EP2394031B1 - Method for installation control in a power plant - Google Patents

Description

The invention relates to a method for system control in a power plant, in which for a plurality of sets of control values each of a set of environmental values on the one hand and the respective set of control values, on the other hand, a functional value of a target function based on a physical model is assigned to the respective sets, wherein the set of control values for forwarding to a control device of the power plant is selected, the associated function value meets a predetermined optimization criterion.

In a power plant non-electrical energy, for example in the form of fossil fuels is converted into electrical energy and made available to a power grid. Depending on the used type of raw material used for the production of electrical energy, for example, a distinction is made between coal-fired power plants, nuclear power plants, gas and steam turbine plants, etc.

Due to the increasing global demand for energy and the shortage of fossil primary energy sources, the price of the raw materials used for electricity generation is currently rising. These increasingly stringent environmental regulations, come respect. Particulate NO _x, SO ₂ and CO _2. Therefore, the aim is to increase the efficiency of power plants, ie their efficiency.

In addition to the cost-intensive further development and renewal of plant components, modern process control technology also optimizes process control, taking current boundary conditions into account. In this case, different optimization criteria such. B. be desired to increase the efficiency or a reduction of pollutant emissions. Decisions that were traditionally based on the experience of operating personnel can now be based on computers and the corresponding procedures Basis of physical models that mathematically model the power plant process.

Usually, such a method comprises a target function, which generates a scalar or vector-valued function value based on a physical model of the corresponding power plant from a set of process values. On the one hand, the process values include those that are determined by external influences (environmental values), such as ambient and cooling water temperatures, and that change during operation. The environmental values represent current boundary conditions that you have no influence on but that have an influence on the process.

On the other hand, the process values also include the control values, such as, for example, the position of an actuator or valve or the amount of fuel supplied, which can be influenced by operating personnel or an automated control device during ongoing operation of the power station, i. H. within certain limits freely selectable process or state variables. Each set of control values in conjunction with the ambient values yields a value of the target function that can be used to evaluate the respective set and usually the set of control values for forwarding to a control device of the power plant is selected, the associated function value meets a predetermined optimization criterion. For example, in the case of a scalar function value, this may be the largest or smallest function value.

In order to find an optimal set of manipulated variables to control the power plant, gradient methods are commonly used to find a minimum or maximum of the objective function. For this purpose, various methods such as the steepest descent method, the (quasi) Newton method, the sequential quadratic programming or the simplex algorithm are known. Common is the gradient method in that starting from a starting value, a local maximum or minimum of the target function is found.

The physical models of power plants that yield the objective function of optimization are mostly non-linear and generally non-convex. Depending on the chosen starting value, therefore, the gradient method may under certain circumstances be a local maximum or minimum, ie. H. find a locally optimized operating state of the power plant, but this does not ensure that it also the globally optimal operating condition is found.

From the US 2004/0240648 A1 A method for plant control is described in which an optimal set of manipulated variables for controlling the plants is determined by using statistical and / or gradient-based optimization methods and physical models of power plants.

The invention is therefore an object of the invention to provide a method for plant control in a power plant and a control device for a power plant, which at the lowest possible tax expenditure improved operation of the power plant with respect to a given optimization criterion such. B. allow an improvement in the efficiency or a reduction of emissions.

With regard to the method, this object is achieved according to the invention in that the number of sets of control values in addition to a starting set and a set determined by the gradient method from the starting set and its assigned function value further comprises a set selected by means of a random generator.

The invention is based on the consideration that an improved operation of the power plant would be possible if In determining the control values of the power plant, an optimized set of control values could also be found globally with regard to the given optimization criterion, such as increasing the efficiency and / or reducing emissions. This could be done, for example, with a Monte Carlo method, which randomly selects control values and compares their functional values and optionally in another Step in the range of the best manipulated variable set another number of randomly selected control values checked. However, such a method is relatively time-consuming and computationally intensive and therefore also computationally comparatively expensive. Therefore, the comparatively faster gradient method should basically be retained, but extended in the manner of a hybrid structure by a random-based system, so that the finding of a global optimum of control values is also made possible. This can be achieved by additionally introducing a set of control values determined by a random generator and its assigned function value of the target function during the gradient process, and this random set of control values when comparing the sets of control values and their respective functional values.

The combination of a gradient-based method with a random model on the one hand ensures the finding of a global optimum for the control values for the system control, on the other hand ensures comparatively fast convergence of the optimization algorithm to suitable control values. Therefore, such a designed algorithm is also suitable for online optimization in the power plant process, d. H. for adapting the control values to the respectively optimum operating state during the ongoing operation of the power plant. For this purpose, the method is advantageously carried out cyclically repeating in the manner of a loop, wherein the selected set of control values of one cycle is the starting set of the cycle following this. As a result, once set and found set of control values can be further improved during operation of the power plant and there is a continuous search for global optima.

This is particularly useful in terms of changing environmental parameters during operation. For example, if an environmental parameter, such as the cooling water temperature, changes, for example, the set of Control values may no longer be the optimal set of control values. In this case, the set of control values is changed so far by means of the continuously executed gradient method that a new optimum with regard to the selected optimization criteria is set again. Due to the complex relationship between the ambient values and the function value of the objective function, however, a change in the ambient values may also result in a new global optimum, which would not be found with a pure gradient method, since this would remain at the local optimum. The connection of the random-based system with the gradient method in cyclic execution makes it possible to find a new global optimum in operation. This new optimum is then forwarded to a control device of the power plant and can there be displayed to the operating personnel and thus enables a rapid response and thus a particularly efficient operation of the power plant.

An online optimization in the plant control of a power plant system makes it possible to determine an optimum set of control values at each operating time, which ensures particularly efficient operation of the power plant. In order to allow this set of control values to be transmitted as quickly as possible to the plant control of the power plant, the selected set of control values is advantageously transferred in the control device to the individual control values respectively assigned control devices of the power plant. By such a direct forwarding of the control values to the corresponding control devices such as the fuel conveyor, a particularly fast, automatic optimization of the power plant operation is achieved. In this case, no intervention of operating personnel is more necessary so that on the one hand automated operation of the power plant is guaranteed and on the other hand, a particularly fast forwarding of the optimum control values to the control devices takes place.

The operation of a power plant, in addition to the external influences, which enter through the environmental values, also other restrictions, under whose consideration the control and optimization must be performed. Such restrictions may in the simplest case be limits of individual variables, such as the cooling water mass flow, or more complex relationships. These can be expressed in the physical model, for example, by equations or inequalities in which several variables occur in combination. In order to adequately take into account such restrictions in the optimization and system control, the objective function advantageously comprises a penalty function. Such a penalty function is designed to provide a value of zero, provided that the restrictions are not violated, and contains a monotonically increasing relationship between the error from the restriction violation and its function value. The addition of the target and penalty functions thus results in a modification of the objective function at which the optimization is carried out. As a result of this forced deterioration of the target function values in the impermissible range, the method provides a set of manipulated variables in which the restrictions are not violated. In addition, the method is thereby able to start even from an illegal starting value, the gradient method and thus the optimization, which is not always the case with other methods for the integration of restrictions. This allows a further simplification of the method.

When determining a set of manipulated variables by means of the gradient method, the gradient serves as an indicator for the direction in which the respective manipulated variables must be changed in order to arrive at an optimum manipulated variable set. It is questionable, however, how far the control values have to be changed, ie which step size should be used in the application of the gradient method. This can be done, for example, by performing a one-dimensional optimization along the search direction in each iteration and thus finding a seemingly optimal step size becomes. However, this results in the search direction being orthogonal to the previous one, since the partial derivative at the current location after the previous search direction was minimized to zero by the one-dimensional optimization in the previous iteration. This effect leads to a zigzag course in narrow valleys of the objective function with very small step sizes and thus to many iterations. Since, however, in the case of online optimization, a fast convergence should be sought, since the sets of control values are to be used directly in the power plant, a step size is advantageously predetermined by the gradient method before the respective determination of the set. A given step size allows the gradient method to be carried out quickly and should be kept constant until one iteration (when minimized) provides a greater function value than the previous one. Then the step size is reduced and the process proceeds from the best value. As a result, a particularly fast execution of the method and a particularly efficient online optimization of the power plant operation is possible.

With regard to the control device, the object is achieved by a control device for a power plant with a random generator module and a gradient module, which data output side are connected to a comparison module, wherein the control device is designed for carrying out said method. Advantageously, such a control device is used in a power plant with a control device and such with the control device data input side connected control device used.

The advantages achieved by the invention are, in particular, that the possibility of finding a global solution by means of the random number generator with the rapidity of the control by the additional consideration of a set of control values selected by means of a random generator Gradient method is connected. The random number generator generates potential starting values for the gradient method, which are adopted if they are better in the sense of the physical model of the objective function than the local optimum previously found by the gradient method. Due to the cyclical application of the process and the use of current environmental values, which can be taken directly from the process control system, the process is online-enabled. If the operating status of the system changes, this information flows into the physical process model online and the optimization algorithm quickly finds the new optimum. The process in the process control technology of a power plant can initially serve as an aid to the operating personnel, but are also switched directly to corresponding actuators for automatic forwarding for a quick reaction of the power plant control technology. As a result, a particularly efficient operation of a power plant plant is made possible with low technical effort.

An embodiment of the invention will be explained in more detail with reference to a drawing. Therein, the FIG shows a schematic representation of the method for plant control of a power plant.

The method illustrated in the FIGURE optimizes cyclically repeating the control values for the power plant to achieve a particularly efficient operation of the power plant. As a result of the cyclical repetition, the process is online-capable, ie it can be integrated directly into the process control technology and determine the currently optimum control values during operation. One possible area of application is, for example, the optimization of the interval between the sootblowing operations in the boiler of the power plant and its duration and the cleaning intervals of the filters in the flue gas cleaning, where a consideration is drawn between short-term malfunction and longer-term increase in efficiency. Two further optimization problems from the power plant area are the determination of the optimum cooling water mass flow, provided that this is regulated, and the litigation in the case of incineration in compliance with emission limits and plant-related restrictions.

The FIG shows the structure of the method as a block diagram. The gradient module 1 is given starting values 3 by a memory module 5, from which the closest optimum is found in a number of steps or iterations with the aid of numerical differentiation. The basis for this optimization is the functional values determined for each set of control values and environmental values on the basis of an objective function 7 based on a physical model.

Restrictions on the manipulated variables are incorporated additively into the objective function 7 by a penalty function. As long as the restrictions are met, the penalty function returns the value zero, so that no modification of the objective function 7 takes place. If the restrictions are violated, the penalty function returns a value greater (less) zero if it is a minimization problem (maximization problem). Due to a steadily increasing (falling) relationship between the error resulting from the violation of the restrictions and the function value of the penalty function, the optimization method working with the target function 7 modified by the penalty function is automatically guided in the direction of the valid range, provided the penalty function has a magnitude greater slope than the objective function. In order to ensure this, a strongly increasing penalty function is used, whereby an optimum of the unmodified objective function becomes the optimum of the objective function 7 only under active consideration of the restrictions within the required accuracy.

Several iterations of the gradient method can already be carried out in the gradient module 1, so that a particularly accurate set of control values of a local optimum can already be found here. The set of control values thus found becomes together with the respective assigned function values the target function 7 to a comparison memory module 9 passed. This compares the current function value with that best (in the sense of the objective function 7) and, in each cycle, switches over that set to the memory module 11 which has the smaller (larger) function value, provided that it is a minimization (maximization).

The gradient method makes it possible to find a local optimum of control values for the operation of the power plant. However, in particular when there is a change in the ambient values which can not be influenced by the operating personnel, there may possibly be another global optimum which can not be found by the gradient method. In order to ensure a particularly efficient operation of the power plant in this case too, a random generator module 13 is provided which generates in each cycle for each control value 15 approximately equally distributed random values within their respective definition range. The randomly generated set of control values 15 is evaluated via the target function 7 and supplied together with the function value of the target function 7 as a first input sentence to the comparison module 17, which receives as a second input set the determined by the gradient method sentence from the comparison memory module 11. The comparison module 17 compares the function values of the two input sets and, in each calculation cycle, switches the input set to the output having the smaller (larger) function value if minimization (maximization) is provided.

In an extension of the system for the treatment of a larger number of control values 15, the addition of a second or further random number generator modules 13 may also be considered. In this way, the optimization space exponentially growing with the number of control values 15 can be searched stochastically more intensively, thus accelerating the finding of the global optimum.

The output of the comparison module 17 is connected to a comparison memory module 19 which stores in the time window in which the gradient method is running the smallest or largest function value with the associated control values from the comparison module 17. If the gradient method converges, the stored set is transferred to the storage module 5 and from there to the control device 21 of the power plant, the storage module 5 being connected upstream of the gradient module 1 and delivering its starting values 3. At the same time, the newly found optimum, which is present in the comparison memory modules 9 connected downstream in the gradient module 1, is forwarded to the memory module 11 before the comparison module 17, and in the next cycle the comparison memory modules 9, 19 are reset.

By means of this design, a found optimum is kept unchanged in the loop until either a better set value set has been replaced from the stochastic part by the result of the last cycle of the gradient process or the position of the optimum has shifted due to a change in the ambient values.

In the following, the individual modules of the method are described in more detail.

The random number generator module 13 has eight analog inputs for indicating the upper (ULx _i ) and lower (LLx _i ) limits of each manipulated value 15 (here: 4). In each calculation cycle, a set of random variables x _i (i = 1, 2, 3, 4) is generated which are applied to the four outputs, each variable being approximately equally distributed within its domain of definition. This is to ensure that the entire domain of variables is covered and that global optimization is successful.

und die der Zufallsvariablen $x_i^t\in \left[{\mathit{ULx}}_{\mathit{i}},{\mathit{LLx}}_{\mathit{i}}\right]$

beschreiben die Gleichungen 1 und 2. In Tabelle 1 sind die Parameter aufgeführt, die für die vier Zufallsgeneratoren im beschriebenen Baustein verwendet wurden: $$y_i^{t+1}=\left(\left({\mathit{ay}}_i^t+b\right)\mathrm{mod}m\right)\mathrm{mod}1$$

$$x_i^t=\left({\mathit{ULx}}_i-{\mathit{LLx}}_i\right)y_i^t+{\mathit{LLx}}_i$$

Tabelle 1: Im Zufallsgeneratormodul 17 verwendete Parameter a b m Variable 1 3,141592653589793 2,718281828459045 3 Variable 2 3,141592653589793 1,526341538658045 2 Variable 3 2,718281828459045 3,141592653589793 3 Variable 4 2,718281828459045 2,268542658582743 2 The random number generator of each variable is based on the linear congruence generator and is a pseudo-random generator, since the same random number sequence occurs at each start is issued. Like many random number generators, the linear congruence generator works with the modulo function, which outputs the remainder of a division. The recursive prescription of random numbers $y_i^t\in \left[0,1\right]$

and the random variables $x_i^t\in \left[{\mathit{ULx}}_{\mathit{i}},{\mathit{LLx}}_{\mathit{i}}\right]$

describe Equations 1 and 2. Table 1 lists the parameters used for the four random number generators in the described building block: $$y_i^{t+1}=\left(\left({\mathit{ay}}_i^t+b\right)\mathrm{mod}m\right)\mathrm{<figure-callout\; id="1x"\; label="mod"\; filenames="imgf0001.png"\; state="\{\{state\}\}">mod</figure-callout>}1$$

$$x_i^t=\left({\mathit{ULx}}_i-{\mathit{LLx}}_i\right)y_i^t+{\mathit{LLx}}_i$$

Table 1: Parameters used in the random number generator module 17 a b m Variable 1 3.141592653589793 2.718281828459045 3 Variable 2 3.141592653589793 1.526341538658045 2 Variable 3 2.718281828459045 3.141592653589793 3 Variable 4 2.718281828459045 2.268542658582743 2

• Z₀ = 0
• wenn Zahl > 1 und Zahl < 2
• Z₁ = 1
• wenn Zahl > 2 und Zahl < 3
• Z₂ = 2
• (...)
• abgerundete $\mathrm{Zahl}={\displaystyle \sum _i}{z}_i$
  

For the realization of the modulo function, the rounded value was subtracted from the result of the division to obtain the remainder. The rounding is done by a case distinction according to the following logic:

• Z ₀ = 0
• if number> 1 and number <2
• Z ₁ = 1
• if number> 2 and number <3
• Z ₂ = 2
• (...)
• rounded $\mathrm{number}={\displaystyle \underset{i}{\Sigma }}{z}_i$
  

In this procedure, the parameters a, b and m must be chosen so that all possible results correspond to a case in the case distinction in order to obtain an approximately equally distributed number sequence.

dient der Festlegung der Minimierung oder Maximierung (1 = Maximierung, 0 = Minimierung), abhängig von der Zielfunktion. Durchgeschaltet wird jeweils (in jedem Zyklus) das Eingangsset f( x ) _j,x _j, bei dem f( x ) _j am größten, wenn der Binäreingang wahr (1) ist, bzw. am kleinsten, wenn der Binäreingang unwahr (0) ist.The comparison module 17 has analog input sets f ( x ₁ , x ₁ , and f ( x ₂ , x ₂ (and optionally f ( x ₃ , x ₃ )) as well as a set of analogue outputs f ( x ) x , The binary entrance $\begin{array}{c}1=\mathrm{Max}\\ 0=\min \end{array}$

is used to determine the minimization or maximization (1 = maximization, 0 = minimization), depending on the objective function. Is switched through in each case (in each cycle) the input set f ( x _j , x _j , where f ( x ) _{j is} greatest when the binary input is true (1), or smallest when the binary input is false (0).

The third input is normally hidden and not connected, which means that the value is zero. So that this does not lead to a malfunction of the comparison module 17, internally at all inputs, if the value zero is present, this is replaced by the smallest (maximization) or largest (minimization) representable value, so that the desired functionality of the filtration is maintained. This must be taken into account in particular if the optimum sought is zero, since this is consequently not taken into account.

The memory module 5, 11 has an analog input set f ( x ) and x , a binary input SET and an analog output set f ( x ) and x , Setting SET to 1 switches the value set at the input to the output, stores it at 0 when SET is reset, and stops at the output until the SET input is set to 1 again.

zur Festlegung der Optimierungsart, einen binären Eingang SET, einen binären Eingang RS (RESET) und einen Satz analoger Ausgänge f( x ) und x. Solange SET und RESET unwahr sind, wird der Wertesatz f( x ) und x gespeichert und am Ausgang ausgegeben, der bisher den größten (Maximierung) bzw. kleinsten (Minimierung) Funktionswert je nach Optimierungsart besitzt. Wird SET auf 1 gesetzt, wird der Eingangssatz f( x ) und x an den Ausgangssatz f( x ) und x durchgeschaltet und bei Zurücksetzen von SET auf 0 gespeichert, wie beim Speichermodul 5. Dieser Satz bleibt gespeichert, bis am Eingang ein Satz mit einem größeren bzw. kleineren f(x) anliegt und den vorerst durch den "SET"-Befehl gespeicherten Satz ersetzt. Der binäre "RESET"-Eingang setzt den Speicher auf den kleinsten $\left(\begin{array}{c}1=\max \\ 0=\min \end{array}=1\right)$

bzw. größten $\left(\begin{array}{c}1=\max \\ 0=\min \end{array}=0\right)$

darstellbaren Wert. Dieser Eingang ist zur Initialisierung erforderlich und muss beim Starten des Algorithmus einmalig mit einem Puls betätigt werden. Ohne diese Maßnahme wäre der Initialwert des Speichers Null und würde evtl. keine neuen Werte speichern (z. B. bei einer Maximierung mit einer Zielfunktion, bei der alle Funktionswerte negativ sind).The comparison memory module 9, 19 has an analog input set f ( x ) and x , a binary input $\begin{array}{c}1=\mathrm{Max}\\ 0=\min \end{array}$

for determining the type of optimization, a binary input SET, a binary input RS (RESET) and a set of analog outputs f ( x ) and x , As long as SET and RESET are untrue, the set of values f ( x ) and x stored and output at the output, which so far has the largest (maximization) or smallest (minimization) function value depending on the type of optimization. If SET is set to 1, the input set f ( x ) and x to the source sentence f ( x ) and x and stored on reset of SET to 0, as in memory module 5. This set remains stored until at the input a set with a larger or smaller f ( x ) and replaces the sentence initially stored by the "SET" command. The binary "RESET" input sets the memory to the smallest $\left(\begin{array}{c}1=\mathrm{Max}\\ 0=\min \end{array}=1\right)$

or largest $\left(\begin{array}{c}1=\mathrm{Max}\\ 0=\min \end{array}=0\right)$

representable value. This input is required for initialization and must be pressed once with a pulse when the algorithm is started. Without this measure, the initial value of the memory would be zero and possibly not store new values (eg, when maximized with an objective function where all function values are negative).

Zuletzt besitzt der Baustein weitere zwei binäre Eingänge $\begin{array}{c}1=\max \\ 0=\min \end{array}$

und RS und vier analoge Eingänge "steps", "minstep", "1/Dx" und "Zykluszeit". Über den Eingang $\begin{array}{c}1=\max \\ 0=\min \end{array}$

wird, wie zuvor beschrieben, die Optimierungsart vorgegeben und am Eingang "Zykluszeit" muss die Rechenzykluszeit, mit der der Optimierungsalgorithmus betrieben werden soll, in Sekunden vorgegeben werden. Über 1/Dx wird der Abstand der Stützstellen für die Bildung des Differenzquotienten vorgegeben und "steps" sowie "minstep" gehen in die Schrittweitensteuerung ein, wie nachstehend beschrieben. Die Ausgänge bestehen aus einem binären Signal "Konv", welches wahr wird, wenn das Gradientenverfahren konvergiert ist, und zwei analogen Ausgängen x_i und x_i + Δx_i für jeden Stellwert.The gradient module 1 has for each control value x _i (here: 4) three analog inputs for determining the upper (U Lx _i ) and lower (LLx _i ) limit and the starting value x _is . There is also an analog input f ( x ) and for each control value x _i an analogue input $f\left(\overrightarrow{x}+{\overrightarrow{e}}_i\mathrm{\Delta }{x}_i\right)\mathrm{,}$

Finally, the block has another two binary inputs $\begin{array}{c}1=\mathrm{Max}\\ 0=\min \end{array}$

and RS and four analog inputs "steps", "minstep", "1 / Dx" and "cycle time". About the entrance $\begin{array}{c}1=\mathrm{Max}\\ 0=\min \end{array}$

As described above, the type of optimization is specified and at the input "cycle time", the computing cycle time with which the optimization algorithm is to be operated must be specified in seconds. The spacing of the interpolation points for the formation of the difference quotient is specified via 1 / Dx, and "steps" and "minstep" are included in the step size control, as described below. The outputs consist of a binary signal "conv", which becomes true when the gradient method has converged, and two analog outputs x _i and x _i + Δx _i for each manipulated value.

verschoben sind. Durch die Auswertung der Zielfunktion an den Stützstellen und Bildung der diskretisierten partiellen Ableitungen, ergibt sich die Suchrichtung. Die normierte Suchrichtung wird durch das Teilen des Suchrichtungsvektors (Gradient), durch den Betrag der größten partiellen Ableitung erreicht, so dass die normierte Hauptsuchrichtungskomponente den Betrag eins hat. Die Anfangsschrittweite wird aus dem Definitionsbereich (U Lx_i - LLx_i) der Stellwerte mit der größten partiellen Ableitung gebildet, indem dieser mit $\frac{{\mathit{steps}}^{1,5}}{\min \mathit{step}}$

multipliziert wird. Der neue Vektor x ^t+1 ergibt sich aus dem vorherigen in Summe mit der über die Schrittweite gestreckten, normierten Suchrichtung. Dieses Verfahren wird so oft wiederholt, bis der Wert der Zielfunktion sich nicht stetig ändert, sondern oszilliert. Haben die nummerisch gebildeten Gradienten dreimal in Reihe ihr Vorzeichen gewechselt, wird der Wert "steps" intern um eins reduziert und das Verfahren läuft mit verringerter Schrittweite weiter. Das Konvergenzkriterium ist erfüllt, wenn die Schrittweite den Wert Null erreicht hat, oder aber sich der Wert der Zielfunktion innerhalb von vier Iterationen nicht ändert. In dem Fall wird der Binärausgang "Konv" wahr und das Gradientenverfahren kann durch Betätigen des "RS"-Einganges und neuen Startwerten neu gestartet werden.The gradient method forms, as the name already suggests, the partial derivatives of the objective function after the manipulated variables in order to determine the direction of optimization. For this purpose, starting from the location vector x x ^t , which in the first iteration of the seed vector x _s is formed, supporting points, each in the direction of a control value x _i order $\frac{{\mathit{ULx}}_{\mathit{i}}-{\mathit{LLx}}_{\mathit{i}}}{1/\mathit{dx}}$

are shifted. By evaluating the objective function at the support points and forming the discretized partial derivatives, the search direction results. The normalized search direction is achieved by dividing the search direction vector (gradient) by the amount of the largest partial derivative so that the normalized main search component has the magnitude one. The initial step size is formed from the domain of definition (U Lx _i - LLx _i ) of the control values with the largest partial derivative by using $\frac{{\mathit{steps}}^{1.5}}{\min \mathit{step}}$

is multiplied. The new vector x ^{t + 1} results from the previous totalized search direction stretched over the step size. This procedure is repeated until the value of the objective function does not change steadily, but oscillates. If the numerically formed gradients have changed their sign three times in series, the value "steps" is internally reduced by one and the method continues with reduced step size. The convergence criterion is met when the step size reaches zero, or the value of the objective function does not change within four iterations. In that case, the binary output "conv" becomes true and the gradient method can be restarted by actuating the "RS" input and new start values.

des Definitionsbereiches der Stellwerte 15, die in unmittelbarer Nähe des Optimums die größte partielle Ableitung aufweist. Darüber lässt sich die geforderte Genauigkeit der Lösung einstellen. Über den Parameter "steps" wird die Anfangsschrittweite festgelegt, die, bezogen auf den Definitionsbereich der Stellwerte 15 mit der momentan größten partiellen Ableitung, um "steps^1,5" größer ist als die Endschrittweite. Mit Hilfe dieser einfachen, heuristischen Schrittweitensteuerung lässt sich die Konvergenzgeschwindigkeit deutlich beschleunigen.By including the limits of each individual control value 15, the optimization problem can be scaled. In this way, consideration is primarily given to the requirement of a specific accuracy of the solution, based on the definition range of the manipulated variables 15. Thus, the size of the smallest increment in the main search direction can be set via "min-step" just before convergence. This is $\frac{1}{\left(\min \mathit{step}\right)}$

the definition range of the control values 15, which has the largest partial derivative in the immediate vicinity of the optimum. This allows the required accuracy of the solution to be set. The "steps" parameter is used to define the initial step size, which is greater by steps ^1.5 than the final step range, based on the definition range of the manipulated variables 15 with the currently largest partial derivative. With the help of this simple, heuristic step size control, the convergence speed can be significantly accelerated.

zur Festlegung der Optimierungsart, zwei analoge Eingänge e und f( x ) und ein analoger Ausgang $f\left(\overrightarrow{x}\right)+p\left(e\right)$

vorgesehen. Hierbei ist e der Fehler durch Verletzung der Restriktionen und f( x ) der Wert der Zielfunktion 7. Aus dem Fehler wird der Strafterm p(e) gebildet und bei einer Minimierung zur Zielfunktion 7 addiert bzw. bei einer Maximierung von der Zielfunktion 7 abgezogen. Die Straffunktion p(e) wird durch Gleichung 3 beschrieben: $$p\left(e\right)=\left(\exp \left(\sqrt{\left|e\right|}\right)+\sqrt{\frac{\left|e\right|}{10}}-1\right)\cdot 1000$$

For the integration of the penalty functions are a binary input $\begin{array}{c}1=\mathrm{Max}\\ 0=\min \end{array}$

for determining the type of optimization, two analog inputs e and f ( x ) and an analog output $f\left(\overrightarrow{x}\right)+p\left(e\right)$

intended. E is the error due to violation of the restrictions and f ( x ) the value of the objective function 7. From the error, the penalty term p (e) is formed and, when minimized, added to the objective function 7 or subtracted from the objective function 7 when maximized. The penalty function p (e) is described by Equation 3: $$p\left(e\right)=\left(\exp \left(\sqrt{\left|e\right|}\right)+\sqrt{\frac{\left|e\right|}{10}}-1\right)\cdot 1000$$

und $g{\left(\overrightarrow{x}\right)}_2>0$

x )₂ > 0 werden als Verbundbausteine mit folgendem Pseudocode eingebunden:

• wenn $g{\left(\overrightarrow{x}\right)}_1<0$
  
• e₁ = 0
• sonst
• e₁ = g(x)₁
• wenn $g{\left(\overrightarrow{x}\right)}_2>0$
  
• e₂ = 0
• sonst
• e₂ = g(x)₂
• e = e₁ + e₂

The restrictions of the form $G{\left(\overrightarrow{x}\right)}_1<0$

and $G{\left(\overrightarrow{x}\right)}_2>0$

x ) ₂ > 0 are integrated as compound modules with the following pseudocode:

• if $G{\left(\overrightarrow{x}\right)}_1<0$
  
• e ₁ = 0
• otherwise
• e ₁ = g ( x ₁
• if $G{\left(\overrightarrow{x}\right)}_2>0$
  
• e ₂ = 0
• otherwise
• e ₂ = g ( x ₂
• e = e ₁ + e ₂

kann diese durch zwei Ungleichungen $h{\left(\overrightarrow{x}\right)}_1<0$

und $h{\left(\overrightarrow{x}\right)}_2>0$

beschrieben werden.For the rarer case of a restriction in the form of an equation $H\left(\overrightarrow{x}\right)=0$

This can be done by two inequalities $H{\left(\overrightarrow{x}\right)}_1<0$

and $H{\left(\overrightarrow{x}\right)}_2>0$

to be discribed.

A method for system control in a power plant in the above-mentioned embodiment satisfies the requirements for integrated use in process control technology and makes it possible to quickly find a globally optimal set of control values 15. Thus, a particularly efficient operation of the power plant is made possible with high efficiency and / or very low pollutant emissions.

Claims (7)

1. Method for the installation control in a power plant, wherein a functional value of a target function (7) based on a physical model is generated for a plurality of sets of variables (15) from respectively a set of environment variables on the one hand and the respective set of variables (15) on the other hand, said functional value being allocated to the respective sets, wherein the set of variables (15) is selected to be transmitted to a control device (21) of the power plant whose allocated functional value complies with a predefined optimisation criterion, wherein, in addition to a starting set and a set determined on the basis of the starting set and the functional value allocated thereto by means of a gradient method, the number of sets of variables (15) further comprises a set selected by a random generator.
2. Method for installation control in a power plant, in which the method according to claim 1 is performed with cyclic repetition in the form of a loop, wherein the selected set of variables (15) of a cycle is the starting set of the cycle following this cycle.
3. Method according to claim 1 or 2, in which the selected set of variables (15) is forwarded in the control device (21) to the respective control devices of the power plant allocated to the individual variables.
4. Method according to one of claims 1 to 3, in which the target function (7) comprises a penalty function.
5. Method according to one of claims 1 to 4, in which, before the determination in each case of the set by means of the gradient method, an increment is predefined.
6. Control apparatus for a power plant with a random generator module (13) designed to determine a random set of variables and a gradient module (1) designed to determine an optimal set of variables, which are connected on the data output side to a comparison module (17) designed to compare sets of variables, wherein the control apparatus is designed to perform the method according to one of claims 1 to 5.
7. Power plant with a control device (21) and a control apparatus according to claim 6 connected to the control device (12) on the data input side.

Images