CN101124386B - Method and device for calculating energy and technical processes - Google Patents

Abstract

The invention relates to a method and device for calculating energy and technical processes. A method for calculating energy and technical processes, particularly the heat circuit of power plants, uses a computational model based upon at least one balance equation of the first law of thermodynamics. The calculation is carried out in the form of an optimization calculation into which at least one technical boundary condition, which is formulated in the form of an inequality, enters as a secondary condition.

Description

Method and device for calculating energy processes and technological processes

technical field

The invention relates to a method and a device for calculating energy processes and technological processes, in particular thermal cycle energy processes and technological processes of power plants, by means of a computational model based on at least one equilibrium equation calculation of the first law of thermodynamics, and a Apparatus for implementing the method. the

Background technique

In a method of this type known from the prior art, static technical processes in the field of energy processes and technological processes are represented as mathematical models by means of physical models. The model has balance equations (mass, energy and impulse balance) of the first law of thermodynamics. Furthermore, it is also possible to predefine certain values for certain variables of the model by inserting boundary conditions in the form of equations. For example, it can be specified that no cold water is injected into the newly generated steam in the temperature control unit. To this end the following conditions are introduced into the formula of the model:

_mjet = 0(1)

In total the model consists of vectors with n equations and the same number of unknown variables. Such a system is called a secondary system. the

After establishing the equilibrium equations and the equations defining the boundary conditions in the domain of phase 1, a first approximate solution of this system of equations is solved by Newton iterations by a simulation program in the domain of phase 2. From this the simulation program again uses phase 1 to verify the boundary condition equations with the approximate solution found and to modify them if necessary. the

In connection with the example described above, it is also roughly checked whether the determined temperature of the live steam exceeds a certain limit value, so that in this case a boundary condition of the form of an equation is introduced, wherein the live steam The temperature is determined as this limit value. Instead, the rate at which cold water is introduced into the temperature-controlled unit is no longer predetermined but defined as a variable. This means that the boundary condition _mjet = 0 is taken out of the system of equations, which leads to the next approximate solution containing the values calculated for _mjet . From this, the simulation algorithm enters phase 2 again, in which further Newton iterations are performed. Phase 1 and Phase 2 will iteratively repeat until a variation is found in the desired bandwidth and meets the desired approximation tolerance.

The implementation of this algorithm is cumbersome and therefore time-consuming. The solution obtained in this way must be tested again for its authenticity. Check the solution for logic errors here. This includes, for example, checking whether the temperature at the output of the heat exchanger is higher than the temperature at its input. Other logical tests include the presence of negative solutions for variables for which such solutions are excluded. If inauthenticity is found in this phase, the entire simulation model has to be modified and recalculated accordingly. Error detection is performed manually and often requires complex checks. the

Contents of the invention

EP 0731397A1 discloses a system for optimizing power plant efficiency. The purpose of the system is to minimize the total cost of operating the plant while satisfying the steam and power requirements and different constraints. Dynamic programming is used for this. the

Therefore, the technical problem to be solved by the present invention is to overcome the above-mentioned shortcomings, especially to propose a method and device for calculating energy processes and technological processes, which can be used to perform calculations faster and more easily Eliminate errors. the

In such optimization calculations, the optimization algorithm determines the minimum or maximum value of the objective function within the range described by the subordinate conditions in the form of equations or inequalities. For optimization, nonlinear programming (NLP) methods can be used, for example. By introducing at least one technical boundary condition into the optimization calculation as a subcondition, upper and lower limits for the optimization variables can be taken into account in the optimization calculation. In connection with the above example, it is possible, for example, by considering the inequality as a subordinate condition:

Tnew _steam ＜T _max (2)

Limit the temperature of incoming fresh steam to the maximum temperature. the

According to the present invention, the solution to the optimization problem is generally expressed mathematically as follows:

$\underset{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Subordinate condition c(x)＝0 (4)

h(x)≤0 (5)

x ^L ≤ x ≤ x ^U (6)

in,

Φ is the objective function to be minimized or maximized;

x is a vector consisting of continuous optimization variables, with n elements to be determined by optimization calculations;

c is a vector with m elements consisting of boundary condition functions expressed in the form of equations, where these boundary condition functions are mainly composed of equilibrium equations of the first law of thermodynamics;

h is a vector consisting of boundary condition functions expressed in the form of inequalities;

x ^L is a vector of fixed lower bounds of the optimized variables, some of which can be -∞, in which case the variables behave as if they had no lower bound;

Please note that expressions (5) and (6) are both expressed as boundary conditions in the form of inequality, and the expression of the upper and lower limits according to expression (6) is only a simplification of the expression according to the corresponding inequality of expression (5). the

The invention is based on the recognition that with the calculation of the physical model according to the invention implemented in the form of an optimization calculation, it is possible to carry out an inherent calculation of all technical boundary conditions. Corresponding energy and technological processes can thus be calculated in the usual calculation cycle. The iterative execution of the various calculation phases and the adaptation of boundary conditions between them, as in the prior art calculations based on simulation models, are no longer necessary. Since an overall optimization of the system is additionally carried out, possible errors in the boundary conditions specified in the form of threshold values for certain variables can be eliminated more quickly. The possible non-matching thresholds for variables are actually easy to see from the optimization results, since the variable values calculated by the optimization algorithm are generally quite different from the non-matching thresholds. Since the optimization algorithm optimizes the integrity of many variables, the corresponding individual variables in the optimization result are not close to the non-matching threshold, because otherwise the result would generally fail significantly unfavorably for many other variables, thus making the optimization The result is excessively bad as a border. the

In a preferred refinement of the invention, at least one logical condition is introduced into the optimization calculation as a dependent boundary condition. The at least one logical condition is preferably introduced into the optimization calculation in the form of an inequality. Such a logical condition can be, for example, that the temperatures at two different locations of a device are unequally related to one another. Thus, for example, it can be specified that the temperature at the heat exchanger input must be higher than the temperature at the heat exchanger output. Since such logical conditions are directly taken into account by the calculation method in an embodiment of the invention, there is no need for a subsequent plausibility check for this. the

In the calculation method according to the invention, the quadratic simulation tasks given by the calculation technology model are preferably converted into optimization tasks. In this case, the boundary conditions present in the computational technology model in the form of equations are transferred to the objective function of the optimization calculation. Now, consider the remaining balance equations in the computational technology model as dependent conditions. the

Furthermore, the optimization calculation is preferably also based on a quadratic objective function for calculating the minimum square distance of the optimization variable from a predetermined threshold value. In this way, the objective function to be minimized in the optimization task consists of the sum of the squared distances of the optimization variables or the transition functions associated therewith with the respective threshold values. With such an objective function, mismatched selected threshold values can be detected relatively quickly and errors can thus be eliminated quickly. The reason for this is that, in the solution found by the optimization calculation, the completeness of the optimization variables is as close as possible to the respective threshold value. But if a particular threshold is chosen non-matchingly, the optimization algorithm brings the variable corresponding to it slightly, approximately negligibly, close to the threshold, if the distance of the other variables in the sum from their threshold is thus greatly increased, which from From a technical point of view, the thresholds are inconsistent. As a result, such mismatched threshold values in the solution resulting from the optimization calculation can usually be recognized immediately due to the large distance between the optimization variable and its threshold value, and can thus be corrected in a targeted manner. the

However, some optimization algorithms work more efficiently with linear objective functions than with quadratic objective functions. In particular, quadratic objective functions generate a large number of items in the Hesse matrix in some algorithms, thus allowing too much freedom in the update of the Hesse matrix. Spend. Therefore, to employ such an algorithm it is expedient that the optimization calculation is based on a linear objective function. the

Furthermore, it is also preferred that at least one technical boundary condition expressed as an equation is introduced as a subordinate condition in the optimization calculation. This increases flexibility when defining optimization problems. the

It is also expedient to derive at least one logical condition from the second law of thermodynamics. This means that specific inequalities between the temperatures at different locations of the system, which result from the second law of thermodynamics, can be introduced as subordinate conditions into the optimization calculation. As a result, a plausibility check of the solution found by the calculation algorithm becomes superfluous with regard to the necessary entropy increase in the irreversible process. the

Furthermore, the invention relates to a device for carrying out the method according to the invention. the

Description of drawings

Embodiments of the present invention will be described in detail below with reference to the drawings. in,

FIG. 1 schematically shows the solution space of two optimization variables bounded by technical boundary conditions in the form of inequalities. the

Detailed ways

The embodiments of the invention described below are used for the calculation of the thermal cycle of a thermal power plant. To this end, the thermal cycle is first described by means of the equilibrium equation c(x) (mass, energy and impulse balance) of the laws of thermodynamics as a function of the optimization variable x _i . Accordingly, the threshold y _{s,i of these optimization variables xi or the threshold y s,i of} the variables resulting from the optimization of variables _xi using the internal transformation vector b(xi _{) is} defined. Such an internal transformation vector b( _xi ) can represent, for example, the relationship between the entropy specified as a threshold value and the temperature specified as an optimization variable. Furthermore, a boundary condition h(x) in the form of an inequality is defined for the optimization variable _xi .

Referring to FIG. 1 , the fresh water rate for fresh steam injection in the temperature control unit can be determined to have a minimum value of 0, for example with the boundary condition _{minjection≥0} by means of the inequality. Another boundary condition may 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 _injection and T _{live steam} are functionally dependent on each other, since more injected water will reduce the temperature of live steam. This functional dependence is contained in the equilibrium equation c(x). Furthermore, specific optimization variables can be limited by a lower limit x ^L and an upper limit x ^U.

Therefore, the following optimization problem for calculating the minimum square distance between the optimization variable and the predetermined threshold is expressed as:

$\underset{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Subordinate condition: c(x)＝0 (8)

h(x)≤0 (9)

x ^L ≤ x ≤ x ^U (10)

The optimization problem can thus be solved using a suitable optimization algorithm. The resulting values for the optimization variables are optimized to the greatest extent such that the sum of their squared distances from the predetermined threshold assumes a minimum value. If a mismatch threshold for the optimization variable x _i is to be predetermined for the system, this inconsistency threshold can be recognized immediately in the solution, since the value given as a result of the optimization calculation for this variable corresponds to the result for the other variables ratio, with a significant distance from its corresponding threshold. Then, for such cases, modify the thresholds for the corresponding variables and repeat the entire optimization calculation.

As an alternative to the least quadratic solution formula above, a linear solution formula can also be chosen as follows:

$\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Subordination condition y _s -b(x)＝pu (12)

p, u≥0 (13)

c(x)＝0 (14)

h(x)≤0 (15)

x ^L ≤ x ≤ x ^U (16)

是线性的。一些解算法利用线性目标函数工作更有效。  Here, p and u are auxiliary variables. Therefore the objective function

is linear. Some solution algorithms work more efficiently with linear objective functions.

Claims (11)

1. A method for calculating energy processes and technological processes by means of a calculation-technical model of at least one equilibrium equation based on the first law of thermodynamics, said calculation being carried out in the form of an optimization calculation, characterized in that in the optimization calculation In , a technological boundary condition expressed in the form of inequality is introduced as a subordinate condition for each of the two optimization variables (xi ₎ , and the two optimization variables (xi ₎ are functionally dependent on each other. 2. The method according to claim 1, characterized in that said energy process and process flow process is an energy process and process flow process of a thermal cycle of a power plant. 3. The method as claimed in claim 1, characterized in that at least one logical condition is introduced into the optimization calculation as a dependent condition. 4. The method according to claim 1, characterized in that the secondary simulation tasks given by the computational-technical model are converted into optimization tasks. 5. The method according to any one of claims 1 to 4, characterized in that the optimization calculation is based on a quadratic objective function for calculating the minimum square distance between the optimization variable ( _xi ) and a predetermined threshold value . 6. The method according to any one of claims 1 to 4, characterized in that the optimization calculation is based on a linear objective function. 7. The method according to claim 5, characterized in that at least one technical boundary condition expressed as an equation is introduced as a subordinate condition in the optimization calculation. 8. The method according to claim 6, characterized in that at least one technical boundary condition expressed as an equation is introduced as a subordinate condition in the optimization calculation. 9. The method as claimed in claim 3, characterized in that at least one logical condition is derived from the second law of thermodynamics. 10. A device for calculating energy processes and technological processes, having computing means for calculating energy processes and technological processes by means of a computational technical model based on at least one equilibrium equation of the first law of thermodynamics, wherein said calculation Implemented in the form of an optimization calculation, characterized in that the calculation means are also used to introduce a technique expressed in the form of an inequality for each of the two functionally interdependent optimization variables (xi ₎ in the optimization calculation Boundary conditions serve as subordinate conditions. 11. The arrangement according to claim 10, characterized in that said energy process and process flow process are energy process and process flow processes of a thermal cycle of a power plant.