EP1701005A1 - Method and apparatus for the calculation of energy and technical processes - Google Patents

Abstract

The method involves using a computational model based upon a balance equation of the first law of thermodynamics. The calculation is carried out in the form of an optimization calculation into which a technical boundary condition, which is formulated in the form of an inequality, enters as a secondary condition. A logical condition is received as secondary condition into the optimization calculation. An independent claim is included for a device.

Description

The invention relates to a method for calculating energy and process engineering processes, in particular the heat cycle of power plants, by means of a computer based on at least one balance equation of the first law of thermodynamic law computational model and an apparatus for performing this method.

zu den Gleichungen des Modells hinzugefügt. Insgesamt besteht das Modell dann aus einem Vektor mit n Gleichungen und der gleichen Anzahl an unbekannten Variablen. Ein solches System wird als quadratisches System bezeichnet.In a generic method known in the prior art stationary technical processes in the field of energy and process engineering are formulated by a physical model to form a mathematical model. This model has the balance equations of the first thermodynamic law (mass, energy and momentum balance). Furthermore, for certain variables of the model, fixed values can be specified by the inclusion of boundary conditions in the form of equations. For example, it can be specified that no cooling water is sprayed into a tempering unit of freshly generated steam. This is the condition $${\mathrm{m}}_{\mathrm{spray}}=0$$

added to the equations of the model. Overall, the model then consists of a vector with n equations and the same number of unknown variables. Such a system is called a quadratic system.

After establishing the balance equations and the equations defining the boundary conditions in the context of a phase 1, a Newton iteration for finding a first approximation solution of the present equation system is then carried out by a simulation program in the context of a phase 2. thereupon Once again, the simulation program turns to Phase 1, in which the boundary condition equations are checked using the found approximate solution and modified if necessary.

Following on from the example given above, it is checked, for example, whether the determined temperature of the live steam has exceeded a certain limit value, in which case a boundary condition is introduced in the form of an equation in which the live steam temperature is set to this limit value. In return, the feed rate of the cooling water in the temperature control unit is then no longer fixed, but defined as a variable. That is, the boundary condition m _spray = 0 is taken out of the equation system, with the result that the next approximate solution contains a calculated value for m _spray . The simulation algorithm then returns to Phase 2, where another Newton iteration is performed. Phase 1 and Phase 2 are repeated iteratively until the variables are within the desired bandwidths and the desired tolerances of the approximate calculation are fulfilled.

The implementation of this algorithm is relatively cumbersome and therefore time consuming. The solution thus obtained must continue to be checked for plausibility. The solution is checked for logical errors. This includes, for example, checking whether the temperature at the outlet of a heat exchanger is higher than at its inlet. Other logical checks include the occurrence of negative solutions to variables for which such solutions are excluded. If implausibilities are discovered in this phase, the entire simulation model must be revised and then recalculated. The fault identification is done manually and usually requires extensive investigations.

The invention has for its object to overcome the above-mentioned disadvantages and in particular a method and to provide a device for the calculation of energy and process engineering processes, allowing faster calculation and faster and easier troubleshooting.

als Nebenbedingung begrenzt werden.This object is achieved according to the invention with an aforementioned method for calculating energy and process engineering processes, which is characterized in that the calculation is carried out in the form of an optimization calculation into which at least one technical boundary condition formulated as an inequality enters as a secondary condition. In such an optimization calculation, an optimization algorithm determines the minimum or maximum of an objective function in a specific permissible range described by constraints in the form of equations or inequalities. For example, non-linear programming (NLP) methods are available for optimization. By including the at least one technical boundary condition as a constraint in the optimization calculation, upper and lower bounds for the optimization variables can be taken into account in the optimization calculation. Following on from the previous example, for example, the temperature of the supplied live steam to a maximum temperature by taking into account the inequality $${\mathrm{T}}_{\mathrm{live\; steam}}<{\mathrm{T}}_{\mathrm{Max}}$$

be limited as a constraint.

$$\mathrm{Nebenbedingungen}\hspace{0.17em}c\left(x\right)=0$$

$$h\left(x\right)\le 0$$

$$x^L\le x\le x^U$$

wobei
Φ die zu minimierende oder maximierende Zielfunktion ist,
x ein Vektor aus kontinuierlichen Optimierungsvariablen mit n durch die Optimierungsrechung zu bestimmenden Elementen ist,
c ein Vektor aus in Form von Gleichungen dargestellten Randbedingungsfunktionen mit m Elementen ist, wobei diese Randbedingungsfunktionen im Wesentlichen aus den Bilanzgleichungen des ersten thermodynamischen Hauptsatzes gebildet sind,
h ein Vektor aus in Form von Ungleichungen dargestellten Randbedingungsfunktionen ist,
x ^L ein Vektor aus festen unteren Grenzen für die Optimierungsvariablen ist, wobei manche untere Grenzen - ∞ betragen können, in welchem Fall Variablen ohne einer unteren Grenze dargestellt werden, sowie
x ^u ein Vektor aus festen oberen Grenzen der Optimierungsvariablen ist. Manche oberen Grenzen können + ∞ betragen, in welchem Fall Variablen ohne einer oberen Grenze dargestellt werden.The optimization problem solved according to the invention can be represented mathematically in general as follows: $$\underset{x}{\min }\mathrm{\Phi }\left(x\right)$$

$$\mathrm{constraints}c\left(x\right)=0$$

$$H\left(x\right)\le 0$$

$$x^L\le x\le x^U$$

in which
Φ is the objective function to be minimized or maximized,
x is a vector of continuous optimization variables with n elements to be determined by the optimization calculation,
c is a vector of boundary condition functions with m elements represented in the form of equations, these boundary condition functions essentially being formed from the balance equations of the first thermodynamic law,
h is a vector of constraint functions represented in the form of inequalities,
x ^{L is} a vector of fixed lower bounds for the optimization variables, some of which may be lower bounds - ∞, in which case variables without a lower bound are represented, as well
x ^{u is} a vector of fixed upper bounds of the optimization variable. Some upper bounds can be + ∞, in which case variables without an upper bound are represented.

It is noted that both the expression (5) and the expression (6) represent boundary conditions in the form of inequalities and the representation with upper and lower limits according to expression (6) merely a simplified representation of correspondingly formulated inequalities according to expression (5). is.

The invention is based on the recognition that by means of the calculation of the physical model carried out according to the invention in the form of an optimization calculation, an inherent calculation of all technical boundary conditions is possible. Thus, a calculation of the corresponding energy or process engineering process in a continuous calculation cycle is possible. Iterative runs of different calculation phases with adjustments of the boundary conditions between them, as in the simulation model based calculation of the prior art are no longer necessary. Since an overall optimization of the system continues to be carried out, it is possible to remedy possible errors in the case of specified boundary conditions for certain variables more quickly. A possibly inappropriate setpoint for a variable is in fact easily apparent from the optimization result, since the variable value calculated by the optimization algorithm generally differs significantly from the inappropriate setpoint. Since the optimization algorithm strives to optimize a set of many variables, in the optimization result, the corresponding single variable will not be very close to the inappropriate setpoint, as this will generally result in much less favorable results for many other variables, thereby rendering the optimization result as a whole excessive would be worsened.

In an advantageous development of the invention, at least one logical condition enters into the optimization calculation as a secondary condition. Advantageously, this at least one logical condition enters into the optimization calculation in the form of an inequality. Such a logical condition may e.g. Relate temperatures at two different locations of a device in the form of an inequality. For example, it may be specified that the temperature at a heat exchanger inlet must be higher than the temperature at the heat exchanger outlet. Since such logical conditions are taken into account directly by the calculation method in the embodiment according to the invention, a subsequent plausibility check in this regard is no longer necessary.

Advantageously, in the inventive calculation method, a quadratic simulation task given by the computational model is reformulated into an optimization task. In this case, for example, the existing in the form of equations in the computational model boundary conditions transferred to the objective function of the optimization calculation. The remaining balance equations from the computational model are now considered as constraints in the optimization calculation.

In addition, the optimization calculation is advantageously based on a quadratic target function for calculating the smallest quadratic distances of the optimization variables of predefinable target values. The objective function to be minimized in the optimization task then consists of the sum of the quadratic distances of the optimization variables or conversion functions dependent thereon from the respectively assigned nominal values. With such an objective function, it is possible to quickly find inappropriately selected setpoint values and thus fast troubleshooting. This is due to the fact that in the solution found by the optimization calculation, the totality of the optimization variables is as close as possible to the respective assigned setpoint values. However, if a certain setpoint is chosen inappropriately, the optimization algorithm does not appreciably approximate the variable associated therewith to this setpoint, if this would result in a greater increase in the distance of the other optimization variables to their setpoints, which would be the case for a single setpoint that is technically inconsistent would. As a result, due to a large distance between an optimization variable and its desired value, such an inappropriate target value is usually immediately apparent in the solution resulting from the optimization calculation and can thus be corrected in a targeted manner.

However, some optimization algorithms work more efficiently with linear objective functions than with quadratic objective functions; in particular, quadratic objective functions in some algorithms generate a considerable number of entries in the Hesse matrix, which can lead to too many degrees of freedom for updating the Hesse matrix. To use such algorithms, it is therefore appropriate if the Optimization calculation is based on a linear objective function.

Furthermore, it is advantageous if at least one technical boundary condition formulated as an equation enters into the optimization calculation as a secondary condition. This increases the flexibility in defining the optimization problem.

Furthermore, it is expedient if at least one logical condition is derived from the second thermodynamic law. That is, certain inequalities between temperatures at different locations of a system resulting from the entropy set can already be included in the optimization calculation as a secondary condition. A subsequent plausibility check of the solution found by the calculation algorithm with respect to approximately mandatory entropy increases in irreversible processes is thus superfluous.

The invention further relates to a device for carrying out the method according to the invention.

An embodiment of the invention will be explained in more detail with reference to the accompanying schematic drawing. In the figure, the figure shows an illustration of the solution space of two optimization variables bounded by technical boundary conditions in the form of inequalities.

The embodiment of the invention described below is used to calculate the heat cycle of a cogeneration plant. For this purpose, the heat cycle is first described by means of balance equations c (x) of the thermodynamic law (mass, energy and momentum balance) as a function of optimization variables x _i . Then, command values are y _{s, i} this optimization variables x _i and of the optimization of variable _i of an internal transformation vector b (x _i) arising variable x defined using. Such an internal conversion vector b (x _i ) can, for example, the relationship represent between the entropy specified as the desired value and the temperature that predetermines as the optimization variable. Furthermore, boundary conditions h (x) are defined in the form of inequalities for the optimization variables x _i .

With reference to the _figures , in such a boundary condition, for example by means of the inequality m _spray ≥ 0, the fresh water rate sprayed into a temperature control unit for live steam can be set to a value of at least zero. A further boundary condition can limit the temperature of the live steam (T _{live steam} ) to a maximum value T _max (T _{live steam} ≦ T _max ). However, the two optimization _variables m _spray and T _{live steam} are functionally interdependent since a higher addition of water spray reduces the live steam temperature. This functional dependence is contained in the balance equations c (x). Furthermore, certain optimization variables may also be limited by lower limits x ^L and upper limits x ^U.

Nebenbedingungen: $$\mathrm{c}\left(\mathrm{x}\right)=0$$

$$\mathrm{h}\left(\mathrm{x}\right)\le 0$$

$${\mathrm{x}}^{\mathrm{L}}\le \mathrm{x}\le {\mathrm{x}}^{\mathrm{U}}$$

Then, the following optimization problem is set up for the calculation of the smallest quadratic distances of the optimization variables from the given target values: $$\underset{x}{\min }{{\displaystyle \underset{i}{\Sigma }\left(y_{s.i}-b\left(x_i\right)\right)}}^2$$

Constraints: $$\mathrm{c}\left(\mathrm{x}\right)=0$$

$$\mathrm{H}\left(\mathrm{x}\right)\le 0$$

$${\mathrm{x}}^{\mathrm{L}}\le \mathrm{x}\le {\mathrm{x}}^{\mathrm{U}}$$

Then this optimization problem is solved with a suitable optimization algorithm. The values obtained for the optimization variables are optimized in such a way that the sum of their quadratic distances from the predefined setpoints assumes a minimum value. If a setpoint for an optimization variable x _i, which is inappropriate for the system, has been specified, then this discrepant setpoint can be recognized immediately on the solution, since the for this variable, as a result of the optimization calculation resulting value has a considerable compared with the results of the other variables distance from its associated setpoint. For such a case, the setpoint for the corresponding variable is then corrected and the entire optimization calculation is repeated.

Nebenbedingungen: $${\mathrm{y}}_{\mathrm{s}}-\mathrm{b}\left(\mathrm{x}\right)=\mathrm{p}-\mathrm{u}$$

$$\mathrm{p},\mathrm{u}\ge 0$$

$$\mathrm{c}\left(\mathrm{x}\right)=0$$

$$\mathrm{h}\left(\mathrm{x}\right)\le 0$$

$${\mathrm{x}}^{\mathrm{L}}\le \mathrm{x}\le {\mathrm{x}}^{\mathrm{U}}$$

As an alternative to the least-squares approach outlined above, a linear approach can also be chosen as follows: $$\underset{p.u}{\min }{\displaystyle \underset{i}{\Sigma }\left(p_i+u_i\right)}$$

Constraints: $${\mathrm{y}}_{\mathrm{s}}-\mathrm{b}\left(\mathrm{x}\right)=\mathrm{p}-\mathrm{u}$$

$$\mathrm{p}.\mathrm{u}\ge 0$$

$$\mathrm{c}\left(\mathrm{x}\right)=0$$

$$\mathrm{H}\left(\mathrm{x}\right)\le 0$$

$${\mathrm{x}}^{\mathrm{L}}\le \mathrm{x}\le {\mathrm{x}}^{\mathrm{U}}$$

ist hiermit linear. Manche Lösungsalgorithmen arbeiten effizienter mit einer linearen Zielfunktion.Here, p and u are auxiliary variables. The objective function ${\displaystyle \underset{i}{\Sigma }\left(p_i+u_i\right)}$

is hereby linear. Some solution algorithms work more efficiently with a linear objective function.

Claims (8)

Method for calculating energy and process engineering processes, in particular the heat cycle of power plants, by means of a computational model based on at least one balance equation of the first thermodynamic law,
characterized in that the calculation is performed in the form of an optimization calculation, in which at least one formulated in the form of an inequality technical boundary condition enters as a secondary condition. Method according to claim 1,
characterized in that at least one logical condition enters as a constraint in the optimization calculation. Method according to claim 1 or 2,
characterized by reformulating a quadratic simulation task given by the computational model into an optimization task. Method according to one of the preceding claims,
characterized in that the optimization calculation is based on a quadratic target function for the calculation of the smallest quadratic distances of the optimization variables (x _i ) from predetermined target values. Method according to one of the preceding claims,
characterized in that the optimization calculation is based on a linear objective function. Method according to one of the preceding claims, characterized in that at least one formulated as an equation technical boundary condition enters as a constraint in the optimization calculation. Method according to one of the preceding claims,
characterized in that at least one logical condition is derived from the second thermodynamic law. Apparatus for carrying out the method according to any one of the preceding claims.

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