function H described in formula (34). As described above, this Hamilton function H depends on a calculated system loss L _b , the adjusted adjoint λ _a and the current state of charge SoC _{2 of} the second energy store. In this case, the calculated system loss L _b in formula (35) is to be understood as a system loss L. Thus, the system loss L is here referred to as the calculated system loss L _b , since this for the actual existing battery storage system 1 is calculated.

As can also be seen from formula (34), the calculated system loss L _{b is} dependent on the power loss of the first battery P _{v, 1} , the power loss of the second battery P _{v, 2} and the power loss of the DC / DC converter P _{v, dcdc} ,

The from the control unit 52 determined optimal control variable I ₂ ^* is provided by the second current I ₂ , that of the second battery 3 regulated electricity. To the first current I ₁ or in the out 1 known battery storage system 1 the current at the output of the DC / DC converter 4 , That is, the converter current I _1d , to control a difference between the optimal control variable I ₂ ^* and the current target values is determined. This is done for example by means of a differentiator 53 ,

4 shows a device according to the invention 60 for generating the optimal adjoint λ *. The device 60 for generating the optimal adjoint λ *, comprising a computing unit 61 . For example, a processor configured to perform the method described above for determining an optimized system behavior of the hybrid battery storage system 1 perform. The device 60 has an input 62 through which the values necessary to provide the battery storage system can be provided 1 define. The device 60 has an exit 63 on which the optimal adjoint λ * is provided.

It is further explicitly pointed out that the methods according to the invention can be carried out in a corresponding manner if the optimal control variable u * in the method for determining an optimized system behavior of the hybrid energy storage system 1 and the optimal control quantity I ₂ * in the method for controlling the hybrid energy storage system 1 Describe the output from the first battery storage power.

In addition to the above disclosure is made explicitly to the disclosure of 1 to 4 directed.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 102013014667 A1 [0009]

Claims (15)

A method for determining an optimized system behavior of a hybrid energy storage system (1) having at least a first energy store (2) and a second energy store (3) by determining an optimal adjoint (λ *), comprising: - performing a first iteration loop (10) in multiple passes wherein successive passes each have one possible adjoint (λ) associated with it, wherein on each pass of the first iteration loop (10) a second iteration loop (20) is carried out, comprising the steps of: determining respectively an optimal control quantity (u *) for successive times of a given time period, wherein the optimal control quantity (u *) is a quantity describing an energy received or delivered by the second energy store and is determined based on a minimum of a Hamiltonian (H), the Hamiltonian Function (H) associated with the energy storage system (1) is dependent on a modeled system parameter (L _m ), the possible adjoint (λ) and a memory state (SoC ₂ ) of the second energy store (3), the modeled system parameter (L _m ) being a parameter to be optimized of the hybrid energy storage system (1 ), and is determined according to a predetermined power profile, which is traversed by the energy storage system (1) in the predetermined period of time, and • calculating a final storage state (SoC _2E ) of the second energy store (3), the second energy store (3) after having the predetermined period of time when the energy absorbed or emitted by the second energy store (3) was controlled in the predetermined period according to the respective optimal control variable (u *), - detecting whether the final memory state calculated by means of the second iteration loops (20) ( SOC _2E ) of the second energy store (3) is within a predetermined interval and providing a optimal adjoint (λ *) corresponding to the possible adjoint (λ) of the pass of the first iteration loop (10) for which it has been detected that the final memory state (SoC _2E ) is within the predetermined interval. Method according to Claim 1 , characterized in that the optimal control quantity (u *) describes a stream to be delivered by the second energy store (3), and / or the modeled system parameter (L _m ) is a modeled system loss, and / or the store state is a state of charge, wherein the final memory state (SoC _2E ) is a final state of charge, and / or the interval is a charging interval. Method according to Claim 1 , characterized in that the first iteration loop (10) performs a bisection method to determine the possible adjoint (λ). Method according to Claim 1 characterized in that - determining the optimal control quantity (u *) in each pass of the second iteration loop (20) is performed by executing a third iteration loop (30), wherein successive passes in the third iteration loop (30) each represent a possible control value (u) is associated, wherein in each pass of the third iteration loop (30) a value of the Hamilton function (H) according to the respective run of the third iteration loop (30) associated possible control variable (u) is calculated and the possible control variable (u ) is determined as an optimal control quantity (u *) at which the value of the Hamiltonian (H) has a minimum value, or - the determination of the optimal control quantity (u *) in each pass of the second iteration loop (20) by an analytic Calculation takes place. Method according to one of the preceding claims, characterized in that the predetermined interval is an interval around an initial storage state (SOC _2A ) of the second energy store (3), which the second energy store (3) has at the beginning of the predetermined period. Method according to one of the preceding claims, characterized in that the modeled system parameter (L _m ) based on a DC resistance of the first energy store (2), a DC resistance of the second energy store (3), one of the energy storage system (1) to be delivered for the respective time Power (P) according to the predetermined power profile and an efficiency of a DC / DC converter (4) via which the first energy storage (2) and the second energy storage (3) are connected in the energy storage system (1) is determined. Method according to one of the preceding claims, characterized in that in calculating the value of the Hamiltonian function (H) an addition of the modeled system parameter (L _m ) takes place with a derivation of the memory state (SoC ₂ ) of the second energy store (3) was multiplied by the possible adjoint (λ). Method for controlling a hybrid energy storage system (1) comprising at least a first energy store (2) and a second energy store (3), comprising: - detecting a first input value and a second input value, the first input value including a precalculated value of an optimal adjuster (2) λ *) and the second input value describes a deviation of a memory state (SoC ₂ ) of the second energy store (3) from a reference memory state (SOC _{2, Soll} ), - adapting the optimal adjuncts (λ *) for a current memory state (SoC ₂ ) of the second energy store (3) based on the first and the second input value in order to determine a matched adjuster (λ _a ), - providing an energy target value (I _ges ) which describes an energy which is consumed by the first energy store (2) and to provide the second energy store (3) together, - determining an optimal control variable (I ₂ ^* ) basi on the adjusted adjoint (λ _a ) and the energy target value (I _tot ), the optimal control quantity (I ₂ ^* ) being a quantity describing an energy received or delivered by the second energy store, and the optimal control quantity (I ₂ ^* ) is determined according to a Hamilton function (H) associated with the energy storage system (1), the Hamilton function (H) being dependent on a calculated system parameter (L _b ) of the hybrid energy storage system (1), the adapted adjunct (λ _a ) and the current memory state (SoC ₂ ) of the second energy store. Method according to Claim 8 , characterized in that the storage state is a state of charge, and / or the energy target value (I _ges ) is a current target value, and / or the optimal control variable (I ₂ ^* ) describes a stream to be delivered by the second energy store (3), and / or the calculated system parameter (L _b ) is a system loss of the hybrid energy storage system (1). Method according to one of Claims 8 or 9 , characterized in that the calculated system parameter (L _b ) is dependent on a power loss of the first energy store (2) and a power loss of the second energy store (3) and in particular further dependent on a power loss of an energy converter (4), via which the first Energy storage (2) and the second energy storage (3) in the energy storage system (1) are connected. Method according to one of the preceding Claims 8 to 10 , characterized in that the optimal control variable (I ₂ ^* ) is computationally determined, or the optimal control variable (I ₂ ^* ) is determined in tabular form, wherein in the tabular determination a table is queried in which different combinations of values of the adjusted adjunct ( λ _a) and values of the current target value (I _tot) is assigned an optimum control variable (I ₂ ^*). Method according to one of the preceding Claims 8 to 11 , characterized in that the adaptation of the optimal adjoint (λ *) by means of a PI controller (7) takes place. Method according to one of the preceding Claims 8 to 12 , characterized in that the optimal adjoint (λ *) is obtained by the method according to any one of Claims 1 to 6 is produced. An apparatus for generating an optimal adjoint (λ *), comprising a computing unit, which is adapted to the method for determining an optimized system behavior of a hybrid energy storage system (1) according to one of Claims 1 to 7 perform. Device (50) for controlling a hybrid energy storage system, comprising a control unit (54), which is adapted to the method for controlling a hybrid energy storage system according to one of Claims 8 to 13 perform.

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