SUNDARAM, Senthil, Kumar (H-503, Akme BalletDoddanekund, KR Puram 7 Bangalore, 56003, IN)
SELVARAJ, Gopinath (No. 1, Kaza StreetFF Road, South Gat, Tamilnadu 1 Madurai, 62500, IN)
BHAT, Shrikant (E-1 Rambag Complex, Ramakrishna NagarKhamla Road, 5 Nagpur, 44001, IN)
SHANMUGAM, Mohan, Kumar (No. 19, Alagiri StreetManavalanaga, Tiruvallur 2 Chennai, 60200, IN)
SUNDARAM, Senthil, Kumar (H-503, Akme BalletDoddanekund, KR Puram 7 Bangalore, 56003, IN)
SELVARAJ, Gopinath (No. 1, Kaza StreetFF Road, South Gat, Tamilnadu 1 Madurai, 62500, IN)
BHAT, Shrikant (E-1 Rambag Complex, Ramakrishna NagarKhamla Road, 5 Nagpur, 44001, IN)
| WE CLAIM: 1. A method for optimizing load scheduling for a power plant having one or more power generation units, the method comprising: detecting an event indicative of a need for adapting one or more constraints for an objective function used in load scheduling; analyzing the objective function to determine adaptive constraint values for the one or more constraints for optimally solving the objective function; using the adaptive constraint values of one or more constraints to solve the objective function; and using the solution of the objective function with the one or more adapted constraint values to operate the one or more power generation units of the power plant. 2. The method of claim 1 wherein the step for analyzing the objective function comprises: determining one or more manipulated variables along with respective priorities that are dominant terms in the objective function; and selecting the one or more adaptive constraint values for the one or more manipulated variables. 3. The method of claim 2, wherein the one or more adaptive constraint values are pre-configured and have pre-assigned associated priorities. 4. The method of claim 2, wherein the one or more adaptive constraint values are estimated using a sensitivity analysis. 5. The method of claim 2 wherein the manipulated variables are at least one of flexible manipulated variables or tight manipulated variables. 6. The method of claim 5 wherein the step for analyzing the objective function further comprises: selecting one or more adaptive constraints to relax and/or to tighten based on the flexible manipulated variables and tight manipulated variables; and estimating adaptive constraint values for the selected one or more adaptive constraints. 7. The method of claim 1 wherein the step for analyzing the objective function comprises determining a long term effect and a short term effect on the load scehduling due to the use of the adaptive constraint values prior to applying the adaptive constraint values. 8. The method of claim 7, wherein the long term effect is determined by modifying the objective function to include a compensation term to compensate for the long term effect on the power plant by using the solution of the objective function with the one or more, adapted constraint values. 9. A constraint analysis module within an optimizer for optimizing load scheduling for a power plant having one or more power generation units, the constraint analysis module comprising: an adaptive constraint evaluation module for detecting an event indicative of a need for adapting one or more constraints for an objective function used in load scheduling, for analyzing the objective function to determine adaptive constraint values for the one or more constraints for optimally solving the objective function, and for using the adaptive constraint values of one or more constraints to solve the objective function, wherein the optimizer uses the solution of the objective function with the one or more adaptive constraint values to generate set-points that are used to operate one or more power generation units. 10. The constraint analysis module of claim 9 further comprising: an adaptive penalty module to calculate a compensation term corresponding to an effect of using the one or more adaptive constraint values in long term load scheduling; and a decision module to select adaptive constraint values based on the long term effect and a short term effect on the power plant due to the use of the adaptive constraint values. |
PLANT
TECHNICAL FIELD
The invention relates generally to a system and method for process optimization for power plants and more specifically to load scheduling optimization in the power plant by using adaptive constraints in the optimization method and system.
BACKGROUND
Typically a power plant consists of several units, each having a set of equipments contributing to different stages of power generation. Such equipments include for example, boilers, steam turbines and electrical generators. For the optimal running of the power plant, one of the critical aspects is the optimal load scheduling between the different units and thei respective equipments in order to meet a given power demand.
Load scheduling has a major impact on the productivity of the power generation process. The purpose of load scheduling is to minimize the power production time and/or costs, by deciding the timing, values etc. of different operating parameters for each of the equipments in order to meet the power demand effectively and efficiently. The load sheduling is usually optimized by an optimizer in the power plant control system.
The goal for the optimization exercise, for example, cost minimization is expressed as an objective function for the optimization problem. The optimization method solves such an objective function within the identified constraints. Almost all of the operational parameters can be experessed as cost function and the optimizer is deployed to solve the cost function associated with variety of operations and then- consequences (e.g. penalty for not meeting the demand). The solution from the optimizer provides setpoints for the various operations to achieve the desired optimized results. Typically the optimizer uses techniques suet as Non Linear Programming (NLP), Mixed Integer Linear Programming (MILP), Mixed Integer Non Linear Programming (MINLP), etc to solve the objective function. In the formulation of the objective function, there is a desire to include as many terms (fuel cost, emission reduction cost, start-up and shutdown cost, ageing cost, maintenance cost, penalty cost) in the objective function for considerations to work everything possible optimally. When several such terms are considered in the objective function formulation, the solving of the objective function becomes difficult as there is reduction in the degree of freedom to make adjustments in operating parameters i.e. set points for different equipments, in order to achieve the optimal solution for the power plant. The necessary number of terms to be considered for a particular objective function is based on how the process control system has been designed and the values of constraints. If the number of terms is more i.e. it considers almost all possible aspects of the power plant in one go or has very tight constraints then there is possibility that the objective function may not have a solution. It may be noted here that the problem of no solution as described herein may also occur when there are conditions that are not considered in the power plant model or not controllable in the power plant from the results of optimizer.
Currently, in situations, where the objective function is not solved within a reasonable time given a set of constraints, the power plant is operated in a sub-optimal way. In addition to no-solution situations, there are other situations where one is unsure if the optimized solution is the best solution i.e. the solution is the best among the multiple solutions available or is the most suitable to operate the plant in stable manner even if the solution appears to be slightly sub-optimal. More often, one does not know if there were different constraints values, whether a better solution could have been possible.
The invention describes a method to identify and treat such situations so that the optimizer provides an acceptable solution in a defined manner. More specifically the present technique, describes a system and method for solving the objective function for a power plant operation by identifying and relaxing some constraints.
BRIEF DESCRIPTION
According to one aspect of the invention a method for optimizing load scheduling for a power plant having one or more power generation units is provided. The method includes detecting an event indicative of a need for adapting one or more constraints for an objective function used in load scheduling. On detection of such an event, the method includes analyzing the objective function to determine, adaptive constraint values for the one or more constraints for optimally solving the objective function and using the adaptive constraint values of one or more constraints to solve the objective function. The method finally includes using the solution of the objective function with the one or more adapted constraint values to operate the one or more generators of the power plant.
According to another aspect of the invention, an optimizer for optimizing load scheduling for a power plant having one or more power generation units includes a constraint analysis module having an adaptive constraint evaluation module for detecting an event indicative of a need for adapting one or more constraints for an objective function used in load scheduling. The adaptive constraint evaluation module analyzes the objective function to determine adaptive constraint values for the one or more constraints for optimally solving the objective function, and uses the adaptive constraint values of one or more constraints to solve the objective function. The optimizer then uses the solution of the objective function with the one or more adaptive constraint values to generate set-points that are used to operate one or more power generation units. DRAWINGS
These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: FIG. 1 is a block diagram representation of a simplified generic fossil fired power plant (FFPP) according to one embodiment of the invention;
FIG.2 is a block diagram representation of the control system for the power plant of FIG.1; and FIG. 3 is a block diagram representation of the constraint analysis module in an optimizer of the control system of FIG. 2.
DETAILED DESCRIPTION
As used herein and in the claims, the singular forms "a," "an," and "the" include the plural reference unless the context clearly indicates otherwise.
The system and method described herein relates to optimization of power plant operation to meet the desired power demand under conditions of non-convergence of an solution with existing constraints or under conditions when it is not clear that the solution with exisiting constraints is a best solution. The system and method described herein ensure that the power plant is operated by properly defining the constraints, their values and by ensuring there is an optimal solution every time i.e. the degree of freedom is available for solving the objective function and hence the optimization solution is dynamically improved while still considering all the terms defined in the objective function. To achieve the optimized solution, the novel modules and methods of the invention advantageously provide for adapting the value of constraints dynamically to solve the objective function and induce benefiting solutions. Such adaptations are done within the permissible beneficial outcomes (short-term and long-term) of the power plant.
These aspects are explained herewith in reference to the drawings. FIG. 1 is a block diagram representation of a simplified generic fossil fired power plant (FFPP) 10 that is controlled by a control system 12 that includes an optimizer 14 to obtain the optimal solution for operating the power plant. The FFPP 10 consists of three FFPP units, 16, 18, 20 running in parallel. Each FFPP unit has three main equipments namely, a boiler (B) 22, a steam turbine (ST) 24 that is mechanically coupled with an electrical generator (G) 26. Under operation, steam loads, generally referred to as ui, u 2 and u 3 are representative of the steam generated by the respective boiler and the corresponding fuel consumption is expressed as yn, y 2 i, y 3 . The manipulated variables un, ua and UB are binary variables which define the state of the boiler whether it is "off or "on". The steam from the boiler is given to the steam turbine to work the generators. The power output from the generators is expressed as yi2, y22, y 32 -
The control system 12 is used to monitor and control the different operating parameters of the power plant 10 to ensure the power plant is operated at the optimum conditions. For optimal running of the power plant, as explained earlier, one of the critical aspects is the optimal load scheduling between the different FFPP units as shown in FIG. 1, and the calculation for the optimized solution is done at the optimizer 14.
In the exemplary embodiment, the objective of a load scheduling optimization problem is to meet the power demand by scheduling the load among the three FFPP units, subject to different constraints such as the minimization of the fuel cost, start up cost, running cost, emission cost and life time cost. The optimizer 14 receives inputs from the power plant, and applies optimization techniques for the optimal load scheduling. Based on the optimal solution, the control system 12 sends commands to different actuators in the power plant to control the process parameters.
According to aspects of the present technique, the optimizer 14 includes novel modules to handle the above mentioned situations of non-convergence of an solution with existing constraints or under conditions when it is not clear that the solution with exisiting constraints is the best solution. These novel modules and the associated methods are explained in more detail in reference to FIG. 2
FIG.2 is a block diagram representation of the optimizer 14 within the control system 12 as explained in reference to FIG.l. The modules within the optimizer 14 use the inputs from power plant database 28 that provides historic power plant operating data, power demand forecast model 30 that provides future power demand forecasts, user input 32 for any specific user needs, and power plant model 34 for providing simulated data for the power plant and the power plant 10 for providing current operating data.
The optimizer 14 includes an optimization solver module 36 to solve the objective function, for example as per the equations 1-16 given below. In the exemplary optimization method for the above FFPP power plant, the objective function being considered is a cost function that needs to be minimized as given by equation. 1. The optimization problem is solved within the constraints as defined by equations, from 10 to 16, to obtain the optimal load schedule for the power plant. The optimization of a power plant is done by minimizing the following cost function by choosing the optimal values for u 's: min J
Where,
+c 's.t fixed +C 's.t life + Q + Q 'boiler fixed 'boiler life - E (1) Each of the term in the cost function (J) is explained below.
Cdem is the penalty function for not meeting the electric demands over the prediction horizon:
T+M-dt
Cdem ~ Σ ^dem el ∑yi2(t) - D dem el (t) (2) where k dem el {t) is the suitable weight coefficient and D iem el {t) , for t = T,...,T + M - dt is the forecast of the electric demand within the prediction horizon and. y , yii, y i are the power generated by the respective generators. Here M is the length of the prediction horizon, T is the current time and dt is the time interval
Cfaei is the cost for fuel consumption represented in model for FFPP by the outputs y\ \, yn,yi \ and thus the total cost for fuel consumption is given by, C fuel = (3
where k i fIiel is the cost of fuel consumption^, / .
^emission is the cost involved in reducing the pollutant emission (NO x , SO x , CO x ) produced by the power plant and is given by, T+M-dt n
^emission ^ 1 ^7 emission f (-^<2 ( ) (4)
<=r i=l
where fc t gmisssian is the cost coefficient for producing the power y i2 . C * startup % tne cost f° r me start up of the steam turbine given by
Γ+Λ/-2Λ
C st stamp = Σ stamp max{ M/1 (/ + dt) - U n (t),0) (5)
t=T where k st startup represents a positive weight coefficient.
Cst fixed represent the fixed running cost of the steam turbine. It is non-zero only when the device is on and it does not depend on the level of the steam flow u 2 .
T+M-dl
C st fixed = ∑k sl fixeJ U n (t) (6)
t=T where k st represent any fixed cost (per hour) due to the use of the turbine.
Cst life describes the asset depreciation due to loading effect and is defined as,
NumComponents
C st life — Σ LT comp j oad (t
comp=\ (7)
and therefore,
LT compjoad dt) * cos t EOH (8)
\ Load base J Here, LT comp laai is the life time cost of the component which could be boiler,
Load
turbine or generator for the given load, the term, on RHS of equation 8 calculates the rate of (Equivalent Operating Hours) EOH consumption with respect to the base load Load base ). This term should be multiplied by the total time during which the unit is running at that load. The optimizer calculates the EOH consumption for each sampling time and eventually adds the EOH consumption at every sampling instance into the cost function.
The terms, C boiler stanup s tol . fer ^ ed ? C boiler ljfi e t c . are similar to the equivalent terms in the steam turbine and we omit their description.
E is the term for revenues obtained by the sales of electricity and the credits from emission trading. This term has to take into account that only the minimum between what is produced and what is demanded can be sold:
T+M -dl n
where, Pi, e i( is the cost coefficient for the electrical energy generated.
The above stated optimization problem is subjected to one or more of the following constraints: a) Minimum & Maximum load constraints for boilers and turbine coupled with generators, etc., ui,min≤ u i≤ u i,max
γ^ ίη ≤ y„ 2 ≤ y irma _ r (10) b) Ramp up and ramp down constraints -^-≤ ra7n Prr.a
d(uj) .
d t - r ' am P 'nmuinn ( 12 ) c) Minimum up time and down time constraints
This constraint ensures a certain minimum uptime and downtime for the unit. Minimum downtime means that if a unit is switched off, it should remain in the same state for at least a certain period of time. The same logic applies to minimum uptime. This is a physical constraint to ensure that the optimizer does not switch on or off the unit too frequently. if t off < downtirae mm then u u = 0 (13) if t on < upt-me miI1 then u u = 1 (14) where, t off is the counter which starts counting when the unit is switched off and when t off is less than the minimum downtime, the state of the unit u, should be in off state. d) spare unit capacity constraints
' spare, mm —— J J V sspnaarree—— J V& spare, max (15) e) tie line capacity constraints, etc.,
Typically, while obtaining the optimal output, there is a desire to consider all the different aspects or terms in the formulation of the objective function like Cession, C fuel* ife, etc along with the related constraints. It will be known to one skilled in the art that each of these terms is a function of manipulated variables uu, a and and that the constraints are related to these manipulated variables.
As explained earlier, when several such terms are considered in the objective function formulation, the solving of the objective function becomes difficult as there is reduction in the degree of freedom to make adjustments in operating parameters i.e. set points for different equipments, in order to achieve the optimal solution for the power plant. Also, there are situations where the solution obtained may not be the best solution, as explained earleier. The actions after encountering these situations are explained in more detail herein below.
The constraint analysis module 38 is activated when there is a condition of non- convergence of the objective function or it is not clear if the solution obtained by the optimization solver module 36 is the best solution, both these situations create an "event" that is indicative of a need for adapting one or more constraints.. On detection os such event the constraint analysis module 38 is activated to calculate new constraint values to solve the objective function.
The constraint analysis module 38 determines the new constraint values as explained in reference to FIG. 3.
Referring now to FIG. 3, the constraint analysis module 38 includes an adaptive constraint evaluation module 40 to select one or more adaptive constraints, i.e. constraints whose values can be altered, and the values for these adaptive constraints to solve the objective function. In the exemplary embodiment, the adaptive constraint evaluation module 40 analyzes using the power plant model 34 and the objective function, which of the manipulated variable(s) maybe relaxed through its constraints for optimization, referred herein as "flexible manipulated variables" and by how much in terms of values, and also which of the manipulated variables cannot be relaxed, referred herein as "tight manipulated variables". Accordingly, the adaptive constraint evaluation module 40 selects the constraints to be relaxed which are referred herein as "adaptive constraints" and the new values of such constraints referred herein as "adaptive constraint values" in order to arrive at an optimal solution.
In one specific embodiment, the adaptive constraints and the adaptive constraint values may also be pre-configured, e.g. the adaptive constraint evaluation module 40 has pre-configured definitions for desirable constraint values and also acceptable adaptive constraint values allowing for deviation from the desirable constraint values (i.e. how much the constraint value can vary may be predefined). The acceptable adaptive constraint values may be the same as or within the limits specified by the manufacturer or system designer to operate the plant.
Further, it is possible to have priorities that are pre-assigned to different flexible manipulated variables based on their impact and importance with respect to the solution of objective function (minimization problem). Priorities may also be determined to select the adaptive constaints and adaptive constraint values through techniques like sensitivity analysis or principal component analysis. In one example, the most sensitive constraint with respect to the solution of the objective function is assigned the highest priority so that it's value is selected first as the adaptive constraint value to solve the objective function.
Similarly there may be priorities pre-assigned to the adaptive constraint values also, i.e. within the acceptable values for adaptive constraints there may be two or more sets of values that are possible and these may be prioritized for selection and use. In this embodiment, the adaptive constraint evaluation module 40 selects the preconfigured acceptable adaptive constraint values based on priority already defined alongwith, if it is available.
In the situation where no solution still results after applying the prioritized adaptive constraint, the solution may be attempted by relaxing more than one adaptive constraints at same time, based on the priorites. In another embodiment, the adaptive constraint evaluation module 40 may deploy techniques such as principal component analysis to determine which cost function is most significant and then identify which manipulated variable is significant term or dominated term, as "flexible manipulated variable" or "tight manipulated variable" and use the acceptable constraint values to simulate (e.g. through Monte-Carlo method ) and to identify what may be the value for the flexible manipulated variable that may be suitable as an adaptive constraint value being as close as possible to the existing (or desired) constraint value, that results in a solution. In this case, through simulation or by use of other statistical techniques (methods typically used in design of experiments), it is determined which ones and how many constraints to be relaxed i.e how many adaptive constraints can be considered and by what extent i.e what would be the values of such adaptive constraints. As one would recognize, the determination of adaptive constraints and their value is another optimization problem to optimally determine which adaptive constraints to be relaxed and by how much to produce effect as close to the desired or recommended settings for the power plant.
However, in another example, it is possible that none of the selected adaptive constraint values satisfy the solution, i.e the objective function is indeed not solvable even if multiple constraints associated with corresponding flexible manipulated variables are relaxed. In this case, the constraints associated with tight manipulated variables may also be relaxed based on priority (least priority relaxed first) or as determined through simulation to find conditions that provide an solution. This solution, though sub-optimal solution (not resulting from the desired constraints) is selected to satisfy the objective function.
In yet another embodiment, where the constraint analysis module 38 is activated because it is not clear if the solution obtained with the current constraints is the best solution, in this scenario, the analyis module considers the existing constraint values (defined within the acceptable values of constraints), the tight manipulated valriables and the flexible manipulated variables to find a new solution. It may be noted that such activation may be carried out periodically and in purpose to determine if indeed the solution practised is the best solution i.e such events happen in pre-programmed manner after every finite cycles. Alternatively, such event may also be user triggered. The adaptive constraint evaluation module 40 selects the associated constraints both for tight and flexible manipulated variables for adapting their values such that the tight manipulated variables are not impacted or they are further tightened to improve the solution. Thus, here, instead of only relaxing the constraints, some constraints are tightened and some others are relaxed. This ensures, a solution is obtained and that the solution is also the best among the possible solutions (more stable and profitable solution over long term).
In the case, where the values of the adaptive constraints are determined through simulation, the adapative constraint values may be selected as the acceptable values of constraints as initial conditions and the new adapative constraint values are arrived at algorithmically, where some of the adaptive constraints values are for the tight manipulated variable and the values are such that it helps operate the plant with as tight a value as possible for the tight manipulated variable. Such an operation may be advantageous when the functions resulting from the tight manipulated variable influences multiple aspects/functions of the plant and having tighter control over the tight manipulated variable helps have better control over all the related aspects/functions of the plant.
The constraint analysis module 38 thus finds the optimal solution of the objective function i.e. the optimal load scheduling solution that is sent to the control system for further action by the control system to deliver set-points through process controllers for operating parameters of different equipments in the power plant In another embodiment, the constraint analysis module 38 may include additional modules for example a decision module 40 to analyze the impact of using the adaptive constraint values on the power plant operation in short term and long term. The term short-term effect as used herein is used to indicate the immediate effect of new values (recommended adaptive values of constraints to be used in the optimization problem). It will be appreciated by those skilled in the art that when the power plant is being operated by the solution obtained by changing at least one of the constraints from its first values i.e using the adaptive constraint values, there shall be an effect in the overall operation of the power plant different from the first values and impacting the power plant differently from that of the first values. This impact is being referred to be associated with the term 'long term effect'.
In long term it is not desirable that that the operation of power plant should be undesirably deviated from its expected trajectory and since the long term effect is an outcome of a condition different from the initial or desired conditions expressed with the objective function with the initial or desired constraints,the decision module compares the impact of adaptive constraints in long term to help decision making.
In one embodiment, the objective function is modified to include a compensation term to compensate for the effect on power plant operation in long term by using the adaptive constraints. The compensation term is calculated by the adaptive penally module 42 over the long term (long term is a prediction horizon or the time period for which the power plant model, forecast modules and data such as demand forecast can reliably be used to forecast plant trajectory ). The modified objective function that includes the compensation term is checked to ascertain if the use of adaptive constraint values brought any significant benefit in the power plant operation as shown in equations 17 and 18 given below in the Example section. The benefit may also be ascertained with respect to other alternative solutions in any time span within the prediction horizon.
In another embodiment, the decision module 40 may seek user intervention or use configured significance values to determine if the optimizer should continue with the modification as done using the adaptive constraints based on the benefit over long term. In another embodiment, the decision module may be used to compare the new solution i.e value of objective function with the adaptive constraints with that obtained prior to applying the adaptive constraints and observe the effect of both of these in short or long term. The selection is then based on the values that are beneficial to the plant (without too much side affects expressed as compensation term wherein the side affects are less significant than the benefit from the new solution resulting from adapted constraints).
An example illustrating some aspects of the method described herein above is presented below for clearer understanding of the invention.
EXAMPLE: Referring back to FIG. 1, electric generators Gl, G2 and G3 are said to be operated nominally (typical value) for 45 MW production and have the maximum capacity of 50 MW power. Here, nominal capacity is used as the upper bound for the generator capacity constraint (desired constraint) in the optimization problem. In situations where the demand requirement is high, keeping the nominal capacity as the upper bound may lead to "No solution" or solution with high penalty for not meeting the demand. For such situations, values of the constraints are adapted to have the upper bound between nominal and maximum value in order to find the optimal solution. The method of adapting the constraints is discussed in the following section. The value of the cost function, with the current constraints value i.e. with upper bound on all generators as 45 MW, is obtained from the optimization solver module of FIG. 2. This cost function is used in the adaptive constraint evaluation module of the constraint analysis module (FIG. 3) to find the dominant cost terms in equation 1 and dominant variables which contribute to the cost function. The dominant variables are identified using statistical analysis tool such as Principal Component Analysis (PCA). For example, consider the case where all the generators Gl, G2 and G3 have the nominal capacity of 45 MW. Assume that Gl has the lowest operating cost of all the three and G2 has lower operating cost than G3. From the Forecast Model, if the power demand is less than 135 MW, then the optimizer will choose to run all the three generators less than or equal to its nominal value of 45 MW to meet the power demand. But if the power demand is 140 MW, then some of the generators capacity has to be relaxed and operate up to its maximum capacity of 50 MW to meet the power demand. The adaptive constraint evaluation module makes use of the power plant model (like relation between depreciation cost and load as given in eqn. 8) together with PCA technique to decide upon which generator capacity constraint has to be relaxed to the maximum value of 50 MW in order to meet the demand constraint. This analysis, say identifies the cost terms Cdem and C sti uf e as the dominant cost terms in the cost function given in equation 1. Also the analysis is said to identify the capacity of generators Gl and G2 as the dominant variable and its upper bound capacity constraint value may be advantageous to be relaxed up to 50 MW. The Monte-Carlo simulation may be used to identify the new constraints values corresponding to the dominant variables (also in consideration with statistical confidence limits) that gives least cost function value. For the example, changing the upper bound of the capacity constraint in equation 10 for the generators Gl and G2 between 45 MW and 50 MW may lead to the decrease in efficiency of the generator. The simulation results may be used in deciding the optimal value between 45 and 50 MW which gives least cost function value and also considering the EOH (Equivalent Operating Hour) value of the generator. The upper bound of the capacity constraint y max as given in equation 10 is changed based on the analysis results. The short term cost function value (JST) based on the adapted constraints is calculated using equation 1 with adapted constraint value in the equation 10 may not consider the consequence of using the new adapted constraint values and it may be desirable to use the objective function that considers the long term effect for such purposes. Adaptive Penalty module makes use of the demand forecast and power plant model to calculate the penalty value of adapting the constraint value on the long term. This penalty value is used as additive term to short term cost function to calculate the long term cost function value (JLT) as given by eqn. 17. For the example considered, JLT is given by eqn. 18.
JLT = JST + Penalty (17)
where, C lifg is the depreciation cost calculated from equation 8, on operating the generators Gl and G2 with the adapted value of capacity constraint over long time horizon. The suitability of short term cost function or that of long term cost function is based on the conditions (e.g. demand forecast and use of relaxed constraints) of the plant, therefore this is better judged based on the significance values preconfigured or user intervention facilitated by Decision Module. The new adapted constraint value may only be used in the optimization solution if the benefit from lowering the penalty from not meeting the demand by operating the generators above its nominal value is significant compared with the penalty associated with depreciation of the generators.
While only certain features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.
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