EP4295258A1

EP4295258A1 - Method for ascertaining the charge state of a phase-change material

Info

Publication number: EP4295258A1
Application number: EP22709985.0A
Authority: EP
Inventors: Dominik PERNSTEINER; Alexander Schirrer; René Hofmann; Stefan Jakubek
Original assignee: Technische Universitaet Wien
Current assignee: Technische Universitaet Wien
Priority date: 2021-02-17
Filing date: 2022-02-15
Publication date: 2023-12-27
Also published as: WO2022175212A1; AT524238B1; AT524238A4

Abstract

The aim of the invention is to determine the charge state of a phase-change memory cell. According to the invention, this is achieved in that at least two different thermodynamic state variables are detected at provided measurement points (M) of the phase change memory cell (2); a system model (10) is used to ascertain a predicted starting variable vector y_{M, k}, a predicted system state vector x_{M, k}, and sensitivities E of the ascertained predicted starting variable vector y_{M, k} as partial derivatives of the predicted starting variable vector y_{M, k} according to the system state vector x of the system model (10); a correction X_korr for the predicted system state vector x_{M, k} is ascertained at the time interval k using the predicted starting variable vector y_{M, k}, the sensitivities E of the predicted starting variables y_{M, k}, and measured starting variables y_k in order to ascertain an estimated system state vector x_{M, k}, from which the charge state SOC is ascertained, for the at least one phase-change memory cell (2) at the time interval k.

Description

Procedure for determining the state of charge of a phase change storage device

The present invention relates to a method for determining the state of charge of a phase change memory with at least one phase change memory cell in predetermined time steps, the thermodynamic state of the phase change memory cell locally distributed over the at least one phase change memory cell being determined using a system model and the system model showing the relationship between an input variable vector with predetermined input variables, a system state vector with specified system state variables, an output variable vector with specified output variables and based on specified model parameters using at least one system model equation.

A phase change storage as a thermodynamic system stores energy in the form of latent heat of a phase change material. The amount of heat supplied is used for a phase change of the phase change material, e.g. a phase change from solid to liquid, and is stored as latent heat in the phase change material. When the phase change is reversed, the latent heat is released again. Depending on the phase change material used, the phase change takes place at a certain temperature (e.g. in the case of pure substances or eutectics) or in a narrow temperature range (so-called Mushy Region). Phase change storage is used, for example, to store heat in industrial processes, in building technology, district heating, etc. The current state of charge is an important parameter for the use of the phase change memory, for example as a basis for regulating the operation of the phase change memory. However, the state of charge is not generally defined, but there are a wide variety of possible definitions for the state of charge, such as in Zsembinszki G., atal., "Evaluation of the State of Charge of a Solid/Liquid Phase Change Material in a Thermal Energy Storage Tank", Energies 2020, 13, 1425.

A complete set of independent state variables clearly describes a thermodynamic system and thus also the state of charge of a phase change storage device. It is assumed that knowledge of the thermodynamic state within the system is sufficient to determine a chosen formulation of the state of charge in the form SOC = SOC (x). The SOC designates the selected formulation of the state of charge (SOC) as a function of the system state vector x, which contains the entire thermodynamic state. Essentially, the state of charge states how much heat (or energy) is stored in the phase change accumulator or how much heat (or energy) can still be supplied to or removed from the phase change accumulator, often as a dimensionless value such as a percentage. Consequently, knowledge of the thermodynamic state of the phase change material of the phase change memory is of great importance for the operation of a phase change memory. However, it is far from trivial to determine the thermodynamic state of the phase-change material with sufficient accuracy. On the one hand, this is due to the thermodynamic properties of the phase change material, in particular the temperature dependence of certain material parameters, and the phase change storage device, but on the other hand also to the type of thermodynamic change of state (which can depend on how the phase change material is arranged in the phase change storage device).

A phase change memory used in a known Ruths memory to increase the heat storage capacity is described in Pernsteiner D., et al., "Co-simulation methodology of a hybrid latent-heat thermal energy storage unit, Applied Thermal Engineering 178 (2020) 115495. In this case, the Ruths memory is surrounded by the phase change memory in the form of a multiplicity of phase change memory cells in which a phase change material is arranged. Heat is supplied to and stored in the Ruths storage tank by means of steam. The supplied heat is also stored as latent heat in the phase change storage. The stored heat can be extracted again by extracting steam from the Ruths storage tank.

EP 3336473 A1 proposes a method for determining the state of charge of a phase change storage device, in which temperatures are measured at various points and a temperature field in the phase change material is calculated from this in a computing unit, on the basis of which a distribution of a local state of charge (state of charge field) of the phase change material is determined. Although the temperature can be measured easily and reliably, it is only suitable to a limited extent for determining the state of charge of a phase-change storage device. This is due to the fact that the temperature during the phase change either has no significance at all with regard to the stored latent heat, because the temperature during the phase change remains constant (pure substances, eutectics), or the phase change takes place in a narrow temperature range (mushy region), so that even small temperature measurement errors can have a major impact on the local state of charge derived from this. The information content of the measured output (temperature) therefore varies over the possible operating range of the phase change material. It has therefore been shown that with a representation of the thermodynamic state using the temperature field over the entire possible range of the state of charge of the phase change material, as in EP 3336473 A1, only imprecise results can be achieved and in particular a mapping of the melting behavior of pure substances and eutectics is not possible. The reason for this can be seen in the phase change, which is explained in the following simple example.

When heat is added to water in a container, the temperature increases until the phase change occurs, at which point the water begins to vaporize. In the case of an isobaric change of state (pressure remains constant), the temperature remains constant from this moment on. Before that, i.e. until the start of the phase change, the volume remains approximately constant. This means that no meaningful information about the internal energy or enthalpy of the water is obtained with just a volume measurement up to the beginning of the phase change, because the internal energy increases, but this is not significantly reflected in the volume. When the phase change occurs, there is a significant change in density (density falls), i.e. the volume increases sharply. However, just measuring the temperature from the beginning of the phase change does not provide any meaningful information about the internal energy or enthalpy of the water, because the internal energy increases, but this is not reflected in the temperature.

It is thus an object of the present invention to improve the determination of the state of charge of a phase change memory cell.

This object is solved with the features of the independent claims. By using different thermodynamic state variables as output variables, a robust, optimal observability of the thermodynamic system behavior, especially in the area of the phase transition, is ensured. In addition, the sensitivities (also called sensitivities) of the model outputs from the physical relationships are expressed directly as part of the model formulation and are thus used correctly in the observer. This also enables the use of pure substances and eutectics as phase change materials. The ongoing correction of the model also corrects model errors and model parameter errors, which also contributes to increasing accuracy. Only then is it possible to estimate the locally distributed state field of the phase change memory over the entire working range with a high level of accuracy. With the precisely estimated state field, an exact estimate of the state of charge can then also be made.

Further advantageous configurations of the invention and their effects result from the dependent claims and the following description of the invention.

The present invention is explained in more detail below with reference to FIGS. 1 to 4, which show advantageous configurations of the invention by way of example, schematically and not restrictively. while showing

1 shows a phase change memory with a phase change memory cell with a phase change material, 2 shows a sequence according to the invention for determining a locally distributed state of the phase change memory cell,

3 shows the result of the inventive determination of a locally distributed state of the phase change memory cell when determining the state of charge, and FIG. 4 shows an application of the inventive determination of the state of charge when controlling the operation of the phase change memory.

A phase change memory 1, as shown in FIG. 1, comprises a phase change material 3, which is usually arranged in a number of phase change memory cells 2, which are assembled into the phase change memory 1, as for example in the paper by Pernsteiner D., et al. is described. Which phase change material 3 is used, how a phase change memory cell 2 is designed (eg geometry, material, etc.) and how phase change memory cells 2 are assembled into the phase change memory 1 is irrelevant for the invention. The phase change memory cell 2 usually forms a housing, for example made of aluminum or steel, in which the phase change material 3 is arranged. The phase change memory cell 2 can be closed so that no volume change of the phase change material 3 is possible, but can also be open so that a volume change is possible (isobaric state change). The phase change material 3 is usually present in different phases P1, P2, for example solid and liquid, depending on the state of charge. A phase change front 4 forms between the phases P1, P2. The phase change memory 1, or a phase change memory cell 2 of the phase change memory 1, heat Q can be supplied to or removed from at least one specific point (as indicated in FIG. 1). The heat Q supplied or removed is, for example, the heat flowing out of or in a Ruths storage tank. It is also possible to take into account heat Q _v that is drawn off as a result of losses, for example as a result of thermal radiation, thermal conduction or convection.

At least two measurement sensors 5, 6 are provided on the phase change material 3, with which two different thermodynamic state variables are detected at the measurement points M provided, as will be described in detail below. The measurement points M are preferably distributed locally over the phase change memory cell 2 , it being possible for at least one measurement point M to also be arranged in the phase change material 3 .

The invention is based on a system model 10 of the phase change store 1, which describes the thermodynamic state of the phase change store 1 using at least one system model equation, usually an equation system of system model equations. For the modeling of the phase change memory 1 with multiple phase change memory cells 2, it is usually sufficient to model one phase change memory cell 2. The system model 10 of the phase change memory 1 then consists of a large number of individual models of the phase change memory cells 2 involved, it also being possible for heat flows between the phase change memory cells 2 to be taken into account. The system model 10 thus consists of at least one system model equation, usually an equation system of system model equations, a phase change memory cell 2. The system model 10 comprises, in particular, system state variables combined in a system state vector x, an input variable vector u with at least one input variable u and an output variable vector y with at least one output variable y. The system model 10 thus describes the system state at any point in time in the form of the system state vector x and the output variable vector y as a function of the input variable vector u. A known initial state of the phase change memory cell 2 can be assumed for the use of the model. The at least one output variable y of the output variable vector y is one at the

Phase change storage cell 2 (or on the phase change material 3) measurable thermodynamic state variables, such as pressure, temperature, volume, or a measure of energy (such as internal energy or enthalpy). A measurable thermodynamic state variable is also understood to mean a measurable physical variable from which a thermodynamic state variable can be determined, such as density, electrical conductivity, or another measurable material parameter, etc. A thermodynamic state variable can thus be measured directly or can be measured indirectly other measured physical quantities are derived or determined.

In FIG. 1, temperature sensors 5 are provided in the phase change material 3 or on the phase change memory cell 2, for example, in order to measure the temperatures T at predetermined measurement points M as output variables y. When using

Temperature sensors 5, at least one temperature sensor 5 is provided, preferably several temperature sensors 5 distributed over the phase change material 3. In addition, a volume sensor 6 is provided in the exemplary embodiment shown, in order to measure a volume change as a further output variable y at a measuring point M. However, it should be expressly pointed out that other thermodynamic state variables can also be measured as output variables y by means of measuring sensors and also at other and/or several measuring points M of the phase change material 3 or the phase change memory cell 2. Such a system model 10 describes in particular the local distribution of the system state variables x in the system (here for example in the phase change material 3 of a phase change memory cell 2), for example as a field of specific enthalpy, specific internal energy, Gibbs energy or temperatures.

At least one input variable u of the input variable vector u can be dem

Phase change material 3 supplied or the process heat Q removed from this can be used. The heat Q _v removed due to usual losses, for example through thermal radiation, convection or thermal conduction into the environment or heat dissipation to adjacent phase change memory cells 2, can be considered as a (further) input variable u of the model. The input variables u are known, for example, due to the operational management of the phase change storage device 1 (supplied, removed heat), or can also result from the known structural design of the phase change storage device 1 or a phase change storage cell 2 (e.g. heat flow due to losses).

The system model 10 also includes model parameters Q, such as the density of the phase change material 3, the heat capacity of the phase change material 3, the thermal conductivity of the phase change material 3 or the dynamic viscosity of the phase change material 3, with a model parameter Q also depending on at least one thermodynamic state variable, for example the temperature T , can be. One or more model parameters Q can also be combined in a model parameter vector Q.

It should be noted that between the system state vector x, which represents the dependent variable in the system model 10, and the thermodynamic state variables, e.g. specific enthalpy h, temperature T, pressure p, specific volume v, which describe the thermodynamic state of the phase change material 3, to distinguish is. The system state vector x can contain thermodynamic state variables, but also other physical variables describing the phase change material 3 or the phase change memory cell 2 .

The thermodynamic system model 10 of the phase change memory 1 can be described in the form of a system of differential equations (at least one system equation) and can generally be written in the usual way as are written with the time t, the output variable vector y with the output variables y, the input variable vector u with the input variables u, the system state vector x with the system state variables x and the model parameters Q, which are summarized in the model parameter vector Q. The input function f _E and the output function f _A result from the modelling. The modeling also determines which system state vector x, as well as which input variable vector u and which model parameter vector Q are used. The system state variables x are described therein in a locally distributed manner, for example in FIG. 1 with a predetermined resolution in the x and y directions.

The system model 10 can preferably express the parameter dependency or the required sensitivities, explained further below, over the entire working range of the phase change memory 1 in order to be able to appropriately inform the optimal observer described below. It is also assumed that the sensitivities of the output variables y can be formed with respect to the system state vector x and possibly also with respect to the model parameters Q .

The output function f _A is formulated such that the output variables y are expressed at least at the measuring points M of different thermodynamic state variables, ie at the points at which the at least two measuring sensors 5, 6 are arranged. The output variables y are a function of the system state variables x, which in turn are expressed by the input function f _E . The system state variables x are thus known over the entire phase change material 3 . An output variable y can thus be a system state variable x at the measuring point M of the measuring sensor 5, 6, for example. If, for example, the temperature at the phase change material 3 is measured with a temperature sensor 5 at a specific measuring point M, then the temperature determined with the system model 10 (in this case as system state variable x) at this measuring point M corresponds to the output variable y. If the output variable y is not a system state variable x of the system model 10, for example the volume of the phase change material 3, then such an output variable y can be determined from the existing system state variables x of the system model 10.

The thermodynamic modeling of the phase change material 3 can be formulated on the basis of the conservation laws, ie the conservation of mass, the conservation of energy and the conservation of momentum, for example as in the document Pernsteiner D. et al. described for the isobaric case. The system model 10 includes such a Formulation at least the conservation of energy. The phase change material 3 can thus, for example, generally be calculated using the partial differential equations be described in a temperature formulation representing the transient energy balance equation (conservation of energy), the continuity equation and the Navier-Stokes equation (from top to bottom). The continuity equation and the Navier-Stokes equation are optional, which is indicated by the square brackets. The phase change material 3 can also be described equivalently in an enthalpy formulation, in which the enthalpy h is the dependent variable and not the temperature T (as in the example above). A formulation in another thermodynamic state variable is also conceivable. In the case of changes of state other than isobaric, other formulations result.

Therein "" denotes the scalar product, T denotes the temperature field T (x, y, z, t) for a Cartesian coordinate system [x, y, z] at time t (whereby any other coordinate system can also be used) for the phase change material 3 (in the two-dimensional case corresponding to T (x, y, /)) and v=[v _x , v _y , v _z ] denotes the velocity field of the phase change material 3 with the spatial velocity components v _x (x, y, z, t), v _y (x, y, z, /), v _z (x, y, z, t) (or v=[v _x , _vy ] with v _x (x, y, /), _vy (x, y, t) in the two-dimensional case). V = (d / dx, d / dy, d / &) denotes the Nabla operator for a Cartesian coordinate system [x, y, z] (in the two-dimensional case correspondingly V = {dldx, d/dy) ). p denotes the density of the phase change material 3, c the heat capacity of the phase change material 3, k the thermal conductivity of the phase change material 3 and m the dynamic viscosity of the phase change material 3, which are known for a specific phase change material 3. The heat capacity c can depend on the temperature T, for example according to In it, D l _m denotes the specific latent heat (relative to mass), T _m the melting temperature of the phase change material, e the temperature range of the phase change (mushy region) and c _s and c _L the heat capacities of the

Phase change material 3 in the two possible phases (e.g. solid, liquid) of the phase change material 3, which are known for a specific phase change material 3. / denotes the force density acting on the phase change material 3 in the form of the buoyant force of the phase change material 3, which can be expressed in the form / = pG, with the density p (which is usually formulated as a function of temperature, for example with a well-known Boussinesque approximation) and the cosO

acceleration vector G (in the two-dimensional case) the gravitational acceleration sinO g as a function of the position of the phase change material 3 in space. If the phase change memory cell 2 with the phase change material 3 is inclined by the angle F relative to the vertical and the Cartesian coordinate system is also inclined with the phase change memory cell 2, then a component of the gravitational acceleration g results in the two coordinate directions x, y.

The pulse source term S _v can be chosen so that this term for a

Phase change memory cell 2 becomes zero in a first phase P1 (eg in the liquid state) and assumes a very large value in a second phase P2 (eg in the solid state). In between, the value of the pulse source term S _v depending on the proportion of the phases

P1, P2 can be determined. The pulse source term S _v can also be chosen differently for other possible phase states. The momentum source term S _v can also be omitted entirely.

The system model 10 is completed by at least one boundary condition that can be derived from the specific configuration of a phase change memory cell 2 . Boundary conditions are defined at the edges R1, R2, R3, R4 of the phase change memory cell 2, for example. For example, the upper and lower edges R2, R4 can be defined adiabatically (ie without heat exchange) in the form q | _{Д2 Д4} = 0 , with the specific heat flow q . In the exemplary embodiment shown, heat is supplied or removed at the lateral edges R1, R3. Accordingly, at these edges R1, R3, the boundary conditions with the specific heat flow over the edges

R1, R3 can be defined as follows, q \ _m =cc _out (T(x,y,t)-T _out ) and q \ _R3 = a _n (T(x,y,t)-T _n ) .

Therein a _out , a _n denote the known heat transfer coefficients at the edges R1, R3 and T _out , T _{jn denote} the known edge temperatures at the walls of the edges R1, R3. The boundary conditions of the system model 10 are thus formulated using the input variables u. With the known heat flows Q , Q _v at the edges

(e.g. by measurement) the temperatures along the edges can be determined.

For the velocity field v=[v _x , v _y ] v | can be used as a boundary condition _{A1 R2 R3 A4} = 0 . Furthermore, for each solid phase change material 3 in the

Phase change memory cell 2 are recognized as a boundary condition v = 0. The same can be assumed for a phase change material 3 that is not completely liquid.

The above partial differential equations with the boundary conditions describe the thermodynamic state of the entire phase change material 3 in the phase change memory cell 2 under consideration in a two-dimensional model using the local temperature field T (x, y, t) and the local velocity field v=[v _x , v _y ]. The temperature field T (x, y, t) and the velocity field v=[v _x , v _y ] are therefore the system state variables x of the model. The input variables u (supplied and dissipated heat) are mapped via the boundary conditions. The output variables y correspond at least to the variables determined at the measuring points M of the measuring sensors 5, 6.

The system model 10 described above is in particular also able to simulate the heat transfer in the phase change material 3 due to convection and conduction with high accuracy, which ultimately also makes it possible to describe the thermodynamic state of the phase change material 3 with greater accuracy.

However, this system of differential equations cannot usually be solved directly in the present form. Therefore, the differential equations, at least the energy equation and the Navier-Stokes equation (if any), are preferably spatially discretized and solved numerically, as for example also in Pernsteiner D. et al. described. Among other things, finite element methods (FEM), finite volume methods (FVM) or finite difference methods (FDM) can be used for this purpose. These are known numerical methods for solving partial differential equations.

The basic idea of the FDM is to approximate the spatial derivatives in the differential equation at a finite number (="finite"), equidistant grid points by difference quotients. The approximated solutions of the differential equation at the grid points can then be calculated using the corresponding system of equations. Preferably the continuity equation and the Navier-Stokes equation of the model are solved with FDM.

With a FEM or FVM approach, the calculation area becomes the

Phase change memory cell 2 (with the phase change material 3) is divided into a large number of finite elements. Approach functions are used for these elements (e.g. local Ritz approaches, Galerkin approach per element), which describe how an element reacts to external influences and boundary conditions. These formulation functions are used for all elements in the differential equations to be solved, resulting in a system of equations taking into account the initial, boundary and transition conditions. This system of equations is solved step by step (in a given time step) progressively in time. These solutions of the system of equations represent the approximate solution of the underlying differential equation over the simulated time period. The energy equation of the model is preferably solved with FEM.

For example, for a FEM approach, bilinear rectangular elements with four nodes can be used to obtain the finite element representation of the temperature field T = /V{ } (analogously also in the case of another thermodynamic state variable such as the enthalpy h). In it, N = [N _y , N ₂ ,...,N _non \ denotes the vector of the approach functions for the number non of the nodes of the elements and {.} stands for a vector ( non x 1) with the values at the nodes of the Elements. Using this finite element representation and applying Galerkin's method leads to a system more ordinary

Differential equations C † + K\T} = R (the matrices C , K and the vector R result), which can be solved to obtain the values of the temperature at the nodal points of the elements. In an analogous way, the velocity field components can be expressed and calculated.

Since FEM and FDM methods usually result in very large systems of equations, known methods of model reduction can also be used to reduce complexity by reducing the number of system-descriptive FEM / FVM or FDM equations without significantly increasing the characteristic behavior change. The computing time can thus be significantly reduced, in particular to such an extent that the simulation can be carried out in or faster than real time (in the sense of a specified time step to be observed in which the calculation must be completed) with currently easily available computers.

To calculate the locally distributed thermodynamic state of the phase change material 3 with the system model 10 could first with the Energy equation, the temperature field T (x, y, t) can be determined numerically (e.g. with FEM), or in an enthalpy formulation the enthalpy field. With the temperature field T (x, y, /), or the enthalpy field, the velocity field v=[v _x , v _y ] with the velocity rock components v _x , v _y can then optionally be determined numerically from the continuity equation and the Navier-Stokes equation (e.g. with FDM). For example, the temperature field T (x, y, t) is taken into account via the force density /. In this way, the required output variables y can be determined at the measuring points M provided.

With such a system model 10 of the phase change material 3, for example in a phase change memory cell 2 or a phase change memory 1, the locally distributed thermodynamic state of the phase change material 3 can be determined at any point in time t , usually in predetermined discrete time steps k , from a variable measured on the phase change material 3 , for example Temperatures T, and starting from the thermodynamic state at a previous point in time (usually in the previous time step k- 1), can be determined, for example in the form of a temperature field T (x, y, z, t) and a velocity field v=[v _x (x, y , z, /), v _y (x, y, z, /)] over the phase change material 3.

The thermodynamic system model 10 of the phase change memory cell 2 described above can be used in an observer to reconstruct the system state vector x of the system model 10 from the known input variable vector u (e.g. due to the process control of the phase change memory 1) and known (e.g. measured) output variables y. A state of charge SOC of the phase change material 3 can then be determined, for example, with the system state vector x. This procedure is described in EP 3336 473 A1, for example.

However, this procedure is not expedient in the present application due to the generally erroneous measured variables of the output variables y to be expected and due to the model errors. For example, the temperature measurements themselves are generally subject to errors (calibration errors, noise in the measurement signal, etc.), and the thermodynamic system model 10 naturally also contains model and model parameter errors. In order to balance out these errors in a well-defined manner, a different procedure is used according to the invention in order to obtain a more accurate and reliable estimate of the state of charge SOC, as explained with reference to FIG. As explained at the beginning, the information content of a measurable output variable y can change with changing system state variables x in the system state vector x. In order to avoid this problem, at least two different thermodynamic state variables are used as output variables y in the system model 10 and the sensitivities E of these output variables y are taken into account. The corresponding sensitivities E of the measurable output variables y with regard to changes in the system state vector x quantify the information content of the measured variables. The sensitivities E are expressed as a derivation of the output variables y according to the i > 1 system states x _t in the system state vector x, i.e. dy dy . These derivatives can be determined numerically or analytically dx dx _l '' dx _t .

If the system model 10 contains unknown or uncertain model parameters Q, then the system state vector x can be expanded by them in order to also estimate the unknown model parameters Q with the system state vector x. Consequently, model parameters Q to be estimated can also be contained in this extended system state vector x. The sensitivities E are thus expressed in terms of this extended system state vector x. The sensitivity E thus includes the derivatives of the output variables y according to the system state vector x, which may include the model parameters Q to be estimated. These derivatives can be determined numerically or analytically.

The invention is therefore based on a thermodynamic system model 10 as described above, which has at least two different thermodynamic state variables at certain measuring points M provided as output variables y, for example temperature, volume, pressure, electrical conductivity, etc., of which preferably at least one output variable y about the working area of the

Phase change memory cell 2 always has a non-zero sensitivity E F 0 . Temperature or enthalpy and volume or pressure, for example, are suitable as such thermodynamic state variables. This ensures good observability of the system model 10 in the entire working area of the phase change material 3.

Based on the system model 10 of the phase change memory cell 2 and the known input variable vector becomes at the current time step k the system state vector x _{M k} predicted with the system model 10 (which the predicted model parameters q _{M ]ί} as indicated in FIG. 2) and the predicted output variable vector y _{M k} , which contains the output variables y _k at the measuring points M, is determined (for example as described above). In a sensitivity calculation unit 12, the sensitivities E of the predicted output variables y _{M k} _with regard to the

System state variables x are determined in the system state vector x, e.g. E dx current time step k, the output variables y _k are also measured at the measuring points M of the measuring sensors 5, 6. Also the input variables in the input variable vector can be measured using suitable measuring sensors, or can also be obtained from other sources. The predicted output variables y _{M k} , the measured output variables y _k and the sensitivities E are transmitted to an observer 11 . Depending on the difference between the predicted output variables y _{M k} and the measured output variables y _k , as well as the sensitivities E, a correction x ^ _k of the system state variables x in the system state vector x is determined in the observer 11 . The observer 11 can also determine a correction Q_korr _k of the model parameters Q in the model parameter vector Q of the model 10, which can be contained in the system state vector x, as indicated in FIG. To determine the correction(s), the observer 11 can also use the system model 10 of the phase change memory cell 2, as indicated in FIG. In a correction unit 13, the predicted system state x^ _k determined with the system model 10 in the current time step k is corrected with the correction x^ _k in order to determine the estimated system state x^ in time step k. The state of charge SOC can then be determined in a state of charge calculation unit 14 from the estimated system state x^.

It should be noted that the sensitivities E do not necessarily have to be determined in each time step k because it can be assumed that the sensitivities dy

E _M,k in the phase change memory cell 2 does not change rapidly. It is therefore sufficient if the sensitivities E are determined in larger, predetermined time steps (for example a whole multiple of the time step k). This can help reduce the computational burden of determining the estimated system state to reduce. The system model 10, the sensitivity calculation unit 12, the correction unit 13 and the state of charge calculation unit 14 are usually software components that are implemented on computer hardware, or else on distributed computer hardware, and run there. Of course, other implementations are also conceivable, such as an integrated circuit (IC), for example an application-specific integrated circuit (ASIC) or a field programmable gate array (FPGA).

The system model 10 is thus continuously adapted according to the invention based on measurements of the output variables y _k in order to be able to estimate the locally distributed thermodynamic state of the phase change memory cell 2 more precisely.

The sensitivities E are taken into account in the observer 11 in order to make the correction _k of the system state vector x, and, if necessary, the correction 0 _{korr k} of the model parameter vector Q of the system model 10 to determine. The correction x _{korr !c} of the system state vector x and, if necessary, the correction Q_ korr _k of the model parameter vector Q_ _k is therefore dependent on the sensitivities E , the predicted output variables y _{M k} and the measured output variables y _k . After the sensitivities E of the output variables y are defined in relation to the system state vector x (which can also include the model parameters Q to be estimated), those components of the system state vector x that have the greatest influence on the output variables y are corrected the most. At the same time, because of these sensitivities E, only those output variables y that are influenced by the current state of the phase change material 3 are taken into account for the correction of the system model 10 .

The observer 11 could be designed, for example, as a known extended Kalman filter or a known moving horizon estimator.

In each time step k, a moving horizon estimator uses a cost function J _k as a function f ₃ of the output variable vector y _k actually measured at the intended measuring points M, the output variables y _{M k} estimated at these measuring points M using the system model 10, the sensitivities E and the correction x^ _k of the system state vector , and if necessary (expressed by the square brackets) the correction of the model parameter vector Q, , i.e. J _k =f _J (y _M^k ,y _k ,E,x _{corr k} [,0 _{corr k} ]) , in order to determine the corrections x _{korr k} , q^ _{01Ύ ΐz} from this by optimizing the cost function J _k . In the cost function J _k , m preceding time steps can also be taken into account (hence moving horizon), for example in the form f _j [A ]) This objective function J _k is optimized in each time step k jk-m+ 1 (usually minimized, but maximization is also conceivable) by those corrections x _{korr k} of the system state vector x , and possibly the corrections 0 _{korr k} of the model parameter vector Q, that minimizes the deviation between the estimated outputs y _{M k} and the actually measured outputs y _k . Mathematically, this can be expressed, for example, in the form min (J _k ) - » c^ _k ,0 _{corr k} will.

Considering m measurements of past time steps, the cost function J _k could be of the form J _k , with the Euclidean vector norm , be expressed (here without considering model parameters to be corrected). Of course, another vector norm could also be used. The target function J _k can be optimized iteratively in each time step k, for example, with the corrections x _{korr k} , and possibly 0 _{korr k} , being changed in each iteration step according to predetermined rules of the optimization algorithm used. The optimization algorithm used ensures that the value of the target function J _k converges towards an optimum (maximum, minimum). The iteration is terminated and the corrections determined in the last iteration step are terminated by a defined termination criterion of the optimization, for example a certain number of iteration steps or a deviation of the values of the objective function of successive iteration steps , and if necessary _k , are used in the correction unit 13 for correcting the system model 10 . A well-known gradient method is often used for optimization, in which new corrections are made in each iteration step , and if necessary _k , along the dy

gradient of the output variable y is sought. It can be seen that the gradient dx corresponds to the sensitivities E, which means that the sensitivities E are taken into account in the optimization. As is known, an extended Kalman filter is based on a calculation rule in order to estimate the current system state vector ^ and possibly the model parameter vector _{Q_k} to be estimated, starting from a known, past system state vector x and possibly model parameters Q . For this purpose, a Jacobian matrix of the output equation f _A of the system model 10 is also used in the calculation specification of the extended Kalman filter. The Jacobian matrix contains the

Derivatives of the output variables y according to the system state vector x and, if necessary, according to the model parameter vector Q, and thus the sensitivities E , which are provided by the model formulation described above. In this way, the sensitivities E are taken into account in the Extended Kalman Filter.

The corrections x^ _k , and if necessary Q^ _{01Ύ k} , could directly the estimated

System state vector x^ or the estimated model parameter vector be. In this case, the correction of the (predicted) system state vector x^ _k determined with the system model 10 in the correction unit 13 consists in that the determined

(Predicated) system state vector x _{M k} is replaced by the correction x _{korr k} , so the estimated system state vector is ^ = x^ _k . However, it is also possible to define the corrections x^ _k and possibly ^ _{01Ύ k} as changes Dc^ in the system state vector x _{M k} predicted using the system model 10, and possibly changes Aq^ in the predicted model parameter vector § _{M k} . The estimated system state vector x^ then results, for example, in c^=x^ _k +Ax _k , and the estimated model parameter vector results in 0 _{M k} +A0 _k .

The model parameter vector Q is preferably corrected for the next time step k+1, i.e. it is only in the next time step k+1 that the model parameters Q in the model parameter vector Q of the system model 10 are corrected with the corrections determined in the previous time step k

Q _{jiorr k} to be updated.

The corrected system state vector x^ represents an optimal estimate of the locally distributed thermodynamic state of the phase change material 3 and can be used for the optimal estimate of the state of charge SOC. For example, an energy measure can be used as the state of charge, for example a current enthalpy based on a total enthalpy of the phase change material 3 in a specific phase P1, P2 (e.g. solid or liquid). However, the state of charge SOC can also be calculated in any other way, as explained at the outset. The state of charge is usually an absolute value for the phase change material 3 and not a variable that is distributed locally over the phase change material 3 (a field). In general, the state of charge SOC describes the still available heat storage capacity of a phase change memory cell 2 in relation to a defined nominal value. The nominal value can be the known total possible latent heat of the phase change memory cell 2, for example.

Through the total enthalpy of a storage cell H, the SOC can, for example

H can be expressed in the form SOC= — — , with the determined current total enthalpy

H _g of the phase change material 3 in the phase change memory cell 2 and the known potential enthalpy H _nom (nominal value) of the phase change material 3 in the phase change memory cell 2.

The state of charge SOC can of course also simply be extrapolated to the entire phase change memory 1, consisting of a plurality of phase change memory cells 2.

The thermodynamic state variables in the system state vector x are variables distributed locally over the phase change material 3, for example in the form of an enthalpy field or temperature field over the phase change material 3. This can be used, for example, to determine the entire energy content (e.g. enthalpy content) of the phase change memory cell 2, for example by integrating the enthalpy field. The state of charge SOC of the phase change memory cell 2 can in turn be determined directly from this. Furthermore, other important parameters such as a locally distributed degree of melting, the structure of the phase distribution (liquid/solid/gaseous) in the phase change material 3, or the position and course of the melting front 4 can also be determined from state variable fields of system state variables x.

The result of the correction of the system model 10 as proposed according to the invention has been illustrated in FIG. The curve SOC _R shows the real profile of the state of charge of a phase change memory cell 2 over time t as a result of a predetermined time profile of the input variables T _jn , T _out der

Phase change memory cell 2, which has been determined, for example, using a thermodynamic simulation. The curve SOC u shows the time course of the state of charge for the same phase change memory cell 2 with the same course of the input variables, which is based on an uncorrected system model 10 deviating initial conditions was determined. It can be seen that the model errors and deviations inherent in the system model 10 are retained and are reflected in the state of charge. The curve SOC c shows the profile of the state of charge for the same phase change memory cell 2 and the same profile of the input variables that was determined using a system model 10 corrected according to the invention. You can see that any model errors are quickly corrected and the state of charge then follows the real course very well. The state of charge was of course determined in the same way in the various curves.

The determined state of charge SOC of the phase change memory cell 2 or of the phase change memory 1 can be used to regulate the operation of the phase change memory 1 (consisting of at least one phase change memory cell 2), as shown in simplified form in FIG. A phase change storage device 1 with at least one phase change storage cell 2 stores heat Q from an industrial process 20, e.g. a process of steel production and processing, or supplies heat Q to an industrial process 20, e.g. a district heating network, the source of the heat Q for the phase change storage device 1 and the sink for heat Q from the phase change memory 1 do not necessarily have to be the same. The flow of heat between the phase change storage device 1 and the industrial process 20 is regulated with a controller 21 . The controller 21 processes the current state of charge SOC of the phase change storage 1 in order to regulate the heat flow, for example with the aid of at least one actuator 23 (e.g. a pump, a heat exchanger, etc.) for influencing the heat flow. The state of charge SOC is determined in a state determination unit 22, which can be designed according to FIG. 2, for example. The controller 21 and the status determination unit 22 can of course also be integrated in a common unit, for example computer hardware could be provided on which the controller and the status determination are implemented as software.

Claims

patent claims

1. Method for determining the state of charge of a phase change memory (1) with at least one phase change memory cell (2) in predetermined time steps k, wherein the thermodynamic state of the phase change memory cell (2) locally distributed over the at least one phase change memory cell (2) is determined using a system model (10). and the system model (10) calculates the relationship between an input variable vector u with specified input variables u , a system state vector x locally distributed over the phase change memory cell (2) with specified system state variables x , an output variable vector y with specified output variables y and using

Describes model parameters Q using at least one system model equation, characterized in that at least two different thermodynamic state variables are detected at provided measuring points (M) of the phase change memory cell (2) and the output variable vector y these at least two different thermodynamic ones

State variables at the measuring points (M) as output variables y that with the system model (10) based on known input variables u at time step k a predicted output variable vector y _{M k} and a predicted system state vector x ^ _k are determined that with the determined predicted system state vector x _{M k} sensitivities E of the determined predicted output quantity vector y _{M k} as dy

Derivatives E _M,k of the predicted output quantity vector y _{M k} after the dx

System state vector x of the system model (10) can be determined that at time step k the at least two different output variables y _k are measured at the measuring points M, that at time step k using the predicted output variable vector y _{M k} , the sensitivities E of the predicted output variables y _{M k} and a correction x _{korr k} of the system state vector x is determined from the measured output variables y _k and the predicted system state vector x^ _k determined with the system model (10) is corrected with the correction ^ _{GG ί} of the system state vector x in order to obtain an estimated system state vector x^ at time step k to determine for the at least one phase change memory cell (2) and that based on the estimated system state vector x ^ of State of charge SOC of the at least one phase change memory cell (2) for the current time step k according to a predetermined calculation rule SOC=SOC{x _k ) is determined.

2. The method as claimed in claim 1, characterized in that the system model equation contains a transient energy balance equation of the phase change material (3) of the at least one phase change storage cell (2) formulated with at least one thermodynamic state variable.

3. The method according to claim 2, characterized in that the system model equation contains a Navier-Stokes equation and a continuity equation of the phase change material (3) of the at least one phase change memory cell (2).

4. The method according to claim 1, characterized in that the

System model equation contains at least one of the at least one phase change memory cell (2) or the phase change material (3) of the phase change memory cell (2) dependent boundary condition.

5. The method according to claim 1, characterized in that the system state vector x of the system model (10) contains model parameters Q of the system model (10) to be estimated.

6. The method according to any one of claims 1 to 6, characterized in that the dy

Sensitivities E _M,k are determined in predetermined larger time steps than the time steps k dx.

7. The method according to any one of claims 1 to 6, characterized in that the

Correction ^ _{GG ί} of the system state vector x as an estimated system state vector is used by replacing the predicted system state vector x _{M k} with the correction ^ _{GG ί} .

8. The method according to any one of claims 1 to 6, characterized in that as a correction ^ _{GG ί} of the system state vector x a change D ^ the predicted

system state vector is determined and the estimated system state vector ^ is determined as the sum of the predicted system state vector x _{M k} and the change D ^.

9. The method according to claim 1, characterized in that based on the predicted output variable vector y _{M k} , the sensitivities E of the predicted output variables y _{M k} and the measured output variables y _k at time step k, a correction of the Model parameter vector Q is determined and the estimated model parameter vector Q_ _k of the system model (10), the correction ^ _{orr t} of the model parameters Q is used.

10. The method according to claim 1, characterized in that based on the predicted output variable vector y _{M k} , the sensitivities E of the predicted output variables y _{M k} and the measured output variables y _k at time step k, a change A0 _k in the model parameter vector Q is determined and as an estimated model parameter vector Q_ _k a sum of the predicted model parameter vector § _{M k} and the change Dq^ of the model parameter vector Q is used.

11. The method as claimed in claim 9 or 10, characterized in that the estimated model parameter vector Q_k of the system model (10) is used for the next time step _k +1.

12. Phase change memory (1) with at least one phase change memory cell (2) and a state of charge calculation unit (14), which determines a state of charge SOC of the phase change memory (1) in predetermined time steps using a locally distributed thermodynamic state of the phase change memory cell (2), wherein a system model (10 ) it is provided that the thermodynamic state of the phase change memory cell (2) locally distributed over the at least one phase change memory cell (2) from a relationship between an input variable vector u with predetermined input variables u , a system state vector x locally distributed over the phase change memory cell (2) with predetermined system state variables x , an output variable vector y with predetermined output variables y and determined using model parameters Q using at least one system model equation, characterized in that on the phase change memory cell (2) at intended measuring points (M) at least two Measuring sensors (5, 6) are arranged, which detect different thermodynamic state variables, the output variable vector y containing these at least two different thermodynamic state variables at the measuring points (M) as output variables y, that the system model (10) based on known input variables u at time step k a predicted output vector y _{M k} and a predicted

System state vector x _{M k} determined that a sensitivity calculation unit (12) is provided, from the determined predicted system state vector x ^ _k dy _Mk

Sensitivities E of the predicted output variables y _{M k} as derivatives E = - ' des

- ' dx predicted output variable vector y _{M k} according to the system state vector x of the system model (10) determined that the measuring sensors (5, 6) at time step k measure the at least two different output variables y _k at the measuring points M that an observer (11) provided is that at the time step k based on the predicted

Output quantity vector y _{M k} , the sensitivities E of the predicted output quantities y _{M k} and the measured output quantities y _k determine a correction ^ _{GG ί} of the system state vector x, that a correction unit (13) is provided, which uses the system model (10) to determine the predicted system state vector x^ _k corrected with the correction ^ _{GG ί} of the system state vector x and at time step k an estimated system state vector for the at least one phase change memory cell (2) and that the state of charge calculation unit (14) uses the estimated system state vector x^ to determine the state of charge SOC of the at least one phase change memory cell (2) at the current time step k according to a predetermined calculation rule SOC=SOC ( x^ ).

13. Use of the method according to any one of claims 1 to 11 for controlling the operation of a phase change memory (1) consisting of at least one phase change memory cell (2), wherein in a controller (21) an actuator (23) for supplying or dissipating heat (Q ) the determined state of charge SOC of the at least one phase change memory cell (2) is used in the phase change memory (1).