CA2510839A1

CA2510839A1 - Method and apparatus for providing economic analysis of power generation and distribution

Info

Publication number: CA2510839A1
Application number: CA002510839A
Authority: CA
Inventors: Frederick C. Huff; Xu Cheng; Peter N. Francino
Original assignee: Emerson Process Management Power and Water Solutions Inc
Current assignee: Emerson Process Management Power and Water Solutions Inc
Priority date: 2004-06-25
Filing date: 2005-06-27
Publication date: 2005-12-25
Anticipated expiration: 2025-06-27
Also published as: US20050286179A1; GB2415809B; CA2510839C; DE102005029818A1; HK1082300A1; US7474080B2; GB2415809A; US7190149B2; CN1737838A; US20070162189A1; US20050285574A1; IN2014DE02634A; US7288921B2; GB0513131D0; CN1737838B; US7385300B2; US20080004721A1

Abstract

An economic dispatch program optimally allocates load demand specifying real power and reactive power to be generated by a power plant among various power generators in a manner so that each of the power generators are operated within its optimal operating space as defined by a reactive capability curve. Allocating a power demand with consideration of the reactive capability curves of the power generators results in optimal generation of real power and reactive power as specified by the load demand. Alternatively, the economic dispatch program allocates load demand specifying real power and reactive power to be delivered by a power grid among various power plants wherein one or more of the various power plants have capacity limits exhibited by reactive capability curves.

Description

METIl<OD AND APPARATUS FOR PROVIDING ECONOMIC ANALYS1S OF
POWER GENERAT1 ON AND DISTRIBU7~.ON
TECHNICAL FIELD
[0001] This patent relates generally to computer software; and more particularly to computer software used in electric power generation and distribution systems.
BACKGROUND

[0002] Almost every aspect of life in the twenty-first century involves the use of electric power. However, most users of electricity do not realize that, before electricity reaches their premises, it navels through a complex network of electric pov~er generation and distribution systems. The complexity of power generation and distribution is frequently underscored by blackouts, such as those that occurred over most of the northeastern United States and Canada on August 14'h and 15a' of 2003, which make it clear that the various processes and systems involved in the generation and the distribution of electricity require very careful planning.

[0003] In the United States, electric power generation and distribution was traditionally highly regulated by federal government agencies, such as the Federal Energy .
Regulatory Committee (FERC), as well as by utility commissioners of various stales. These regulating bodies set performance standards and requirements for the generation and the distribution of electric power for the utility companies (hereinafter referred to as "utilities") which generated and distributed electric power, For example, these regulating bodies specified the requirements for real power at various points on the electric distribution systems. In response to the specified requirements, the utilities determined how much electricity to produce, where to groduce it, and how to distribute it.

[0004] Utilities generate electricity using various types of power generators, which may be categorized depending on the energy used to generate electricity, into thermal, nuclear, wind, hydroelectric; eic., generators. Each of these various types of generators operates under different sets of constraints. For e~:ample, an output of a thermal generator is a function of the heat generated in a boiler, wherein the heat generated per hour is constrained by the amount of fuel that can be burned per hour. Additionally, the output of the thermal generator may be limited by various environmental regulations that specify the maximum output of certain hazardous gases that can be emitted by the thermal power generator.
Similar types of constraints exist with other types of power generating systems.
[0005 Once the utilities received the requirements for real power to be delivered, the utilities determined which generation unit to use at what )evel. In making this determination, the utilities took into consideration the constraints on each of the available power generators.
Moreover, to minimize the cost of power generation, the utilities typically Dried to find the optimum combination of power generation using any of a number of sophisticated mathematical and forecasting models available for planning the generation of electricity.
Specifically, computer programs generally known as economic dispatch programs were available to help utilities make decisions related to the operation of electric generators based on real power requirements.
[0006] As is well known, electric power includes both real power, which is given in megawatts (MWs), and reactive power, which is given in mega volt-amperes reactive (MVARs). Because, utilities traditionally received requirements for electric power in real power only, traditional economic dispatch programs determined optimum operating solutions only in terms of real power. As a result, these programs allowed utilities to determine optimal operation of various generators based on a specified real power, but did not take into account the reactive power requirement. However, it is necessary to keep a certain level of reactive power on the electric distribution grids to avoid damage to transformers and other electrical distribution equipments. As a result, utilities still have to generate and distribute at least sonic reactive power. In the past, because the levels of reactive power were not mandated by the regulators, reactive power levels on grids were maintained mostly based on mutual understandings between various utilities and loosely defined best practices for power generation. Moreover, because the rates charged by utilities for power were trariitionaIly highly regulated, and were generally tied to the cost of producing the electric power, utilities generally did not pay much attention to the cost of generation and delivery of the reactive power, as the utilities could easily pass on the added cost of producing the reactive power to their customers.
[0007] However, over the last couple of decades there has been considerable de-regulation and restructuring within the electric power industry of the United States, which has substantially increased competition among utilities and made utilities snore aware of their cost structures: In particular, due to increased competition, the utilities can no longer automatically charge their customers higher prices because of higher production costs. As a result, utilities have become more conscious of the costs associated with generating and distributing both real electric power and reactive electric power, and are less likely to provide reactive power to properly maintain distribution grids without being adequately compensated.
[0048] In this environment, to maintain the necessary level of reactive power on distribution grids, the North American Electric Reliability Council {NERC), a utility industry trade group, has started providing specifications for levels of reactive power to be maintained by utilities. As a result, when a utility is making the determination as to which generator technology to use for generating electricity, the utility has to take into account not only the real power to be produced, but also the reactive power to be produced.
[0049] Unfortunately, the task of optimizing the production of both real power and reactive power is highly complex, due to the relationships between the two, and none of the various economic dispatch programs available on the market allows optimizing the production of both real power and reactive power.
BRIEF DESCRIPTION OF TIIE DRAWINGS
{0010] Fig. 1 illustrates a block diagram of a power distribution system; , (0011] Fig. 2 illustrates a block diagram of a power generation plant;
(4412 Fig. 3 illustrates a flowchart of an example economic dispatch program used by the power generation plant of Fig. 2;
(0013] Fig. 4 illustrates a flowchart of an example mathematical solver used by the economic dispatch program of Fig. 3;
[0014] Fig. 5 illustrates a block diagram of an electric power plant using eherraal power generators;
(40153 Fig_ 6 illustrates a reactive capability eusve of a combustion turbo-generator;
and [OOlb] Fig. ? illustrates a reactive capability curve of a steam turbine generator.

DETAILED DESCRIPTION
[0017] Generally speaking, an economic dispatch program operates as described herein to allocate a load demand of a power system among various available power generation resources. An example of such an economic dispatch program allocates a load demand of a power plant to various power generators, wherein the load demand specifies the total real power requirements as well as the total reactive power requirements of the power plant. The oconon~ic dispatch program may use various capacity limits associated with the generators, including reactive capability curves of one or more generators, which provide relationships between the power factors of the generators, the real power' produced by the generators and the reactive power produced by the generators. An alternative example of an economic dispatch program operates to allocate a load demand of a power grid to various power plants, wherein the load demand specifies the real power reguireriients as well as the reactive power requirements of the power grid, and wherein one or more power plants has reactive capacity limits exhibited by, for example, reactive capability curves.
[00183 Fig. 1 illustrates a power distribution system 10 having a power grid connected to a load grid 14. The power grid 12 may transmit both real power, measured in megawatts (MWs) and reactive power, which is a product of the voltage and the out-of-phase component of an alternating current, and is measured in mega volt-amperes reactive (MVARs). 'Ihe example load grid 14 of Fig, 1 may provide power to various industrial and residential customers who use power consuming devices, such as air conditioning units, electrical motors, lights, appliances, ere. In particular, the load gild 14 may provide real power to devices such as Light bulks, etc., and provide bath real power and reactive power to devices such as electric motors, transformers, ere. As a result, it is necessary that the power grid 12 maintains a certain Level of real power and reactive power available on the lead grid 14 at all times.
[0419] As indicated in Fig. 1, the power grid 12 may also be connected to one or more utility grids 16, 18. In this example, the utility grid 16 is cormected to a second power grid 20, and the utility grid 18 is illustrated as being formed of one or more power plants 22-26, which may include any of various types of power plants, such as nuclear power plants, hydroelectric power plants, thermal power plants, etc_ Additionally, each of the power plants 22-2fi may include any number of individual power generators. As discussed above, the operation of the utility grid 18 can be highly complex. As a result, to maintain the utility grid I8 running smoothly, it is necessary that each of the power plants 22-26 be managed with very high precision. Moreover, it is desirable that an operator of the utility_grid 18 ensure that the utility grid 18 is able to maintain and provide. real power and reactive power at all points throughout the utility grid 18 in a manner that nunimizes the total cost of the utility grid 18. To accomplish such an optimal operation, the utility grid 18 may use an economic dispatch program, like the one described herein, which takes into consideration both the real power and the reactive power required on the utility grid 18, the power grid 12 or the load grid 14, to allocate required load demands between the power plants 22-26.
[0020] At the, plant level, each of the plants 22-26 faces the challenge of operating one or more power generators so that each of the power plants 22-26 can meet its respective power demand with sufficient accuracy as well as at the least possible cost.
In this context, an operator of any of the powei plants 22-26 may use an economic dispatch program to allocate the required Toad demands between various power generators. In this manner, an economic dispatch program can be used at various levels within the power distribution system 10, such as at the utility grid level, at the plant level, at a generator level, etc.
Irrespective of the level at which an economic dispatch program is used, this program allocates required load demands between various available resources in some optimal manner.
[0021] Fig. 2 illustrates a block diagram of a power plant 100 that may use an economic dispatch module 102 to allocate a load demand 104 among various power generators 106-110. The load demand lU4 may specify one or more of the amount of real power to be deli vered by the power plant 100, the amount of reactive power to be delivered by the power plant 100, and time and place of the delivery of the real andlor the reactive power. The economic dispatch module 102 may use various information associated with the generators 106-110, such as the availability, the operating condition and the efficiency of each of the generators 106-110, in determining how to best allocate the load demand 104 among the generators 106-110. If desired, the economic dispatch module 102 may be implemented as software stored on a memory of a computer and operable on a controller of the computer, as hardware, as firmware or as any combination thereof.
[0022) Fig. 3 illustrates a flow chart of an example economic dispatch program that may be implemented by the economic dispatch module 102. Generally speaking, the economic dispatch program 140 determines the allocation of the Load demand l04 among various power generators 106-110 by solving an objective function, which raay be provided to the economic dispatch program 140 by the administrator of the power plant 100 to determine an optimal operation point of the plant_ To perform such an optin>ization, the economic dispatch program i40 receives various information about the power plant 100, such as parameters used to define the operation of the plant 100, values of some of these parameters, relationships between these parameters including reactive capability curves of the various generators used in the plant 100, and constraints on the operation of the power plant.
[0023) Specifically, a block 142 receives an objective function for the power plant 100, which is to be optimized using the economic dispatch program 140. An example of such an objective function may specify the total cost of producing a given amount of real power and a given amount of reactive power as a function of the amount of fuel necessary to generate the power. In an alternate implementation, the objective function may specify total envssions during production of a given amount of real power and a given amount of reactive power as a function of the amount of emissions per a unit of fuel used in generating the power. 4f course, any other desired objective function may be used. The block 142 may receive the objective function in any desired manner,Isuch as in the form of an entry in a spreadsheet stared on the ~onomic dispatch module 102, as a series of selections on a graphical user interface (GLJI) based menu presented to the administrator, ete.
[00243 Upon receiving the objective function, a block 144 identifies various parameters used to define the operation of the power plant 100. Typically, these parameters are specified or used in the objective function, and the values of one or moms of these parameters are varied to find the optimal value of the objective function.
Generally speaking, the economic dispatch program 140 treats some of these paratt~ters as s:onstants whose values cannot be altered by the economic dispatch program I40, some of these parameters as controllable or manipulated variables whose values may be controlled by iht economic dispatch prograxn 140, and some of these parameters as dependent variables whose values are to be determined by the economic dispatch program 140.
[0025] Generally speaking, the objective function of the plant IQO is given as an equation including one or more parameters of the plant 100, wherein values of some of these parameters may be obtained by solving one or more relationships specifying the operation of the plant 100 including relationships specified by the reactive capability curves of the various generators used in the plant 100. The economic dispatch program 140 may determine which parameters are to be treated as constants, as manipulated variables or as dependent variables based on the objective function received by the block 142. The economic dispatch program 140 may siso make such determinations using other infornration about the power plant 100, such as a database file stored in the economic dispatch module 102 wherein the database file has various objects, with each object identifying different equiprrtent within the power plant 100. For example, if the objective function specifies the total cost of operating the power plant 100, the economic dispatch program 140 may treat the cost of fuel, the cold gas generator temperatures, the cold gas generator pressures of the generators 106-110, etc., as constants. In this case, the economic dispatch program 140 may also treat the amount of real power and the amount of reactive power, as specified by the load demand 104, as constants when determining the optimal operating point for the power plant 100.
[0026 1n an alternate example, if the objective function specifies the Wtal emission of a pollutant gas by the power plant 100, the economic dispatch program 140 may treat the emission of NOx per unit fuel used by the power plant 100 as a constant and the cost of fuel as a controlled variable (value of which may vary based on the type and quality of fuel used).
Moreover, even though a given implementation of the economic dispatch program 140 treats a particular parameter as tt constant, an alternate implementation of the economic dispatch program 140 may treat that particular parameter as a manipulated variable or as a dependent variable.
[0027] Examples of various manipulated variables for the power plant 100 include the rates of fuel flows into the getieratotg 10C-l I0, the uperating power factors of the generators 106-110, etc. Generally speaking, manipulated variables are those that can be changed or altered within the plant 100 to specify different operating points of the plant 100. A person of ordinary skill in the art will know that some of the variables treated as manipulated variables within a given implementation of the economic dispatch program 140 may be treated as dependent variables in an alternate implementation of the economic dispatch program 140, while some of the variables created as dependent variables within a given implementation of the economic dispatch program 140 may be treated as manipulated variables in an alternate implementation of the ~onomic dispatch program 140.
[0028] Upon determining which parameters are to be used to define the operation of the power plant 100, a block 146 receives values of the various constants. The economic disgatch program 140 receives values of some of the constants, such as the amount of real power and the amount of reactive power to be produced by the power plant 100, from the load demand 140. Generally, a user may provide values of some of the constants, such as cost of gas used by the generators 106-110, the heating value of the fuel;
etc. In an alternate implementation, the economic dispatch module 102 may be communicatively connected to a power plant control system that supplies values for various constants such as the cost of fuel,' the cost of NH3, etc., to the economic dispatch pmgram 140. The econoraic dispatch program 14.0 may also store the values of the various constants at a periodic rate, in response to an instruction from the user, or based on other predetermined criteri a, into a memory of the economic dispatch module I02.
[0029] A block 148 determines relationships between the var;ous parameters identified by the block 142, including relationships specified by the reactive capability curves of the generators 106-110. Such relationships may define values of various dependent variables as functions of one or more of the parameters. An example of such a mathematical relationship is a function that defines the value of the heat generated by the generator 106 as a function of the race of fuel flow in the generator 106 and as a function of the heating value of the gas flowing through the generator 106. Xet another example of such a relationship is a reactive capability curve of the generator 108, which provides the value of reactive power generated by the generator 10$ as a function of the cold gas temperature and as a function of the cold gas pressure of the generator 108. Of course, any other known or desirable relationship may be used instead of or in addition to the relationships enumerated herein.
[0030] The economic dispatch program 140 znay receive the various relationships fmm a user in the form of a spreadsheet, from a database file stored on the economic dispatch module 102 wherein the database file has various objects, each object identifying an _ , , CA 02510839 2005-06-27 - -equipment within the power plant 100, etc, or in any other desired manner_ Alternatively, a plant control system, which may be communicatively connected to the economic dispatch module 102, may provide one or more such relationships to the economic dispatch program 140. Furthermore, as shown at the block 148 of F g. 3, the economic dispatch program 140 may update these relationships based an a periodic basis or based on any other predetermined criteria.
j0031] Next, a block LSO identifies various constraints on the operation of the power plant 100: An example of a constraint that may be used is that the total reactive power generated by all of the generators 106-110 must be equal to the amount of reactive power required to be produced by the power plant 100, as specified by the load demand 104.
Another example of a constraint is that the fuel flow into each of the generators 106-110 cannot be less than zero. The economic dispatch program 140 may receive the various constraints from a user in the form of a spreadsheet, from a database filestored on the economic dispatch module 102 wherein tha database fife has various objects, each object identifying an equipment within the power plant 100, or in any other manner.
Alternatively, a plant control system, which may be communicatively connected to the economic dispatch module 102, may specify one or more such constraints to the economic dispatch program I40 [0032] Subsequently, a block 152 determines an optimal solution for the operation of the Bower plant 100 by solving the various relationships to obtain an optimal solution of the objective function received by the block 142. In determining the optimal solution, the economic dispatch program 140 generally uses the values of the various parameters as identified by the block 144, the values of the constants as determined by the block 146, the relationships among the various parameters as defined by the block 148, the constraints as identified by the block 150. In particular, the economic dispatch program 140 varies the manipulated variables in some systematic manner to identify a set of dependent variable values which result into an optimal value for the objective function.
[0033] Fig. 4 illustrates a flowchart of a program tgenerally known as solver) 160 that .
may be used to solve the objective function of the power plent 100 subject to the various constraints of the power plant x00. The example sotver I60 determines Ehe optimal solution for the objective function by using an iterative algorithm, generally known as the evolutionary algorithm, wherein a set of candidate solution points within the constraints are selected, a set of localized solutions corresponding to the set of candidate solution points is obtained and one of the set of localized solutions is selected as the optimal solution of the objective function.
[0'034] Specifically, a block 162 identifies a set of candidate solution points for the objective function, wherein each of the candidate solution points is determined by a set of manipulated variables defining an operating point for the power plant 100. The block 162 ' may determine the set of candidate solution points by analyzing data regarding past operation of the power plant 100, by obtaining these solution points from a model or a user, etc. If desired, such data may be stored in a database located on the econonnic dispatch module 102.
[0035] A block 164 solves the objective function for one of the set of candidate solution points and stores an initial value of the.objective function. During the solving process, the block 164 uses one or more of the relationships identified by the block 148 to deterniine values of the various dependent variables at the one of the set of candidate solution points. The block 164 then solves the objective function using these dependent variables, the constants and the manipulated variables defined by the selected set of candidate solution points, checks to determine if the values of the various dependent variables are within the constraints identified by the block 150, and, if not, limits these values to the constraints.
[0036] 5ubseqvently, a block 166 changes values of one or more of the controlled variables based on some predetermined criteria and solves the objective function to determine an altered value of the objective function. The solver 160 may determine the direction and the amount of the change to be made to the controlled variables based on predetermined criteria which may be specified by the administrator of the power plant 100 or which may be determined randomly; pseudo-randomly, or in some predetermined or iterative manner.
[0037] A block 168 compares the initial value of the objective function and the altered value of the objective function to determine which value is more optimal, the direction in which the value of the objective function has changed and the amount by which the value of the ohj~:ctive function has changed. Based on the result of the cornparison, the block 168 may determine whether the values of the manipulated variables are to be further altered or not, and if the values are to be further altered; in which direction and by bow much.
In this manner, the blocks 166 and I68 operate together to iteratively alter the values of the manipulated variables until the block 168 determines that the resulting value of the objective function is an optimal value of the objective function in the vicinity of the one of the set of candidate solution points, also known as a localized optimal solution.
[0038] Once the localized optimal solution is obtained, a block i70 stores the localized optimal solution as one of a set of localized optimal solutions for the objective function. Subsequently, a block 172 determines if there are any more candidate solution points in the set of candidate solution points for which l~alized optimal solutions are to Ix obtained. If so, the control is transferred back Lo the block 164 to find another Localized optimal solution for the next of the set of candidate solution points. If the block 172 determines that a localized optimal solution for each of the set of candidate solution points has been found, it passes control to a block 174, which compares the values of the objective function ai each of the set of localized optimal solutions and determines the most optimal solution for the objective function. The implementation of the solver 160 as described above ensures that even if the objective function of the power plant 100 has multiple localized optimal values, the most optimal of these localized optimal values is obtained.
[0039] The solver 160 may be implemented in the form of software, hardware, firmware or any combination thereof, For example, the solver 160 may be implemented using one of the various off-the-shelf mathematical solution programs, such as the Evolutionary Solvez~ program available fmm Frontline Systems, Inc.
[0040] While the above implementation of the economic dispatch program 140 is described in the context of the generic power planf 100, Figs. S-7 illustrate the functioning of the economic dispatch program 140 in the context of a thermal power plant 200.
In particular, the power plant 200 illustrated in F;tg. 5 is a thermal power plant designed as a combined cycle power plant (CCPP) that can also ho operated as a simple cycle power plant.
As indicated in Fig. 5, a typical CCPP may have several combustion turbo-generators (CTGsj 202 and 204, each with a corresponding heat recovery steam generator (HRSG) 206 and 208 and a common steam turbo-generator (STG) 2x0. The CTGs 202 and 204, which receive fuels such as nature! gas, along with compressed air into their comkustion sections have two primary functions. Firstly, the CTGs 202 and 204 produce electrical power through hydrogen cooled generators 2i2 and 214, which are directly connected to the CTGs 202 and 204.
Secondly, the CTGs 202 and 204 supply hot gases to the I~RSGs 206 and 208. The electrical power generated by the generators 212 and 214 is uploaded to the plant power gad 216, which may be ultimately connected to the utility grid 18 of Fig. 1. The plant power grid 216 may also be connected to-an auxiliary power grid 218, where the auxiliary power grid 218 provides real power and/or reactive power to the plant power grid 226 according to the total power needed to be placed on the plant power grid 216.
[004I] Operating the plant 200 in the CCPP mode, in which the HRSGs 206 and are used along with the CTGs 202 and 204; is economically efficient due to the liRSGs 206 and 208 capturing and using the exhaust energy of the CTGs 202 and 204 for additional power generation. However, it is also possible to operate the CTGs 202 and 204 without the HRSGs 206 and 208, which is known as a simple cycle mode operation but which is less efficient than the CCPP mode. Of course, whether the plant 200 is operated in the CCPI?
mode or in the simple cycle mode, the HRSGs 206 and 208 run only when the CTGs 202 and 204 are used.
[0042] The HRSGs 206 and 208, which forth a link between the CTGs 202 and 204 and the STG 210, receive a supply of hot gases from the CTGs 202 and 204 as well as a fuel such as natural gas from a fuel source (not shown). The HRSGs 206 and 208 use the hot gases and the fuel to generate steam for the STG 210 and, as illustrated in Fig. 5, provide the steam to the STG 210 at three different pressure levels, namely a low pressure (LP) level, an intermediate pressure (1P) level and a high pressure (HP) level. Using the pressurized steam, the STG 210 produces electric power through a hydrogen cooled generator 220, wherein the electric power generated by the generator 220 is uploaded to the plant power grid 216.
[0043] V~Then a power plant operates in the CCP'>y mode, in which the I-iRSGs 206 and 208 are placed downstream from CTGs 202 and 204, duct burners 222 and 224 are typically placed in the inlet paths of the HRSGs 206 and 208. The duct burners 222 an-d 224 are only used when the power plant 200 cannot satisfy the total Bower demand running only the CTGs 202 and 204, .which typically occurs on hot days when the maximum gawer that can be generated by the CTGs 202 and 204 is limited. 'When the duct burners 222 and 224 are used, the additional gas burned in the duct burners 222 and 224 causes the amount of steam produced by the I3RSGs 206 and 208 to increase, thus making more steam available for use in the STG 210 and thereby increasing the power produced by the STG 210.
Therefore, when determining the operating parameters of the plant 200 for the optimal production of power, it is desirable to take into consideration whether or not the duct burners 222 and 224 are to be used.
[0044] The power plant 200 can output a specified combination of real power and reactive power using a number of different combinations of the generators 202, 204 and 210 and the duct burners 222 and 224. Furthermore, each of the generators 202, 204 and 210 and the duct burners 222 and 224 has a variety of operational settings, so that a number of different combinations of operational settings can be used to satisfy a given load demand. As a result, deterraining an optimal combination of the operational settings of the various equipment used in the plant 200 can be a highly complex task. An applicationof the economic dispatch program 140 of Fig. 3 to determine the optimal operational settings for the various equipment used in the power plant 200, taking into account production of both real power and reactive power is described as follows.
[0045] The block 142 of Pig. 3 receives the objective function for the power plant 200. When the goal of the economic dispatch program 140 is to minimize the operating cost of running the power plant 200, the objective function of the powea plant 200 can be provided as follows:
[0046] Minimize (G1_I-1LAT*GAS_COST + d2_HEAT*GA5 COST +
DB 1 HEAT*GAS_COST + DB2 HEAT*GAS_COST) [0047] Various parameters used in this objective function are explained below in Table 1.
Table 1 CONSTAM'S

GAS COST Cost of as used as fuel fn tile power plant HEAT VAL Heatfn value of as used as fast In the lent MW DMD Plant and MW
dem MVAH DMD Plant emand MVAR
d Gi CIT C TG

compressor inlet temperature com ressor inlet tam stature G1 EXT CTG1 haust ex as tam nature G~,EXT CTG2 haust ex as tam nature _ G t CGi' CTGi __ col d as Generator tam stature G2 CGT CTG2 d col Generator tam refute Gi _CGP CTG d 1 as col Generator assure cold as Generator ressune _ STG CGT STG
cold as Generator tam nature ' STG CGP STG
cold as Generator ressure ... , i MANfPULATED
VARIABLES

G1 CTGi FF fuel flow PF ower factor FF fuel flow PF over factor STG STG
PF over factor DB1 D uct Burner ow FF 1 fuel fl DB2 F D uct Burner ow F 2 fuel fl Gi Bitaa switch ON if set turn CTGi ON-turn OFF

G2 Bina switch ON if set turn ON-turn OFF

STG_ON Bina switchset G ON' 0-turn if turn OFF
ST

DBi N Biswitch set i ON: 0-turn O ii turn OFF
DB

DB2 N Bina switchset 2 ON' 0 -O 8 turn turn OFF
DB

DEPENDENT IABLES
VAR

G1 The HEAT heat.
into from the fuel.

G2 The HEAT heat into from the tuei.

DBi EAT T he heat RSGi rom .
H into f ~e H Duct Burner fuel O B2 EAT T he heat RSG2 rom .
H into f the H Duc!
Burner fuel H P1_STM Amount of Hi h Pressure steam from HRSGi H R1 Amount STM of Hot Reheai steam from HRSGi LPt Amount STM of Low Pressure steam from ~HP2_STM Amount of Hi It Pressure steam from H S TM Amount of Hot Reheat steam from L P2_STM Amount of Low Pressure steam from STG_H P Amount of Hi h Pressure steam enteri the STG

5TG R Amount m enterin H of the STG
Hot Reheat stea STG P Amount the STG
L of LP
steam enteri G1_MW CTG1 MW
amount MVAR MVAR
amount MW MW
amount G2_MVAfa CTG2 MVAR:amount MW MW
amount STG STG
MVAR MVAR
amount AUX Plant MW Auxiifa MW

[00483 The block 144 of Fig. 3 identifies various parameters of the power plant 200, which may be used in determining the optiraal operational settings for the power plant 200.
To perform this function, the block 144 of Pig. 3 may present a menu andlor u.se a graphical user interface (GUn based program to receive input from the administrator of the plant 200.
[00492 Next, the b)ock 146 of Fig. 3 determines the values of the various constants listed in the Table 1. The block 146 raay obtain the values of one or more of these constants from a database 'stored on the economic dispatch module 102. hIternatively, to obtain~the values of one or more of these constants, the block 146 may present a menu and/or use a graphical user interface (GUI) based program to receive input from the administrator of the plant 200. In yet another implEmentation, a plant control system, which may be communicatively connected to the power plant 200, may provide values of one or mare of the various constants listed in Table 1.
[0050] Thereafter, the block 148 of Fig. 3 determines the relationships between the various parameters of the power plant 2(?0. Examples of some of the relations between the various parameters of the power plant 200, which may be stored on the memory of the economic dispatch module 102, are listed below in Table 2 as equations 1-20.
Table 2 1 G1 HEAT HEAT_VAL1/1000 =
(G1 FF' 2 G2 HEAT HEAT..VAL/1000 =

FF' HEAT
=

FF'HEAT
VAL

HEAT
=

FFHEAT
VAL

HPi STM
=
F
Gi HEAT

EXT
DBi HEAT

STM
=
F

HEAT

EXT

HEA

STM
=
F

HEAT

EXT
DBi HEA

STM
=
F

HEAT

EXT

HEA
' STM
=
F

HEAT

EXT

HEAT

STM
=
F

WEAT

EXT

HEA

11 STG P =

STM
+
HP
STM

i2 STG R =
H HRi .
STM
+

STM

LP +
= LP2_STM

S

MW=FG1 G1 CIT

CGT

CGP

P

MVAR=
F

HEAT

CIT, CGT
Gi CGP, P

MW
~
F

HEAT, G2_CIT
G2_CGT

CGP

P

MVAR
=
F

HEAT

CIT

CGT

CGP, PF

MW
=
F
STG
HP
STG
HR
STG
LP
STG
CGT
STG
CGP
STG
PF

MVAR
=
F
STG
HP
STG
HR
STG
LP, STG
CGT
STG
CGP
STG
P

AUX
. MW
=
F

MW
+
G2_MW
+
STG_MW

[0051] While the equations 1-13 listed above enuraerate linear relationships between the various parameters of the power plant 200, the equations 14-20 are non-linear functions, of which the equations 14-19 represent the reactive capability carves Qf one or more of the eTGs 202 and 204 and the STG 210. In one implementation, the equations 14-19 rnay capture the reactive capability curves of the CTGs 202 and 204 and the STG
210, and represent neural network models used to define values of the real power and the reactive power generated by the CTGs 202 and 204 and the STG 210 as a function of the parameters included within the brackets on the right hand side of these equations.
[oa5z~ Specifically, the equations 15-i7 of Table 2 represent the reactive capability curves of the CTGs 202 and 204, and are illustrated in Fig. 6 by an estimated reactive capability curve 350 that defines the limits imposed on the real power and the reactive power l5 of a particular CTG at various power factors, generator temperatures, and generator pressures. In Fig. 6, the real power of the GTG is plotted as the abscissa and the reactive power of the C'TG is platted as the ordinate. The curve 350 depicts, for example, that for a cold gas temperature of 24' centigrade and a cold gas pressure of 30,00 PSIG, the optimal operating range of that particular CTG is limited to a region defined between the origin 352, an arc 354, a first line 356 corresponding to the power factor of 0.85 and a second line 358 corresponding to the power factor of -0.95. While the total power (MVA) produced by that particular CTG is the same at each point on any arc within this optimal operating range, where the center of such arc is the origin, such as the arc 354, for points outside the range, the MVA produced by that particular CTG starts to decline due to heat build-up within the CTG.
[0053] The equations 18-19 of Table 2 represent the reactive capability curves of the ' STG 210, and are illustrated in Fig. 7 by an estimated reactive capability curve. 370 that defines the limits imposed on the real power and the reactive power of a particular STG at various power factors, generator temperatures, and generator pressures. In Fig. 7, the real power of the STG is plotted as the abscissa and the inactive power of the STG
is plotted as the ordinate. The curve 370 depicts, for example, that for a cold gas temperature of~42°
centigrade and a cold gas pressure of 45 PSIG, the optimal operating range of that particular STG is limited to a region defined between the origin 372, an arc 374, a first line 376 corresponding to the power factor of 0.85 and a second line 378 corresponding to the power factor of -fl,95. While the MVA produced by that particular STG is the same at each point on any arc within this opdrnal operating range, where the center of such arc is the origin, sueh.as the arc 374, for points outside the range, the MVA produced by the STG starts to decline due to heat build-up within that particular STG.
[0054] Generally, the estimated reactive capability curves for generators such as the CTGs 202 and 204 and the STG 210 are provided by the manufacturer of these generators.
As the reactive capability curves of the generators 202, 204 and 210 provide operating ranges of these generators, if the values of the generator gas temperature and gas pressures in these generators are available, the reactive capability curves of these generators can be used by the economic dispatch program 140 in determining one or more operating poi>ats far the power plant 200. However, in practice, the reactive capability curves of any generators are not steady, and they change over time with use of the generators.

[0055 In these circumstances, to obtain the optimal value of the objective function of the power plant 200, the economic dispatch program 140 may approximate the functions descxibing the actual reactive capability curves for the power plant 200 (e.g., functions 14-19 of Table 2). The economic dispatch program 140 may use techniques, such as neural networks, curve fitting with interpolation, etc. for approximating these functions. An implementation of the neural network apgroximation technique employed by the economic dispatch program 140 may involve operating the generators 202, 204 and 210 at various points of gas pressure and gas temperatures and recording various actual observations of the real power and reactive power of these generators (also known as training the neural network). Subsequently, the trained neural network may be substituted for the functions 14-19 and used in obtaining the optimal value of the objective function of the power plant 200.
The economic dispatch program 140 may continuously or periodically update the neural network based on rea! time data provided by a control system of the power plant 200 and use the updated neural network in obtaining the optimal value of the objective function of the power plant 200.
[0056] Once the economic dispatch program 140 has determined various relationships for the power plant 200, the block 150 of Fig. 3 identifies the constraints applicable to the power plant 200, an example of which are listed below in Table 3.
Table 3 CONSTRAINTS

Gt _MW
+
G2_MW
+

MW
-AUX_MW
=
MW
DMD

G1 MVAR + G2 MVAR + STG ~MVAR = MVA
DMD

G1 FF>a0 Gi FF r= F G1 CIT

G2 FF >= 0 LG1 ~F x 0 G ~i P

G2 PFxO

G2 F as 1 STG PF >= 0 STG PF <=1 DB1 FF a= Q

[0057] ' Having determined the objective function of the power plant 200, the various relationships between the parameters of the power plans 200, and the constraints of the power ,., , plant 200, the block 152 determines one or more optimal operational solutions for the power plant 200 using the solver 1b0 of Fig. 4.
[OU58] One of the advantages of using the reactive capability curves, such as the capability curves 350 and 370, or some model that approximates these et~ves, for determining an optimal operadanal solution for the power plant 200 is that these curves allow itzcorporating the limits imposed on the real power and the reactive power generated by each of the generators 202, 204 and 210, In this manner, the economic dispatch program 140 can use the values of.the real power and the reactive power,as defined by the load demand on the plant grid 216 and determine the optimal operating point for each of the generators 202, 204 and 2I0.
[0059) Of course, while the application of the econonuc dispatch program 140 to the power plant 200 minimizes the cost of operating the power plant 200, in an alternate situation, the economic dispatch program 140 can be applied to the power plant 200 to meet an alternate objective, which may be for example, the minimization of NOx emissions, or some optimal combination of the two. In an alternative implementation, the economic dispatch program 140 may be applied to the entire utility grid 18 to allocate the total demand of the utility grid 18 among the power plants 22-26 so that the total cost of the operating the utility grid 18 is minimized. In yet another alternate implementation, the economic dispatch program 140 may be applied to the entire power grid 12 to allocate the total demand of the power grid 12 among the utility grids 16, 18, etc., so that the total cost of operating the power grid I2 is minimized.
[aoso] Although the forgoing text sets forth a detailed description of nurnemus different enrbudia~lents of the iuventivn, it should be undersWud ihs~t the scope of the invention is defined by the words of the claims set forth at the end of this patent. The detailed description is tv be construed as exemplary only and does not describe every possible embodiment of the invention because describing every possible embodiment would be impractical, if not impossible. Talumerous alternative embodiments could he implemented,.
using either cuneni technology or technology developed after the filing date of this patent, which would still fall within the scope of the clairras defining the invention, [OU61] Thus, many modifications and variations may be made in the techniques and structures described and illustrated herein without departing from the spirit and scope of the present invention. Accordingly, it should be understood that the methods and apparatus described herein are illustrative only and are not limiting upon the scope of the invention.

Claims

What is claimed is:

1. A method of optimizing an operation of a power generation system having a plurality of power generation devices, the method comprising:
obtaining an objective function of the power generation system;
obtaining a plurality of operating constraints of the power generation system;
determining a plurality of relationships between a plurality of parameters of the power generation system, the plurality of relationships including a first relationship specifying an optimal operating range of one of the plurality of power generation devices as a function of a power factor of the one of the plurality of power generation devices; and solving the plurality of relationships to obtain an optimal solution for the objective function within the plurality of operating constraints of the power generation system.

2. A method of claim 1, wherein at least one of the plurality of operating constraints specifies one of (1) a reactive power to be generated by the power generation system and (2) a real power to be generated by the power generation system.

3. A method of claim 1, wherein the first relationship is a reactive capability curve for a power generator.

4. A method of claim 3, wherein the first relationship is a reactive capability curve for one of a (1) a combustion turbo-generator and (2) a steam turbo-generator.

5. A method of claim 1, wherein the first relationship is represented by a neural-network approximation of a reactive capability curve for a generator.

6. A method of claim 1, wherein the objective function specifies a cost of operating the power generation system.

7. A method of claim 6, wherein the objective function specifies the cost of generating (1) a required amount of real power and (2) a required amount of reactive power, by a thermal power plant.

8. A method of claim 6, wherein the objective function specifies the cost of providing (1) a required amount of real power and (2) a required amount of reactive power, on a utility grid.

9. A method of claim 1, wherein the objective function specifies an emission of a first pollutant during an operation of the power generation system,

10. A method of claim 1, wherein the first relationship further specifies the optimal operating range of the one of the plurality of power generation devices in terms of at least one of (1) cold gas generator pressure within the one of the plurality of power generation devices and (2) cold gas generator temperature within the one of the plurality of power generation devices.

11. A method of claim 1, wherein the plurality of parameters of the power generation system include (1) a set of manipulated variables, (2) a set of constants and (3) a set of dependent variables.

12. A method of claim 11, wherein solving the plurality of relationships includes:
selecting a first set of values for the set of manipulated variables, wherein the first set of values represents a first candidate solution point within an operating space of the power generation system;
computing a first value of the objective function using the first set of values;
changing a value of at least one of the set of manipulated variables;

computing a second value of the objective function;
comparing the first value of the objective function and the second value of the objective function;
changing the value of the at least one of the set of manipulated variables based on the comparison of the first value of the objective function and the second value of the objective function; and computing a first optimal solution of the objective function corresponding to the first candidate solution point.

13. A method of claim 12, wherein the first candidate solution point is selected from a plurality of candidate solution points, wherein each of the plurality of candidate solution paints is used to obtain one of a plurality of candidate optimal solutions for the objective function.

14. A method of claim 13, further comprising selecting a most optimal of the plurality of candidate optimal solutions.

15. A method of claim 1, further comprising approximating the first relationship using a neural network.

16. A method of claim 15, further comprising training the neural network by operating the one of the plurality of power generation devices at a plurality of operational points specified by (1) cold gas generator pressure within the one of the plurality of power generation devices and (2) cold gas generator temperature within the one of the plurality of power generation devices, and storing the values of the real power and the reactive power generated by the one of the plurality of power generation devices.

17. A method of claim 15, further comprising updating the neural network based on one of (1) a periodic basis and (2) a predetermined criteria.

18. A method of claim 1, further comprising approximating the first relationship using a curve fitting technique.

19. A method of claim 1, further comprising receiving values of at least some of the plurality of parameters from a control system of the power generation system.

20. A method of operating a power plant having a plurality of power generators;
the method comprising:
receiving a load demand specifying (1) real power to be produced by the power plant and (2) reactive power to be produced by the power plant;
determining an objective function of the power plant specifying an operating condition of the power plant as a function of (1) the real power to be produced by the power plant and (2) reactive power to be produced by the power plant; and determining an optimal value of the objective function.

21. A method of claim 20, wherein determining the optimal value of the objective function includes ascertaining that the power plant is operated in an optimal space of a reactive capability curve of at least one of the plurality of power generators.

22. A method of claim 21, further comprising approximating the reactive capability curve using one of (1) a curve fitting technique end (2) a neural network.

23. A method of claim 22, further comprising updating the reactive capability curve based on one of (1) a periodic basis and (2) a predetermined criteria.

24. A method of claim 20, wherein determining the optimal value of the objective function comprises solving a plurality of relationships between a plurality of parameters of the power plant.

25. A method of claim 24, further comprising using an evolutionary solver for solving the plurality of relationships between the plurality of parameters of the power plant.

26. A method of claim 20, wherein the objective function specifies the cost of generating (1) the real power to be produced by the power plant and (2) reactive power to be produced by the power plant.

27. A method of claim 20, wherein the objective function specifies an emission of a first pollutant during an operation of the power plant.

28. A method of claim 20, wherein the operating condition of the power plant is one of (1) a cost and (2) an emission of a first pollutant.

29. An economic analysis system for optimizing operation of a power generation system having a plurality of power generation devices, the system comprising:
a first module adapted to store an objective function of the power generation system;
a second module adapted to store a plurality of operating constraints of the power generation system;
a third module adapted to store a plurality of relationships between a plurality of parameters of the power generation system, the plurality of relationships including a first relationship specifying an optimal operating range of one of the plurality of power generation devices as a function of a power factor of the one of the plurality of power generation devices; and a fourth module adapted to solve the plurality of relationships to obtain an optimal solution for the objective function within the plurality of operating constraints of the power generation system.

30. An economic analysis system of claim 29, wherein the first relationship is a reactive capability curve of one a generator.

31. An economic analysis system of claim 30, wherein the third module is further adapted to approximate the reactive capability curve using one of (1) a curie fitting model and (2) a neural network model.

32. An economic analysis system of claim 31, further comprising a plant control system module communicatively connected to the third module and adapted to provide values of the plurality of parameters to the third module.

33. An economic analysis system of claim 32, further comprising a fifth module adapted to obtain updated values of at least some of the plurality of parameters and to update the reactive capability curve.

34. An economic analysis system of claim 29, wherein the fourth module is further adapted to solve the plurality of relationships using an evolutionary solver algorithm.

35. An economic analysis system of claim 29, wherein the objective function specifies a cost of operating the power generation system.

36. A method of claim 29, wherein the objective function specifies an emission of a first pollutant during an operation of the power generation system.

37. A power generation system comprising:
a plurality of power generation devices; and an economic analysis system comprising:
a first module adapted to obtain an objective function of the power generation system, a second module adapted to obtain a plurality of operating constraints of the power generation system, a third module adapted to determine a plurality of relationships between a plurality of parameters of the power generation system, the plurality of relationships including a first relationship specifying an optimal operating range of one of the plurality of power generation devices as a function of a power factor of the one of the plurality of power generation devices, and a fourth module adapted to solve the plurality of relationships to obtain an optimal solution for the objective function within the plurality of operating constraints of the power generation system.

38. A power generation system of claim 37, wherein the plurality of power generation devices include at least one of (1) a combustion turbo-generator and (2) a steam turbo-generator.

39. A power generation system of claim 37, further comprising a fifth module adapted to store values of at least some of the plurality of parameters and to approximate the first relationship based on the stored values.

40. A power generation system of claim 39, further comprising a sixth module adapted to update the approximated first relationship on a periodic basis.

41. A power generation system of claim 39, wherein the fifth module is adapted to approximate the first relationship using one of (1) a curve fitting technique and (2) a neural network.