EP1509825A2 - Evaluation et optimisation des previsions en matiere d'equipements de productions d'energie - Google Patents

Evaluation et optimisation des previsions en matiere d'equipements de productions d'energie

Info

Publication number
EP1509825A2
EP1509825A2 EP03747567A EP03747567A EP1509825A2 EP 1509825 A2 EP1509825 A2 EP 1509825A2 EP 03747567 A EP03747567 A EP 03747567A EP 03747567 A EP03747567 A EP 03747567A EP 1509825 A2 EP1509825 A2 EP 1509825A2
Authority
EP
European Patent Office
Prior art keywords
price
time
facilities
optimal
specified
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
EP03747567A
Other languages
German (de)
English (en)
Other versions
EP1509825A4 (fr
Inventor
Ralph D. Masiello
Mihaela Manoliu
Petter Skantze
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
SunGard Energy Systems Inc
Original Assignee
Caminus Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from US10/336,542 external-priority patent/US7389209B2/en
Priority claimed from US10/336,541 external-priority patent/US7474995B2/en
Application filed by Caminus Corp filed Critical Caminus Corp
Publication of EP1509825A2 publication Critical patent/EP1509825A2/fr
Publication of EP1509825A4 publication Critical patent/EP1509825A4/fr
Ceased legal-status Critical Current

Links

Classifications

    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/004—Generation forecast, e.g. methods or systems for forecasting future energy generation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S50/00—Market activities related to the operation of systems integrating technologies related to power network operation or related to communication or information technologies
    • Y04S50/10—Energy trading, including energy flowing from end-user application to grid

Definitions

  • the present invention relates to methods and systems for operational scheduling of facilities, such as electrical energy generation facilities, and valuation of facilities and assets such as generation assets, and more particularly, to methods and systems for determining optimal operational scheduling for facilities, for determining anticipated profitability of facilities, and for determining values of assets such as generation assets.
  • Electrical power generation facilities generally operate to convert fuel into electrical energy for profit.
  • the facilities are a type of energy generation asset, and their value at a given time is based on their anticipated profitability.
  • Investing and trading in generation assets is possible through certain forms of financial instruments, such as real option contracts, whose value can be linked to a generation facility (or facilities), its operation, or the power produced by the facility.
  • the value of such instmments is often associated with the profitability of operation of a facility over a specified period of time.
  • Such profitability can be affected by many factors, including price paths for fuel and other relevant commodities, as well as scheduling of operation of the facility, including, for example, generation rate increases and decreases made during the period.
  • a profitability assessment should naturally assume that an attempt will be made, throughout the period of time, to schedule operation of the facility so as to optimize its profitability.
  • determining optimal scheduling of a facility is important in its own right for scheduling decision-making, as well as being necessary for accurate valuation of generation assets and associated financial instruments.
  • the important tasks of determining optimal scheduling as well as valuing generation facilities pose difficult challenges, due in part to the large number of interdependent variables involved, as well as the uncertainties of such things as relevant future price paths.
  • Optimal scheduling of a generation facility over a period of time is influenced by many variable factors.
  • One set of factors that can influence optimal scheduling includes prices at various times during the period, or price paths, of commodities used by the facility at a rate dependent on the rate of generation of the facility.
  • the market price path for fuel over the period of time can influence optimal scheduling.
  • the market price path, over the period of time, for electricity, as generated by the facility can also influence optimal scheduling.
  • Another set of factors can include constraints associated with operation of the facility.
  • electrical power generation facilities are generally subject to physical constraints including maximum and minimum generation rates while the facility is operating, maximum and minimum operating times, or run-times, and maximum generation rate increases and decreases per unit of time (herein termed, respectively, maximum ramp up and ramp down rates).
  • other constraints can relate to costs associated with specific scheduling actions or conduct under specific circumstances, such as start-up costs and shutdown costs.
  • start-up costs can include the cost of a necessary quantity of a certain type of fuel used for initiation of operation, which can be different and more expensive than a primary operation fuel.
  • the effect of these various constraints on formulating optimal scheduling is sometimes referred to as the "unit commitment" problem.
  • optimal scheduling of one or more generation facilities over a period of time requires informed decision-making over the period of time, taking into account any relevant prices at particular times throughout the period, e.g. price paths, as well as constraints as they apply at particular times throughout the period, including operating limits and costs associated with certain operating actions. Further complicating matters, some constraints can themselves be dependent on previous operation scheduling. It must also be noted that optimal scheduling at a particular time during the period can, and must, take into account circumstances as they have developed prior to, and exist at, that particular time, since an actual operator would be aware of such circumstances. Optimal scheduling at a given time further requires taking into account the current forecasts and probabilities as to relevant future circumstances, including relevant price paths, of which an operator would also be aware.
  • “optimal scheduling” includes scheduling which is optimized in the sense of an actual operator making optimal decisions over the period of time.
  • assessments of optimal scheduling over a period of time from the point of view of an operator during the period of time, must take into account, at various particular times over the period, optimal scheduling decision-making at each of various times, assuming knowledge of present circumstances by the operator and projections regarding future circumstances, as such circumstances and decision-making evolves throughout the period.
  • spark spread option modeling takes into account forecasts and specified uncertainty with regard to such factors as relevant price paths, facility constraints, examples of which are discussed above, are not modelable using such techniques.
  • spark spread option modeling is sometimes used in combination with "hedging" strategies. Hedging strategies, which can involve trading in certain financial instruments such as futures contracts, are used to attempt to reduce risk when investing in markets involving a specified estimated or forecasted uncertainty. Hedging strategies, however, do not remedy or even address the accuracy, and therefore the degree of value, of the underlying technique by which values of instruments are calculated. Spark spread option modeling, whether or not used with hedging, does not take into account relevant constraints, and, as such, cannot provide accurate valuation models for generation facilities and other facilities, nor can such modeling techniques be used to optimize scheduling.
  • Some traditional dynamic programming techniques use, as input, mathematically formulated constraints and a specified price path for fuel and electricity, and use backward iteration to attempt to find a profit-maximizing operation schedule.
  • Traditional dynamic programming is deterministic in that it fails to take into account uncertainty with regard to relevant future price paths.
  • Traditional dynamic programming effectively attempts to determine an optimal schedule for a facility assuming perfect and sure knowledge of future prices, which is, of course, unrealistic.
  • a heat rate curve can specify the efficiency of a generation facility as a function of the facility's generation rate.
  • Existing techniques may only be capable of handling convex or monotonically increasing heat rate curves. In reality, however, generators are often characterized by decreasing heat rate curves.
  • Another method which attempts to combine the advantages of spark spread option based modeling and dynamic programming proceeds as follows. First, based on a forecasted price path and an anticipated specified uncertainty with regard to the price path, a set of possible price paths are generated, using Monte Carlo simulations or otherwise. Next, for each price path scenario, traditional dynamic programming is used to determine what is considered to be an optimal schedule for each price path scenario. Next, profit or loss is determined for each price path scenario using, for each price path scenario, the optimal schedule for that particular scenario.
  • U.S. Patent number 6,021,402 issued on February 1, 2000 to Takriti, discusses scheduling for generators for risk management pu ⁇ oses. Multiple price path scenarios are generated, and decision-tree based dynamic programming is applied to optimize scheduling in each scenario.
  • the present invention provides methods for valuing and optimizing scheduling operation of assets including generation assets such as fuel powered electrical energy generators, and methods valuing financial instruments based on such assets.
  • generation assets such as fuel powered electrical energy generators
  • advantages of dynamic programming are achieved while maintaining mathematical tractability.
  • methods are provided that combine the advantages of stochastic price modeling with the advantages of dynamic programming by using a decision tree based model that together models constraints affecting operation of facilities as well as stochastically models relevant price paths, such as fuel or electrical energy price paths.
  • valuation or optimization is performed jointly for a portfolio of generation facilities, the operation of each of which facilities affects optimization of scheduling of other of the facilities.
  • the invention provides a computerized method for facilitating scheduling of operation of a facility for at least a first time interval of a period of time.
  • the method includes generating a decision tree based model accounting for a combined effect, on the scheduling of the operation of the facility, of: at least one specified forward price path, over the period of time, including at least one price of at least one commodity associated with operation of the facility; at least one specified level of uncertainty with regard to the at least one specified forward price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of the facility.
  • the method further includes applying a dynamic optimization algorithm to the decision tree based model to determine an optimal scheduling option for at least the first interval of time.
  • the method further includes storing in a memory optimal scheduling option information associated with the optimal scheduling option.
  • the invention provides a computerized method for determining an anticipated profitability of operation of a facility over a period of time.
  • the method includes generating a decision tree based model accounting for a combined effect, on scheduling of the operation of the facility over the period of time, of: at least one specified forward price path, over the period of time, including at least one price of at least one commodity associated with operation of the facility; at least one specified level of uncertainty with regard to the at least one specified forward price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of the facility.
  • the method further includes applying a dynamic optimization algorithm to the decision tree based model to determine the anticipated profitability over the period of time.
  • the method further includes storing in a memory anticipated profitability information associated with the anticipated profitability.
  • the invention provides a computer usable medium storing program code which, when executed by a computer, causes the computer to execute a computerized method for facilitating scheduling of operation of a facility for at least a first time interval of a period of time.
  • the method includes generating a decision tree based model accounting for a combined effect, on the scheduling of the operation of the facility, of: at least one specified forward price path, over the period of time, including at least one price of at least one commodity associated with operation of the facility; at least one specified level of uncertainty with regard to the at least one specified forward price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of the facility.
  • the method further includes applying a dynamic optimization algorithm to the decision tree based model to determine an optimal scheduling option for at least the first interval of time.
  • the method further includes storing optimal scheduling option information associated with the optimal scheduling option in a memory.
  • the invention provides a computer usable medium storing program code which, when executed by a computer, causes the computer to execute a computerized method for determining an anticipated profitability of operation of a facility over a period of time.
  • the method includes generating a decision tree based model accounting for a combined effect, on scheduling of the operation of the facility over the period of time, of: at least one specified forward price path, over the period of time, including at least one price of at least one commodity associated with operation of the facility at least one specified level of uncertainty with regard to the at least one specified forward price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of the facility.
  • the method further includes applying a dynamic optimization algorithm to the decision tree based model to determine the anticipated profitability over the period of time.
  • the method further includes storing in a memory anticipated profitability information associated with the anticipated profitability.
  • the invention provides a computerized system for facilitating scheduling of operation of a facility for at least a first time interval of a period of time.
  • the system includes means for generating a decision tree based model accounting for a combined effect, on the scheduling of the operation of the facility, of: at least one specified forward price path, over the period of time, including at least one price of at least one commodity associated with operation of the facility at least one specified level of uncertainty with regard to the at least one specified forward price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of the facility.
  • the system further includes means for applying a dynamic optimization algorithm to the decision tree based model to determine an optimal scheduling option for at least the first interval of time.
  • the system further includes means for storing in a memory optimal scheduling option information associated with the optimal scheduling option.
  • the invention provides a computerized system for determining an anticipated profitability of operation of a facility over a period of time.
  • the system includes means for generating a decision tree based model accounting for a combined effect, on scheduling of the operation of the facility, of: at least one specified forward price path, over the period of time, including at least one price of at least one commodity associated with operation of the facility; at least one specified level of uncertainty with regard to the at least one specified forward price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of the facility.
  • the system further includes means for applying a dynamic optimization algorithm to the decision tree based model to determine the anticipated profitability over the period of time.
  • the invention provides a computerized system for facilitating scheduling of operation of a facility for at least a first time interval of a period of time, including a processor and a memory accessible by the processor.
  • the processor is programmed for: generating a decision tree based model accounting for a combined effect, on optimization of the scheduling of the operation of the facility, of: at least one specified forward price path, over the period of time, including at least one price of at least one commodity associated with operation of the facility, the at least one specified forward price path being determined from information stored in the memory; at least one specified level of uncertainty with regard to the at least one specified forward price path, the at least one specified level of uncertainty being determined from information stored in the memory; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of the facility, the at least one specified constraint being determined from information stored in the memory.
  • the processor is further programmed for applying a dynamic optimization algorithm to the decision tree based model to determine an optimal scheduling option for at least
  • the invention provides a computational method for facilitating scheduling of operation of a facility for at least a first time interval of a period of time.
  • the method includes generating a decision tree based model accounting for a combined effect, on the scheduling of the operation of the facility, of: at least one specified forward price path, over the period of time, including at least one price of at least one commodity associated with operation of the facility; at least one specified level of uncertainty with regard to the at least one specified forward price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of the facility.
  • the method further includes applying a dynamic optimization algorithm to the decision tree based model to determine an optimal scheduling option for at least the first interval of time.
  • the invention provides a computerized method for facilitating joint scheduling of operation of each of a plurality of facilities for at least a first time interval of a period of time.
  • the method includes determining a set of preliminary anticipated optimal schedules for each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules includes generating a decision tree based model for each of the plurality of facilities, each of the decision tree based models accounting for a combined effect, on the optimization of the scheduling of the operation of each of the plurality of facilities, of: at least one specified control price path including at least one price, over the period of time, of at least one commodity associated with the operation of each of the plurality of facilities, the at least one price of the at least one commodity being affected by the operation of each of the facilities over the period of time; at least one specified level of uncertainty with regard to the at least one control price pa h; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules further includes applying a dynamic optimization algorithm to the decision tree based models to determine a set of preliminary anticipated optimal schedules, the set of preliminary anticipated optimal schedules including a schedule for each of the plurality of facilities over the period of time.
  • the method further includes generating a set of liquidity adjusted price paths for the at least on commodity over the period of time, the set of liquidity adjusted price paths being generated based at least on the at least one specified control price path, the set of preliminary anticipated optimal schedules, and a specified liquidity function.
  • the method further includes, utilizing an optimal control price path search algorithm that utilizes iterative performance of the determining step and the generating step with updating of the at least one control price paths according to the liquidity adjusted price paths, determining an optimal control price path and an anticipated optimal set of schedules, the anticipated optimal set of schedules including a schedule for each of the plurality of facilities.
  • the method further includes determining an optimal scheduling option for each of the plurality of facilities based on anticipated optimal set of schedules.
  • the method further includes storing in a memory optimal scheduling information associated with the optimal scheduling option for each of the plurality of facilities.
  • the invention provides a computerized method for determining an anticipated profitability of operation of a plurality of facilities for a period of time.
  • the method includes determining a set of preliminary anticipated optimal schedules for each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules includes generating a decision tree based model for each of the plurality of facilities, each of the decision tree based models accounting for a combined effect, on the optimization of the scheduling of the operation of each of the plurality of facilities, of: at least one specified control price path including at least one price, over the period of time, of at least one commodity associated with the operation of each of the plurality of facilities, the at least one price of the at least one commodity being affected by the operation of each of the facilities over the period of time; at least one specified level of uncertainty with regard to the at least one specified control price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules further includes applying a dynamic programming algorithm to the decision tree based models to determine a set of preliminary anticipated optimal schedules, the set of preliminary anticipated optimal schedules including a schedule for each of the plurality of facilities over the period of time.
  • the method further includes generating a set of liquidity adjusted price paths for the at least on commodity over the period of time, the set of liquidity adjusted price paths being generated based at least on the at least one specified control price path, the set of preliminary anticipated optimal schedules, and a specified liquidity function.
  • the method further includes, utilizing an optimal control price path search algorithm that utilizes iterative performance of the determining step and the generating step with updating of the at least one control price paths according to the liquidity adjusted price paths, determining an optimal control price path and an anticipated optimal set of schedules, the anticipated optimal set of schedules including a schedule for each of the plurality of facilities.
  • the method further includes determining the anticipated profitability of the plurality of facilities based on the anticipated optimal set of schedules.
  • the method further includes storing in a memory the anticipated profitability information associated with the anticipated profitability.
  • the invention provides a computer usable medium storing program code which, when executed by a computer, causes the computer to execute a computerized method for facilitating joint scheduling of operation of each of a plurality of facilities for at least a first time interval of a period of time.
  • the method includes determining a set of preliminary anticipated optimal schedules for each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules includes generating a decision tree based model for each of the plurality of facilities, each of the decision tree based models accounting for a combined effect, on the optimization of the scheduling of the operation of each of the plurality of facilities, of: at least one specified control price path including at least one price, over the period of time, of at least one commodity associated with the operation of each of the plurality of facilities, the at least one price of the at least one commodity being affected by the operation of each of the facilities over the period of time; at least one specified level of uncertainty with regard to the at least one specified control price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules further includes applying a dynamic optimization algorithm to the decision tree based models to determine a set of preliminary anticipated optimal schedules, the set of preliminary anticipated optimal schedules including a schedule for each of the plurality of facilities over the period of time.
  • the method further includes generating a set of liquidity adjusted price paths for the at least on commodity over the period of time, the set of liquidity adjusted price paths being generated based at least on the at least one specified control price path, the set of preliminary anticipated optimal schedules, and a specified liquidity function.
  • the method further includes, utilizing an optimal control price path search algorithm that utilizes iterative performance of the determining step and the generating step with updating of the at least one control price paths according to the liquidity adjusted price paths, determining an optimal control price path and an anticipated optimal set of schedules, the anticipated optimal set of schedules including a schedule for each of the plurality of facilities.
  • the method further includes determining an optimal scheduling option for each of the plurality of facilities based on anticipated optimal set of schedules.
  • the method further includes storing in a memory optimal scheduling information associated with the optimal scheduling option for each of the plurality of facilities.
  • the invention provides a computer usable medium storing program code which, when executed by a computer, causes the computer to execute a computerized method for determining an anticipated profitability of operation of a plurality of facilities for a period of time.
  • the method includes determining a set of preliminary anticipated optimal schedules for each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules includes generating a decision tree based model for each of the plurality of facilities, each of the decision tree based models accounting for a combined effect, on the optimization of the scheduling of the operation of the plurality of the facilities, of: at least one specified control price path including at least one price, over the period of time, of at least one commodity associated with the operation of each of the plurality of facilities, the at least one price of the at least one commodity being affected by the operation of each of the facilities over the period of time; at least one specified level of uncertainty with regard to the at least one specified control price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules further includes applying a dynamic programming algorithm to the decision tree based models to determine a set of preliminary anticipated optimal schedules, the set of preliminary anticipated optimal schedules including a schedule for each of the plurality of facilities over the period of time.
  • the method further includes generating a set of liquidity adjusted price paths for the at least on commodity over the period of time, the set of liquidity adjusted price paths being generated based at least on the at least one specified control price path, the set of preliminary anticipated optimal schedules, and a specified liquidity function.
  • the method further includes, utilizing an optimal control price path search algorithm that utilizes iterative performance of the determining step and the generating step with updating of the at least one control price paths according to the liquidity adjusted price paths, determining an optimal control price path and an anticipated optimal set of schedules, the anticipated optimal set of schedules including a schedule for each of the plurality of facilities.
  • the method further includes determining the anticipated profitability of the plurality of facilities based on the anticipated optimal set of schedules.
  • the method further includes storing in a memory anticipated profitability information associated with the anticipated profitability of the plurality of facilities.
  • the invention provides a system for facilitating joint scheduling of operation of each of a plurality of facilities for at least a first time interval of a period of time.
  • the system includes means for determining a set of preliminary anticipated optimal schedules for each of the plurality of facilities.
  • the means for determining a set of preliminary anticipated optimal schedules includes means for generating a decision tree based model for each of the plurality of facilities, each of the decision tree based models accounting for a combined effect, on the optimization of the scheduling of the operation of the plurality of the facilities, of: at least one specified control price path including at least one price, over the period of time, of at least one commodity associated with the operation of each of the plurality of facilities, the at least one price of the at least one commodity being affected by the operation of each of the facilities over the period of time; at least one specified level of uncertainty with regard to the at least one specified control price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of each of the plurality of facilities.
  • the means for determining a set of preliminary anticipated optimal schedules further includes means for applying a dynamic optimization algorithm to the decision tree based models to determine a set of preliminary anticipated optimal schedules, the set of preliminary anticipated optimal schedules including a schedule for each of the plurality of facilities over the period of time.
  • the system further includes means for generating a set of liquidity adjusted price paths for the at least on commodity over the period of time, the set of liquidity adjusted price paths being generated based at least on the at least one specified control price path, the set of preliminary anticipated optimal schedules, and a specified liquidity function.
  • the system further includes means for utilizing an optimal control price path search algorithm that utilizes iterative performance of the determining step and the generating step with updating of the at least one control price paths according to the liquidity adjusted price paths, determining an optimal control price path and an anticipated optimal set of schedules, the anticipated optimal set of schedules including a schedule for each of the plurality of facilities.
  • the system further includes means for determining an optimal scheduling option for each of the plurality of facilities based on anticipated optimal set of schedules.
  • the system further includes means for storing in a memory optimal scheduling option information associated with the optimal scheduling option for each of the plurality of facilities.
  • the invention provides a system for determining an anticipated profitability of operation of a plurality of facilities for a period of time.
  • the system includes means for determining a set of preliminary anticipated optimal schedules for each of the plurality of facilities.
  • the means for determining a set of preliminary anticipated optimal schedules includes means for generating a decision tree based model for each of the plurality of facilities, each of the decision tree based models accounting for a combined effect, on the optimization of the scheduling of operation of the plurality of the facilities, of: at least one specified control price path including at least one price, over the period of time, of at least one commodity associated with the operation of each of the plurality of facilities, the at least one price of the at least one commodity being affected by the operation of each of the facilities over the period of time; at least one specified level of uncertainty with regard to the at least one specified control price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of each of the plurality of facilities.
  • the means for determining a set of preliminary anticipated optimal schedules further includes means for applying a dynamic programming algorithm to the decision tree based models to determine a set of preliminary anticipated optimal schedules, the set of preliminary anticipated optimal schedules including a schedule for each of the plurality of facilities over the period of time.
  • the system further includes means for generating a set of liquidity adjusted price paths for the at least on commodity over the period of time, the set of liquidity adjusted price paths being generated based at least on the at least one specified control price path, the set of preliminary anticipated optimal schedules, and a specified liquidity function.
  • the system further includes means for utilizing an optimal control price path search algorithm that utilizes iterative performance of the determining step and the generating step with updating of the at least one control price paths according to the liquidity adjusted price paths, determining an optimal control price path and an anticipated optimal set of schedules, the anticipated optimal set of schedules including a schedule for each of the plurality of facilities.
  • the system further ,includes means for determining the anticipated profitability of the plurality of facilities based on the anticipated optimal set of schedules.
  • the system further includes means for storing in a memory anticipated profitability information associated with the anticipated profitability of the 5 plurality of facilities.
  • the invention provides a system for facilitating joint scheduling of operation of each of a plurality of facilities for at least a first time interval of a period of time.
  • the system includes a processor and memory accessible by the processor.
  • the processor is programmed for determining a set of preliminary anticipated optimal schedules for each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules includes generating a decision tree based model for each of the plurality of facilities, each of the decision tree based models accounting for a combined effect, on the optimization of the scheduling of the operation of each of the plurality of facilities, of: at least one specified control price path including at least one price, over the period of time, of at least one commodity associated with the operation of each of the plurality of facilities, the at least one price of the at least one commodity being affected by the operation of each of the facilities over the period of time; at least one specified level of uncertainty with regard to the at least one specified control price path; and, at least one specified consfraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules further includes applying a dynamic optimization algorithm to the decision tree based models to determine a set of preliminary anticipated optimal schedules, the set of preliminary anticipated optimal schedules including a schedule for each of the plurality of facilities over the period of time.
  • the processor is further programmed for generating a set of liquidity adjusted price paths for the at least on commodity over the period of time, the set of liquidity adjusted price paths being generated based at least on the at least one specified control price path, the set of preliminary anticipated optimal schedules, and a specified liquidity function.
  • the processor is further programmed for, utilizing an optimal control price path search algorithm that utilizes iterative performance of the determining step and the generating step with updating of the at least one control price paths according to the liquidity adjusted price paths, determining an optimal control price path and an anticipated optimal set of schedules, the anticipated optimal set of schedules including a schedule for each of the plurality of facilities.
  • the processor is further programmed for determining an optimal scheduling option for each of the plurality of facilities based on anticipated optimal set of schedules.
  • the invention provides a computational method for facilitating joint scheduling of operation of each of a plurality of facilities for at least a first time interval of a period of time.
  • the method includes determining a set of preliminary anticipated optimal schedules for each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules includes generating a decision tree based model for each of the plurality of facilities, each of the decision tree based models accounting for a combined effect, on the optimization of the scheduling of the operation of each of the plurality of facilities, of: at least one specified control price path including at least one price, over the period of time, of at least one commodity associated with the operation of each of the plurality of facilities, the at least one price of the at least one commodity being affected by the operation of each of the facilities over the period of time; at least one specified level of uncertainty with regard to the at least one control price path; and, at least one specified constraint associated with at least a first state of at least one state of at least one operating parameter associated with the operation of each of the plurality of facilities.
  • the determining a set of preliminary anticipated optimal schedules further includes applying a dynamic optimization algorithm to the decision tree based models to determine a set of preliminary anticipated optimal schedules, the set of preliminary anticipated optimal schedules including a schedule for each of the plurality of facilities over the period of time.
  • the method further includes generating a set of liquidity adjusted price paths for the at least on commodity over the period of time, the set of liquidity adjusted price paths being generated based at least on the at least one specified control price path, the set of preliminary anticipated optimal schedules, and a specified liquidity function.
  • the method further includes, utilizing an optimal control price path search algorithm that utilizes iterative performance of the determining step and the generating step with updating of the at least one control price paths according to the liquidity adjusted price paths, determining an optimal control price path and an anticipated optimal set of schedules, the anticipated optimal set of schedules including a schedule for each of the plurality of facilities.
  • the method further includes determining an optimal scheduling option for each of the plurality of facilities based on anticipated optimal set of schedules.
  • Figure 1 is a block diagram depicting a computer system including an anticipated profitability program that utilizes a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 2 is a block diagram depicting operation of the anticipated profitability program depicted in Figure 1, utilizing a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 3 is a block diagram depicting structuring of the model with implicitly modeled constraint(s), as depicted in Figure 2, according to one embodiment of the invention
  • Figure 4 is a flow chart depicting a method for operation of the anticipated profitability program depicted in Figure 2, according to one embodiment of the invention
  • Figure 5 is a block diagram depicting a computer system including an asset valuation program that utilizes a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 6 is a block diagram depicting operation of the asset valuation program depicted in Figure 5, utilizing a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 7 is a flow chart depicting a method for operation of the asset valuation program depicted in Figure 6, utilizing a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 8 is a block diagram depicting a computer system including a scheduling program that utilizes a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 9 is a block diagram depicting operation of the scheduling program depicted in Figure 8, utilizing a model with implicitly modeled constraint(s), according to one embodiment of the invention.
  • Figure 10 is a flow chart of a method for operation of the scheduling program depicted in Figure 9, utilizing a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 11 is a block diagram depicting a computer system including an anticipated profitability program that utilizes price path uncertainty information, according to one embodiment of the invention.
  • Figure 12 is a block diagram depicting operation of the anticipated profitability program depicted in Figure 11 , utilizing price path uncertainty information, according to one embodiment of the invention
  • Figure 13 is a block diagram depicting operation of the model generation algorithm as depicted in Figure 12, according to one embodiment of the invention.
  • Figure 14 is a flow chart depicting a method for operation of the anticipated profitability program depicted in Figure 12, utilizing price path uncertainty information, according to one embodiment of the invention
  • Figure 15 is a block diagram depicting a computer system including an asset valuation program that utilizes price path uncertainty information, according to one embodiment of the invention
  • Figure 16 is a block diagram depicting operation of the asset valuation program depicted in Figure 15, utilizing price path uncertainty information, according to one embodiment of the invention
  • Figure 17 is a flow chart depicting a method for operation of the asset valuation program depicted in Figure 16, utilizing price path uncertainty information, according to one embodiment of the invention
  • Figure 18 is a block diagram depicting a computer system including a scheduling program that utilizes price path uncertainty information, according to one embodiment of the invention
  • Figure 19 is a block diagram depicting operation of the scheduling program depicted in Figure 18, utilizing price path uncertainty information, according to one embodiment of the invention.
  • Figure 20 is a flow chart depicting a method for operation of the scheduling program depicted in Figure 19, utilizing price path uncertainty information, according to one embodiment of the invention
  • Figure 21 is a block diagram depicting operation of an anticipated profitability program that utilizes price path uncertainty information and a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 22 is a flow chart depicting a method for operation of the anticipated profitability program depicted in Figure 21, utilizing price path uncertainty information and a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 23 is a block diagram depicting operation of an asset valuation program that utilizes price path uncertainty information and a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 24 is a flow chart depicting a method for operation of the asset valuation program depicted in Figure 23, utilizing price path uncertainty information and a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 25 is a block diagram depicting operation of an scheduling program that utilizes price path uncertainty information and a model with implicitly modeled constraint(s), according to one embodiment of the invention
  • Figure 26 is a flow chart depicting a method for operation of the scheduling program depicted in Figure 25, utilizing price path uncertainty information and a model with implicitly modeled constraint(s), according to one embodiment of the invention;
  • Figure 27 is a flow chart depicting a method for determining liquidity adjusted anticipated optimal schedules for a group of facilities, according to one embodiment of the invention;
  • Figure 28 is a flow chart depicting a method for using determined liquidity adjusted anticipated optimal schedules for a group of facilities to determine anticipated profitability for the group of facilities over a period of time, according to one embodiment of the invention
  • Figure 29 is a flow chart depicting a method for using determined liquidity adjusted anticipated optimal schedules for a group of facilities to determine a value of an asset, according to one embodiment of the invention.
  • Figure 30 is a flow chart depicting a method for using determined liquidity adjusted anticipated optimal schedules for a group of facilities to determine an optimal scheduling option for each of the group of facilities, according to one embodiment of the invention;
  • Figure 31 depicts a graph of a heat rate function describing efficiency of a generator as a function of generation rate, according to one embodiment of the invention
  • Figure 32 depicts a decision tree for a generator, used in modeling dynamic operating constraints, according to one embodiment of the invention.
  • Figure 33 depicts a graph of a heat rate function with intermediate efficient generation rates, according to one embodiment of the invention.
  • Figure 34 depicts a table of generation rates and associated heat rates for the generator associated with the heat rate function depicted in Figure 33, according to one embodiment of the invention;
  • Figure 35 depicts a decision tree, according to one embodiment of the invention.
  • Figure 36 depicts a decision tree including mapping of operating costs and revenues, according to one embodiment of the invention;
  • Figure 37 depicts a table of prices used in mapping of operating costs and revenues to a decision tree, according to one embodiment of the invention.
  • Figure 38 depicts a graph showing a price forecast and anticipated optimal operating schedule, according to one embodiment of the invention.
  • Figure 39 depicts a spot price probability distribution graph generated by a trinomial tree based model, according to one embodiment of the invention.
  • Figure 40 depicts a trinomial forest, according to one embodiment of the invention.
  • Figure 41 depicts a graph showing an optimal decision rule generated by a stochastic optimization algorithm, according to one embodiment of the invention.
  • Figure 42 depicts a graph showing optimal decision rule for a given time and output level, according to one embodiment of the invention.
  • Figure 43 depicts a table of values associated with an optimal decision rule, according to one embodiment of the invention.
  • Figure 44 depicts a block diagram of framework 4400 for inco ⁇ orating Monte
  • Figure 45 depicts a flow diagram of operation of a generator in a forced outage situation, according to one embodiment of the invention.
  • Figure 46 depicts a flow diagram showing a method of dynamic optimization for operation of a generator inco ⁇ orating a constraint on a number of starts per year for the generator, according to one embodiment of the invention;
  • Figure 47 depicts a block diagram showing a technique for anticipated profitability determination, accounting for actual and shadow cost factors, according to one embodiment of the invention;
  • Figure 48 depicts a graph showing a total generation schedule for a portfolio of generators, according to one embodiment of the invention.
  • Figure 49 depicts a graph showing an imbalance between total generation and load obligations for a portfolio of generators, according to one embodiment of the invention.
  • Figure 50 depicts a liquidity curve characterizing spot prices as a function of net purchase and sale decisions, according to one embodiment of the invention.
  • Figure 51 depicts a block diagram of a generator portfolio operation dynamic optimization technique utilizing a plant model, according to one embodiment of the invention.
  • Figure 52 depicts a block diagram of a generator portfolio operation dynamic optimization technique utilizing a generator portfolio model, according to one embodiment of the invention
  • Figure 53 depicts a generator portfolio liquidity model, according to one embodiment of the invention.
  • Figure 54 depicts a block diagram of a generator portfolio operation dynamic optimization technique to determine liquidity adjusted prices as well as profit and loss, according to one embodiment of the invention.
  • Figure 55 depicts a block diagram of generator portfolio operation dynamic optimization technique utilizing search algorithms in determining optimal shadow costs and optimal shadow prices, according to one embodiment of the invention.
  • the present invention provides computational methods for determining anticipated profit from facilities such as electrical power generation facilities, for determining values for assets based on anticipated profitability of facilities, and for determining optimal operational scheduling options for facilities.
  • methods are provided which utilize a dynamic programming algorithm and a decision tree based model in which one or more operating constraints are implicitly modeled, facilitating computational tractability.
  • methods are provided that utilize a decision tree based model in which numerous constraints are efficiently modeled in terms of only two operational state parameters, specifically, generation rate and runtime.
  • methods are provided that utilize a dynamic programming algorithm and a decision tree based model that accounts for a combined effect of forward price paths with specified uncertainty as well as operational constraints.
  • methods are provided that utilize a decision tree based model that accounts for a combined effect, on scheduling optimization, of stochastic forward price paths as well as operational constraints.
  • methods are provided that utilize a decision tree based model in which a node of a tree is characterized by four parameters, specifically, time, price, generation rate and run time.
  • methods are provided that address profitability, valuation, and scheduling in relation to a group, or portfolio, of facilities, accounting for liquidity factors as well as group, or global, constraints.
  • decision tree and “decision based tree” include any kind of multinomial tree.
  • dynamic programming and dynamic optimization are used interchangeably to describe iterative optimization methods.
  • the term "dynamic programming" is not intended to necessarily imply or utilize computer programming, although computers can be used to perform dynamic programming operations.
  • dynamic programming methods typically utilize backwards iteration through one or more decision trees.
  • a decision tree can include numerous nodes marking intervals in a period of time, and the dynamic programming method can be backwards in the sense of progressing from a final, or latest, node in the period to a first, or earliest, node in the period.
  • a computer program or computer programming can include any type of computer programming that can be utilized to accomplish the methods as described herein on one or more computers, and can include, for example, any of code, applications, software, algorithms, databases, programming modules, application programming interface (API) tools, data mining tools, search engines, and simulation engines such as Monte Carlo simulation engines.
  • API application programming interface
  • forecasted price path information such as forecasted price path information, price path uncertainty information, constraint information, heat rate curves, liquidity functions, and control price paths, which information can be utilized in the methods, programs, and algorithms of the invention.
  • this information can be acquired or derived in a variety of ways.
  • various information may be obtained from an operator or operating entity of a facility or facilities, such as relevant operational constraints that are known to the operator.
  • some information, such as price path and price path uncertainty information can be acquired, derived or estimated based on available public or private records and forecasts.
  • some of the information is acquired based on information available at a given time as well as information acquired based on the best judgment, estimation, or forecast of an operator at a given time.
  • FIG. 1 is a block diagram 100 depicting a computer system including an anticipated profitability program 112 that utilizes a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • a computer 1 16 including a central processing unit 106 (CPU) and a data storage device 108, may be connected to a price path database 102 and a constraint database 104.
  • the data storage device 108 may include an input database 110, an anticipated profitability program 112 and an output database 114.
  • the price path database 102 and constraint database 104 are depicted as being separate, in some embodiments, the databases 102, 104 can be a single database containing both price path information and constraint information.
  • the price path database 102 and constraint database 104 can reside in the computer 116 itself, such as in the data storage device, 108. While the input database 110 and output database 114 are depicted as being separate, they also can be a single database containing input and output information.
  • the databases 102, 104 can be connected to the computer 116 in various ways, including, in some embodiments, through one or more networks which can include one or more local area networks, one or more personal area networks, one or more wide area networks, or the Internet, for example.
  • the databases 102, 104 can be contained by and part of or associated with one or more computers.
  • the data storage device 108 of the computer 116 can include various amounts of
  • the computer 116 can include other components typically found in computers, including one or more output devices such as monitors, other fixed or removable data storage devices such as hard disks, floppy disk drives and CD-ROM drives, and one or more input devices, such as mouse pointing devices and keyboards.
  • output devices such as monitors
  • fixed or removable data storage devices such as hard disks, floppy disk drives and CD-ROM drives
  • input devices such as mouse pointing devices and keyboards.
  • the computer 116 operates under and executes computer programs under the control of an operating system, such as Windows , Macintosh , or UNIX.
  • an operating system such as Windows , Macintosh , or UNIX.
  • computer programs of the present invention are tangibly embodied in a computer- readable medium, e.g., RAM, disks including portable disks, or CD ROMs..
  • computer programs may be loaded from data storage devices into computer RAM for subsequent execution by a CPU.
  • the computer programs include instructions which, when read and executed by the computer, cause the computer to perform the steps necessary to execute elements of some embodiments of the present invention.
  • the price path database 102 provides price path information such as one or more forward or forecasted price paths, such as forecasted market price paths, for one or more goods or services, such as commodities, e.g., fuel and electricity, which are relevant to profitability of a facility.
  • price path information can include a forecasted market price path for one or more types of fuel used by the facility as well as a market price path for electrical energy or power.
  • the constraint database 104 contains constraint information specifying, or allowing determination by the anticipated profitability program 112, of operational constraints relevant to profitability of the facility, such as, for example, maximum and minimum generation rates while the facility is operating, maximum and minimum operating times, or run-times, and maximum generation rate increases and decreases per unit of time (known as maximum ramp up and ramp down rates), start-up costs and shutdown costs.
  • the price path information includes at least a specified price for each of one or more commodities for each of a specified number of points in time, or intervals, in the future during a specified period of time, or sufficient information so that such prices can be determined or estimated by the anticipated profitability program 112.
  • the price path information can include a function for calculating prices over time according to the function, from which prices at various points in time can be obtained, or prices for intervals during the period of time can be estimated.
  • the anticipated profitability program 112 generates a model associated with the facility, which model utilizes one or more implicitly modeled constraints, and utilizes a dynamic programming algorithm to determine anticipated profitability for the facility over the period of time, which anticipated profitability is considered to be reasonable based on optimal scheduling decision-making over the period of time from the point of view of an operating entity for the facility over the period of time.
  • Anticipated profitability can be expressed in various ways, such as monetary units of profit or loss over an interval, intervals, or a period, or in other ways to reflect non-monetary profit or loss as may be appropriate.
  • anticipated profitability is determined as an average, mean, median, or other statistical value derived from multiple possible anticipated profitability scenarios.
  • Figure 2 is a block diagram 200 depicting operation of the anticipated profitability program 112 depicted in Figure 1, utilizing a model 116 with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • the model generation algorithm Utilizing the information, the model generation algorithm generates the model 116, which can be, for example, a trinomial tree based model.
  • the model accounts for a combined effect, on optimization of scheduling, of the price path or paths as well as the constraint or constraints. By affecting optimization of scheduling, the price path or paths and constraint or constraints also affect anticipated profitability.
  • a dynamic programming algorithm 120 is applied or executed to determine and output anticipated profitability information 206, which can be stored in the output databasel 14 of the computer 116.
  • the backwards iterative technique utilized by the dynamic programming algorithm 120 is depicted by arrows 118 and 119.
  • the dynamic programming algorithm 120 utilizes backwards iteration through nodes of a trinomial tree based model, determining profit or loss at each represented time interval of the period, as marked by the nodes. In some embodiments, the dynamic programming algorithm 120 outputs anticipated profitability information including an anticipated profit or loss over the period of time, as well as anticipated profit or loss for each interval of time during the period of time.
  • FIG. 3 is a block diagram 300 depicting structuring of the model 116 with one or more implicitly modeled constraints, as depicted in Figure 2, according to one embodiment of the invention, for an energy generation facility.
  • the model 116 is a trinomial tree based model.
  • a set of nodes 302 is also depicted. Each node is characterized by generation rate Q, in megawatts, or MW, and runtime, or RT, representing, if the facility is represented as generating, or "ON”, an amount of time the facility is represented as having been ON, and if the facility is represented as not generating, or "OFF", an amount of time the facility is represented as having been OFF.
  • Q generation rate
  • MW in megawatts, or MW
  • RT runtime
  • a representation 304 of operational constraints Ci- Included also is a representation 304 of operational constraints Ci- .
  • each constraint is represented by a variable expression, EXPRi-i, each of the expressions characterizing a constraint in terms of the parameters Q and RT.
  • constraints are described herein, among other places, under section headings, "Constraints on the Generation Options,” “Operational Costs,” and “Capturing dynamic constraints in a decision tree.” Details regarding an example of parameters, specifically, Q and RT h , are provided herein, among other places, under section headings, "State Space Model For Generation Asset,” and “Capturing dynamic constraints in a decision tree.”
  • the model 116 includes fewer parameters than constraints.
  • a model that implicitly models at least one constraint means a model that utilizes a single model parameter in formulation of more than one constraint and that contains fewer parameters than constraints. Any constraint that has a unique model parameter used in the formulation of that constraint and no other constraint is referred to as an expressly modeled constraint. Any constraint that is not an expressly modeled constraint, and which is utilized in a model having fewer parameters than constraints, is referred to as an implicitly modeled constraint.
  • Figure 4 is a flow chart depicting a method 400 for operation of the anticipated profitability program 112 depicted in Figure 2, according to one embodiment of the invention.
  • the anticipated profitability program 112 obtains forward price path information (X) relevant to anticipated profitability of the facility.
  • the anticipated profitability program 112 obtains constraint information (Y) relevant to anticipated profitability of the facility.
  • model generation algorithm 114 generates a decision tree based model accounting for a combined effect, on optimization of scheduling of the facility, of X and Y, and in which one or more constraints are implicitly modeled.
  • the dynamic programming algorithm 120 is applied to determine anticipated profitability over the period of time, which can include anticipated profit or loss over the entire period as well as profit or loss for individual intervals of time during the period.
  • FIG. 5 is a block diagram depicting a computer system 500 including an asset valuation program 502 that utilizes a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • the system 500 is in some ways similar to the system of Figure 2; however, the anticipated profitability program 112 is replaced by the asset valuation program 502.
  • the asset valuation program 502 includes the anticipated profitability program 116. While some embodiments of the invention are described including reference to generation assets, it is to be noted that methods and systems according to some embodiments of the invention can be applied with respect to any of various types of assets and are not limited to application with respect to generation assets.
  • FIG. 6 is a block diagram 600 depicting operation of the asset valuation program 502 depicted in Figure 5, utilizing a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • the system 600 is in some ways similar to the system 200 depicted in Figure 2; however, the anticipated profitability program 112 is replaced by the asset valuation program 502, and a valuation algorithm 504 receives output from the dynamic programming algorithm 604, from which the valuation algorithm 504 determines and outputs asset valuation information 602.
  • the asset valuation program 502 can be used to determine or estimate a present value of a generation asset, such as a real option contract, the value of which is dependent upon the profitability or the scheduling of the facility for the period of time or an interval or intervals thereof.
  • the valuation algorithm 504 utilizes the output of the dynamic programming algorithm 120, which can include optimal scheduling information as well as profitability information, determining the value of the asset utilizing a mathematical formulation of the value of the asset based on the information.
  • Figure 7 is a flow chart depicting a method 700 for operation of the asset valuation program 502 depicted in Figure 6, utilizing a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • Method 700 is in some ways similar to method 400; however, at step 702, anticipated profitability is determined for the period or an interval or intervals, as necessary for asset valuation, and, at step 704, the value of the asset is determined based on the anticipated profitability.
  • FIG 8 is a block diagram depicting a computer system 800 including a scheduling program that utilizes a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • the system 800 is in some ways similar to the system 500 depicted in Figure 5; however, the asset valuation program 502 is replaced with a scheduling program 802.
  • Figure 9 is a block diagram 900 depicting operation of the scheduling program depicted in Figure 8, utilizing a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • the operation depicted in Figure 9 is in some ways similar to that depicted Figure 2; however, dynamic programming algorithm 902 is utilized to output scheduling information 904.
  • the dynamic programming algorithm 902 uses backwards iteration to determine an anticipated optimal schedule information for operation of the facility over the period of time, and utilizes this information to determine and output an optimal scheduling option for at least one interval of time during the period of time.
  • the dynamic programming algorithm 902 outputs an optimal scheduling option, or decision, for an interval immediately subsequent to a given time, such as to ramp up or down a generation rate for the interval, which can include how much to ramp up or down the generation rate for the interval, or to start up or turn off the facility for the interval.
  • the scheduling program 802 can be utilized repeatedly at consecutive times, including providing the scheduling program 802 with updated price path and scheduling information at each time, so that the scheduling program 802 can determine and output an optimal scheduling option for each time or time interval.
  • the various programs described herein, including anticipated profitability programs and asset valuation programs can also be used repeatedly at subsequent times and can be provided updated information, to make updated new determinations.
  • Figure 10 is a flow chart of a method 1000 for operation of the scheduling program 802 depicted in Figure 9, utilizing a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • Method 100 is in some ways similar to method 400; however, at step 1002, the dynamic programming algorithm 902 is utilized to determine an optimal scheduling option for one or more intervals of time.
  • Figure 11 is a block diagram depicting a computer system 1100 including an anticipated profitability program 1102 that utilizes price path uncertainty information, according to one embodiment of the invention.
  • the system 1100 is in some ways similar to the system 100 depicted in Figure 1 ; however, an additional price path uncertainty database 1104 provides price path uncertainty information, and anticipated profitability program 1102 utilizes the information among other information.
  • Figure 12 is a block diagram 1200 depicting operation of the anticipated profitability program 1102 depicted in Figure 11 , utilizing price path uncertainty information, according to one embodiment of the invention.
  • the operation depicted in Figure 12 is in some ways similar to that of Figure 2; however, price path uncertainty information is included in the operation of the anticipated profitability program 1102.
  • the model generation algorithm 1204 utilizes price path uncertainty information, or stochastic price path information, as well as price path information, which can include a forecasted price path, and constraint information.
  • the model generation algorithm 1204 generates the stochastic price and state model 1206. Utilizing the model 1206, the dynamic programming algorithm 1208 determines and outputs anticipated profitability information 1204.
  • the price path uncertainty information can include, in some embodiments, the time dependent drift, mean-reversion rate and volatility, respectively, and can include other specified probabilistic characteristics, which can relate to a level of uncertainty with respect to one or more price paths.
  • the anticipated profitability program 1102 utilize the price path uncertainty information to generate simulations of many possible price paths, such as by using Monte Carlo simulations, a Monte Carlo simulation engine, or other simulations or simulation engines.
  • the simulated price paths can be utilized in model generation, as well as application of various algorithms such as dynamic programming algorithms, in determining anticipated profitability, asset valuation, or optimal scheduling. Use of such simulations is described in more detail herein.
  • Figure 13 is a block diagram 1300 depicting operation of the model generation algorithm 1204 as depicted in Figure 12, according to one embodiment of the invention.
  • the stochastic price and state model 1206 is generated by mathematical merger 1306 of a stochastic price submodel 1303 and an operational state submodel 1304.
  • the stochastic price submodel 1303 is generated based on price path information 1320 and price path uncertainty information 1322.
  • the state submodel is generated based on constraint information 1324.
  • the stochastic price and state model 1206 is generated that both stochastically models one or more price paths and models operation states, or state paths.
  • the stochastic price and state model 1206 can therefore be utilized to account for a combined effect, on optimization of scheduling, and on anticipated profitability and asset valuation, of the price path information 1320, such as a forecasted price path, the price path uncertainty information 1322, and the constraint information 1324.
  • a stochastic price and state model can be generated in ways other than merger of submodels, such as being generated without the use of submodels.
  • Subdiagram 1304 depicts trinomial tree based model elements that can be utilized in the operation as depicted by subdiagram 1302. Nodes 1350 of a stochastic price submodel trinomial tree are depicted, each node having parameters of time and price.
  • FIG. 14 is a flow chart depicting a method 1400 for operation of the anticipated profitability program depicted in Figure 12, utilizing price path uncertainty information, according to one embodiment of the invention.
  • the method 1400 is in some ways similar to the method 400 of Figure 4; however, at step 1402, a decision tree based model is generated that accounts for a combined effect of price path information, price path uncertainty information, and constraint information, and, at step 1404, utilizing the model, a dynamic programming algorithm is utilized to determine anticipated profitability information.
  • Figure 15 is a block diagram 1500 depicting a computer system including an asset valuation program 1502 that utilizes price path uncertainty information, according to one embodiment of the invention.
  • the system depicted in Figure 15 is in some ways similar to that of Figure 11; however, the anticipated profitability program 1102 is replaced with an asset valuation program 1502.
  • Figure 16 is a block diagram 1600 depicting operation of the asset valuation program 1502 depicted in Figure 15, utilizing price path uncertainty information, according to one embodiment of the invention.
  • the operation depicted in Figure 16 is in some ways similar to that of Figure 12; however, output of a dynamic programming algorithm 1503 is utilized by a valuation algorithm 1504 to determine and output asset valuation information 1602.
  • Figure 17 is a flow chart depicting a method 1700 for operation of the asset valuation program 1502 depicted in Figure 16, utilizing price path uncertainty information, according to one embodiment of the invention.
  • the method 1700 is in some ways similar to the method 1400 depicted in Figure 14; however, at step 1702, anticipated profitability is determined as necessary to value an asset, and, at step 1704, a value of the asset is determined based on the anticipated profitability information.
  • Figure 18 is a block diagram 1800 depicting a computer system including a scheduling program 1802 that utilizes price path uncertainty information, according to one embodiment of the invention.
  • the system depicted in Figure 18 is in some ways similar to that of Figure 15; however, the asset valuation program 1502 is replaced with a scheduling program 1802.
  • Figure 19 is a block diagram depicting operation of the scheduling program 1802 depicted in Figure 18, utilizing price path uncertainty information, according to one embodiment -38-
  • valuation algorithm 2306 based on which the valuation algorithm determines and outputs asset valuation information 2310.
  • Figure 24 is a flow chart depicting a method 2400 for operation of the asset valuation program 2302 depicted in Figure 23, utilizing price path uncertainty information and a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • the method 2400 is in some ways similar to the method 2200 of Figure 22; however, at step 2402, utilizing the model 2308, the dynamic programming algorithm 2304 determines an anticipated profitability and, at step 2404, the valuation algorithm 2306 determines a value of an asset based on the anticipated profitability.
  • Figure 25 is a block diagram 2500 depicting operation of a scheduling program
  • Figure 26 is a flow chart depicting a method for operation of the scheduling program depicted in Figure 25, utilizing price path uncertainty information and a model with one or more implicitly modeled constraints, according to one embodiment of the invention.
  • the method 2600 is in some ways similar to the method 2200 depicted in Figure 22; however, at step 2602, utilizing the model 2506, the dynamic programming algorithm 2504 is applied to determine an optimal scheduling option or options for an interval, intervals, or a period of time.
  • Figure 27 is a flow chart depicting a method 2700, for determining liquidity adjusted anticipated optimal schedules for a group of facilities, according to one embodiment of the invention.
  • the determined liquidity adjusted anticipated optimal schedules can be utilized in determining anticipated profitability information, asset valuation information, and scheduling information for the group of facilities.
  • the methods of Figures 27-30 utilize methods described elsewhere herein, including, for example, models with implicitly modeled constraints, and stochastic price and state models.
  • At step 2702 at least one specified control price path is obtained.
  • At step 2704 at least one specified level of uncertainty is obtained with respect to the at least one specified control price path.
  • at least one specified constraint is obtained for each of a group of facilities.
  • a decision tree based model is generated for each of the facilities, accounting for a combined effect, on optimization of scheduling, of the at least one specified control price path, the at least one specified level of uncertainty, and the at least one specified constraint.
  • a dynamic programming algorithm is applied to determine a set of preliminary anticipated optimal schedules for the facilities.
  • a set of liquidity adjusted price paths is generated based on the at least one specified control price path, the preliminary schedules, and a specified liquidity function.
  • the determination of preliminary schedules and the generation of the liquidity adjusted price paths are iteratively performed to determine an anticipated optimal schedule for each of the facilities. In some embodiments, not all of the facilities in a group have constraints, and constraint information is not obtained for such facilities.
  • Figure 28 is a flow chart depicting a method 2800, performed by a joint anticipated profitability program 2802, conceptually represented by a broken line box, for using determined liquidity adjusted anticipated optimal schedules for a group of facilities to determine anticipated profitability for the group of facilities over an interval, intervals, or a period of time, according to one embodiment of the invention.
  • the method 2800 commences with the method 2700, as depicted in Figure 27.
  • At step 2804 based on the anticipated optimal schedules determined at step 2700, anticipated profitability of the group of facilities is determined for an interval, intervals, or a period of time.
  • Figure 29 is a flow chart depicting a method 2900, performed by a joint asset valuation program 2902, conceptually represented by a broken line box, for using determined liquidity adjusted anticipated optimal schedules for a group of facilities to determine a value of an asset, according to one embodiment of the invention.
  • the method 2900 commences with the method 2700, as depicted in Figure 27.
  • step 2904 based on the anticipated optimal schedules -40-
  • anticipated profitability information for the group of facilities is determined.
  • the anticipated profitability information is utilized to determine a value of an asset associated with the group of facilities.
  • Figure 30 is a flow chart depicting a method 3000, performed by a joint scheduling program 3002, conceptually represented by a broken line box, for using determined liquidity adjusted anticipated optimal schedules for a group of facilities to determine an optimal scheduling option for each of the group of facilities, according to one embodiment of the invention.
  • the method 3000 commences with the method 2700, as depicted in Figure 27.
  • an optimal scheduling option is determined for each of the facilities for an interval, intervals, or a period of time.
  • the invention provides tools which provide decision support to electric utilities and power marketers with respect to operating, valuing and trading against generation assets.
  • the methods or systems of the invention can be broadly categorized in three stages: (1) a real option model of a generation asset, with detailed modeling of costs and physical constraints as well as market price uncertainty; (2) an integration of the real option model with a Monte Carlo simulation engine, producing as large set of statistics on the operation of the asset, and the associated costs and revenues; and, (3) a second optimization loop which iterates a set of control variables in order to maximize profit under additional constraints.
  • constraints can be long term operating limitations on a single asset, such as maximum number of starts in a year, or cumulative constraints on a portfolio of generator, such as the effect of an illiquid spot market.
  • the real option model examines the price uncertainty in the market and values the physical flexibility of the asset in this context.
  • the technology of the option model can be broken apart into three pieces: (1) a trinomial tree model used to characterize price uncertainty in the market; (2) a model used to capture the costs and operating constraints associated with the asset; and, (3) an optimization algorithm which utilizes -41-
  • the tree based optimization algorithm produces a detailed set of hourly decision rules providing the user with the optimal dispatch decision for the asset as a function of the observed market prices in that hour.
  • this decision rule By combining this decision rule with a Monte Carlo engine for simulating future price paths, one can expand the amount of information provided by the model, including information on fuel usage or emission production, expected number of starts, or expected number of running hours in a given period. Optimizing over Global Constraints
  • a generation asset provides a return on investment for its owners by converting one commodity (fuel) into a second commodity (electricity) at a technology dependent conversion rate (the heat rate).
  • this conversion may be either profitable (the generator is said to be in the money) or unprofitable (out of the money).
  • the operator has the flexibility to vary the output of the generator, including turning it off completely, in order to best capture the value of the spread between the commodities. The value of this optionality is modeled.
  • the most critical component to this is the fuel usage of the plant, dictated by its efficiency. This is generally expressed in terms of the heat rate of the plant (the lower the heat rate the more efficient the generator is). The heat rate itself can vary over the output level of the plant.
  • FIG. 31 depicts a graph 3100 of a heat rate function describing efficiency of a generator as a function of generation rate, according to one embodiment of the invention.
  • NFC- non-fuel cost proportional to the output of the generator, expressed in $/MWh.
  • RT h the number of hours the generator has been in an 'on' state (if it is currently on, or the number of hours the generator has been in an 'off state (if it is currently off). [00169] For each hour during the operation period, the state of the generator is defined by these pair of values (Q h , RT h ). Using this convention, a decision tree is created. The decision tree captures all possible operating paths the generator can take during operating period.
  • the state pair (Q h , RTh), fully characterizes the operation of the generator in any hour. In addition it contains all the information needed to determine which operating states are feasible for the asset in the next operating hour.
  • the current output combined with the maximum ramp up and ramp down rates limit the feasible output levels in the next hour.
  • the output level in hour h+1 is constrained as follows if the generator is running above its minimum level in our h: max ⁇ Q min ,Qh - RDOW ⁇ Qh+I min ⁇ Q Max , Q h - R Up ⁇ for,
  • a decision tree can be created.
  • the decision tree contains all possible operating paths for the asset over the operation period.
  • An example of such a decision tree is given in Figure 32, which depicts a decision tree 3200 for a generator, used in modeling dynamic operating constraints, according to one embodiment of the invention.
  • Figure 33 depicts a graph 3300 of a heat rate function with intermediate efficient generation rates, according to one embodiment of the invention.
  • the user is able to define a series of operating levels at which the plant can be scheduled, and the average heat rate of the generator at these levels, as shown in the table 3400 depicted in Figure 34.
  • Figure 34 depicts a table 3400 of generation rates and associated heat rates for the generator associated with the heat rate function depicted in Figure 33, according to one embodiment of the invention.
  • a decision tree is then created.
  • the tree can have more than three branches at any node. For instance, given the user defined levels shown in the above table, and a plant with Ru p ⁇ Rp o n ⁇ OMW, the decision tree 3500 is created as shown in Figure 35.
  • UDOs allowable outputs
  • the first step in optimizing the dispatch schedule of the asset is to superimpose the known future fuel and power prices on the decision tree. Given these prices it is now possible to map the applicable cost and revenue to each node in the decision tree. To each node is assigned the cost equal to: TFC h + ⁇ NFC h * Q h ) + RC h + FC h And a revenue equal to:
  • Figure 36 depicts a decision tree including mapping of operating costs and revenues, according to one embodiment of the invention.
  • Figure 37 depicts a table 3700 of prices used in mapping of operating costs and revenues to a decision tree, according to one embodiment of the invention.
  • Each node in the last time step is assigned a value (V) equal to the P&L in that period as shown above.
  • the notation (Np) is used for the value of a node in time step i, with output j, and run-time k.
  • reachable nodes • Find all nodes in the last period which are reachable from the selected node; these will be referred to as reachable nodes.
  • the option value is equal to the value of the reachable node minus the cost associated with the branch from the current to the reachable node.
  • the current node is assigned a value equal to the P&L at that node, plus the option value of the best reachable node.
  • FIG. 38 depicts a graph 3800 showing the forecasted price for electricity, and the associated profit maximizing operating schedule for a generator, according to one embodiment of the invention.
  • the scheduling optimization algorithm assumes that the operator of the asset has an exact knowledge of what the spot price of the fuel and power will be in each hour of the operating period. In reality, however, there is significant uncertainty associated with future price levels. Under these conditions the operators objective is to maximize the expected profit from scheduling the asset.
  • the trinomial tree approximation of the price process can be built in two stages.
  • the rules for branching and the transition probabilities to the next time slice _T I+1 are chosen so as to match the conditional mean and variance of the state variable X(t) at T M conditional on the value of X(t) at the given node at T .
  • a price state in the tree will be referred to as a node and label the nodes by (i,j) , where / refers to the time slice T i (and equals the number of times steps from T 0 ) and j indicates the price level.
  • S ; . will denote the price at node (i,j) .
  • Figure 39 depicts a spot price probability distribution graph 3900 generated by a trinomial tree based model, according to one embodiment of the invention
  • the generation option model is valued using a multi-level trinomial tree - trinomial forest - methodology: trinomial tree approximation of the stochastic evolution of the electricity spot price in a one-factor model as outlined above, followed by option valuation by 'backwards induction' through the trinomial forest.
  • a node in the forest is characterized by time, price, and a pair (output level, runtime) characterizing the state of the generator, and thus labeled by (i,j,(Q,RT)) .
  • Ramp up decision value equal to generator output value in current state plus the discounted expectation of the option values at the next time step + 1 from the tree with
  • Ramp down decision value equal to generator output value in current state plus the discounted expectation of the option values at the next time step + 1 from the tree with (max(Q- R Dw ' hb,Q Mil ,),RT + l) .
  • the generator output value V . . . in the current state (i, j, (Q * , RT * )) is:
  • V (i J iQ . RT . )) Q * - hb - S iJ -TC(T i ,Q * )
  • the stochastic optimization algorithm returns two sets of results.
  • FIG. 41 depicts a graph 4100 showing optimal decision rule generated by a stochastic optimization algorithm, according to one embodiment of the invention. Using combined tree and MC methods
  • the trinomial tree based option model returns an accurate valuation of the option.
  • the user may want more detailed information, including: (1) a decision rule for how do dispatch the plant under different market prices; (2) an hour by hour forecast of the expected output of the quantity of power produced by the unit, and a measure of the variability around this forecast; and, (3) expected fuel usage by hour, with a variability measure.
  • the tree based optimization model returns an optimal exercise decision (ramp up/ stay put/ ramp down) at each node in the trinomial forest, as seen in Figure 41.
  • These decision rules are defined only in' discrete price space (for the specific price nodes at each time step in the trinomial tree).
  • a decision rule is needed over a continuous price space. To achieve this, it is taken advantage of that the decision is monotonic in price (see Figure 42) and can therefore be compressed into two critical price trigger levels, the breakpoint between a ramp down and stay -54-
  • FIG. 42 depicts a graph 4200 showing an optimal decision rule for a given time and output level, according to one embodiment of the invention.
  • Figure 43 depicts a table 4300 of values associated with an optimal decision rule, according to one embodiment of the invention.
  • the algorithm assigns an optimal dispatch decision (ramp up/ stay/ ramp down);
  • FIG. 44 depicts a block diagram of framework 4400 for inco ⁇ orating Monte Carlo simulations into a dynamic optimization technique, according to one embodiment of the invention. Inco ⁇ orating Forced Outages
  • the simulation of the unit dispatch can be accompanied by a random process characterizing forced outages of the asset.
  • Two sets of probabilities can be associated with a forced outage: (1) when the asset is in a spinning state (nonzero output level) there is a spinning -55-
  • FIG. 45 depicts a flow diagram 4500 of operation of a generator in a forced outage situation, according to one embodiment of the invention.
  • any of the above constraints can be captured explicitly by appending additional states to the operational model. For instance, a state could be added which tracks the cumulative number of starts up to the current operating hour, or a state could be added which tracks the cumulative number of M Whs of energy the generator has produced so far this year. The effect of this is to add another dimension to the decision tree. While conceptually this is a simple change, it can have a significant effect on the performance of the optimization algorithm. If the maximum number of starts allowed is 100 for instance, this will increase the width of the -56-
  • the algorithm proceeds to modify the hourly decision rules in order to meet this criterion. This can be done by applying a penalty factor to each start up decision for the asset. Since there is already a parameter associated with the start- up cost of the asset, this variable can simply be modified until the long-term criterion is met.
  • FIG. 46 depicts a flow diagram 4600 showing a method of dynamic optimization for operation of a generator inco ⁇ orating a constraint on a number of starts per year for the generator, according to one embodiment of the invention.
  • the same algorithm can be applied for the two other examples mentioned. In the case where the total number of MWh of energy produced is limited, the cost which is incremented is the non-fuel cost component.
  • the valuation of the asset or contract can take place in three steps.
  • the shadow cost is added to the original plant costs, and the combined costs are used to calculate the optimal hourly decision rules.
  • the decision rules are applied to simulated price paths in order to generate a set of operating paths for the asset.
  • FIG. 47 depicts a block diagram 4700 showing a technique for anticipated profitability determination, accounting for actual and shadow cost factors, according to one embodiment of the invention.
  • An electric utility may own a large number of power plants, with varying generation technologies and fuel sources. In addition they typically have long term obligations to provide electricity to end users on a residential, commercial or industrial level.
  • the mix of assets and obligations affiliated with a given entity is referred to herein as its portfolio.
  • An algorithm has been described for arriving at optimal decision rules for a generator given a set of uncertain market conditions.
  • the decision rules are designed to maximize the expected net profit earned from the asset, and they are independent of any other assets or obligations affiliated with the owner.
  • the assumption is that multiple power plants are controlled by the same entity, and their value can be optimized by maximizing the value returned by each plant individually. This assumption will hold true only if the dispatch decision of one set of plants does not effect the revenue received by any other plant in the portfolio. Net profit from a plant is given by:
  • S e is the spot price of electricity
  • S f is the spot price of the fuel
  • TC is the total cost function of the plant depending on the total output Q.
  • the quantity is controlled by the dispatcher on a plant by plant basis, while the spot price of fuel and electricity are treated as exogenous random variables.
  • spot prices are assumed to be independent of the quantity of power produced by the generator, then a profit maximizing dispatch rule can be derived on a plant basis as described earlier in this document. This assumes that the markets for electricity and fuel are sufficiently liquid so that any trade by a single entity does not affect price levels. Unfortunately, markets for electricity often do not fit this criteria. Regions may be severely limited by transmission capacity as to how much power can be imported or exported.
  • the methodology as described herein primarily with reference to use in valuing and scheduling portfolios of generation assets under price uncertainty when markets are imperfect can be generalized to apply to a wider set of asset scheduling and option exercise problems. Specifically, the methodology applies to various situations, including situations in which an entity owns or controls a portfolio of assets (including derivatives) to be scheduled or exercised, where the market is imperfect, and where the resulting price of the underlying commodity or commodities is affected by the scheduling or exercise decisions of the owner or operator of the facility or facilities.
  • the methodology described herein utilizes an iterative approach in which, during each iteration, the exercise strategy for each asset is individually optimized subject to a control price curve. Between each iteration, the control price curve is modified, until the objective function of the owner is maximized.
  • the algorithm consists of four components: the asset model, the market model, asset optimization algorithm, and the portfolio iteration logic.
  • the asset model provides a detailed model of the dynamic costs and constraints associated with the asset or assets.
  • the market model is a model describing the uncertain behavior of market prices. Also, for illiquid markets, the market model provides a description of the impact of a market participant's actions on the market price or prices.
  • the asset optimization algorithm provides an algorithm that takes as inputs the asset model and market model parameters, and generates a set of exercise rules for operating the asset in future periods.
  • a set of input parameters for the market model are designated as the control curve (for example the forward curve).
  • Each asset in the portfolio is scheduled based on the default set of market parameters (first iteration).
  • the portfolio optimization algorithm contains the logic for updating the control curve based on the results from each iteration, until satisfactory optimum or near-optimum scheduling has been reached.
  • the portfolio optimization algorithm can include numerous search methodologies (such as grid or binary searches) as well as optimal control techniques.
  • Figure 48 depicts a graph 4800 showing a total generation schedule for a portfolio of generators, according to one embodiment of the invention.
  • Figure 49 depicts a graph 4900 showing an imbalance between total generation and load obligations for a portfolio of generators, according to one embodiment of the invention.
  • Figure 50 depicts a liquidity curve 500 characterizing spot prices as a function of net purchase and sale decisions, according to one embodiment of the invention. Determining Optimal Dispatch Rules for a Portfolio of Generation Assets
  • a portfolio dispatch decision can be thought of to be an N-dimensional vector (D h ), where each entry is the dispatch decision of an individual generator in the portfolio,
  • a methodology is applied which deconstructs the problem into a series of iterative steps.
  • the perfect market problem spot price is independent of the generators dispatch decision
  • the forward price applied in the creation of the decision rule is used for each individual generator as the confrol variables.
  • the following methodology can be applied:
  • a control price curve is provided. This control price curve is going to be used to alter the behavior of the generator in order to maximize profits.
  • the assets operating costs and constraints are provided.
  • optimal decision rules are calculated for the operating period.
  • Monte Carlo simulations of spot price paths in the operating period are generated based on the actual market forward prices/volatilities/mean reversion rate.
  • the simulated price paths are passed through the decision rules, thus generating a set of simulation based operating schedules for the asset.
  • FIG. 51 depicts a block diagram 5100 of a generator portfolio operation dynamic optimization technique utilizing a plant model, according to one embodiment of the invention.
  • the next step is to consider the aggregate behavior of a group of generators located in the same area, and therefore exposed to the same market prices.
  • Each individual generator is characterized according to the plant module, accounting for its unique operating costs and constraints.
  • the same set of control prices and simulated spot price paths are then send to each of the plant modules.
  • For each simulated spot price path the scheduled production of the individual plants are aggregated to create a total generation path over the operating period.
  • This part of the methodology is referred to as the portfolio model.
  • Figure 52 depicts a block diagram 5200 of a generator portfolio operation dynamic optimization technique utilizing a generator portfolio model, according to one embodiment of the invention.
  • FIG. 54 depicts a block diagram 5400 of a generator portfolio operation dynamic optimization technique to determine liquidity adjusted prices as well as profit and loss, according to one embodiment of -65-
  • a set of simulated spot prices are fed to the model, together with a control price curve with associated volatilities and mean reversion rates.
  • sets of decision rules are created for the individual plants.
  • the simulated price paths are then fed through the decision rules to create schedules.
  • Schedules are aggregated to create a set of total generation paths.
  • Applying the generation schedule, load obligations and simulated price curves to the liquidity function a set of liquidity adjusted price curves are created.
  • the net profit associated with each schedule is then calculated based on the adjusted price paths.
  • the expected profit affiliated with the current set of control prices is calculated by averaging the profit across all the simulated scenarios.
  • Figure depicts 55 depicts a block diagram 5500 of generator portfolio operation dynamic optimization technique utilizing search algorithms in determining optimal shadow costs and optimal shadow prices, according to one embodiment of the invention.
  • the optimization algorithm searches to find a set of control prices which will maximize the expected P&L from the asset. There are any number of possible algorithms which can be applied to accomplish this.
  • the algorithm produces a liquidity adjusted price curve based on the current forward curve, call this curve B. -66-
  • Curve A and curve B represent the upper and lower bounds for the control prices in each operating hour. [00241] When the boundaries have been set, a simple binary or grid search algorithm can be applied in order to determine the control price path which maximizes the expected P&L from the portfolio of assets and load obligations.

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Abstract

L'invention porte sur des procédés et systèmes permettant de déterminer les bénéfices anticipés d'installations industrielles telles que des centrales électriques et la valeur de leurs actifs en fonction de leur rentabilité, et les options relatives à leurs conditions optimales d'exploitation. L'invention porte par ailleurs sur des procédés et systèmes utilisant un algorithme dynamique de programmation et un modèle à base d'arbre décisionnel modélisant implicitement une ou plusieurs des contraintes d'exploitation de manière à faciliter la traçabilité comptable. L'invention porte également sur des procédés et systèmes utilisant un algorithme dynamique de programmation et un modèle à base d'arbre décisionnel tenant compte des effets combinés de l'évolution des coûts, avec une certaine marge d'incertitude, et des contraintes d'exploitation. L'invention porte en outre sur des procédés et systèmes traitant de l'évaluation et de la prévision de la rentabilité d'un groupe ou d'une gamme d'installations en tenant compte des facteurs de liquidités, ainsi que des contraintes propres à un groupe ou universelles.
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US7698233B1 (en) 2007-01-23 2010-04-13 Southern Company Services, Inc. System and method for determining expected unserved energy to quantify generation reliability risks
US9957843B2 (en) 2013-12-31 2018-05-01 General Electric Company Methods and systems for enhancing control of power plant generating units
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CN109711728B (zh) * 2018-12-27 2023-04-18 陕西师范大学 基于电力不确定性和低碳诉求的双层多目标电力调度方法
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6021402A (en) * 1997-06-05 2000-02-01 International Business Machines Corporaiton Risk management system for electric utilities
US6185483B1 (en) * 1998-01-27 2001-02-06 Johnson Controls, Inc. Real-time pricing controller of an energy storage medium
US6223101B1 (en) * 1997-06-30 2001-04-24 Kabushiki Kaisha Toshiba District heat supply plant controller

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6321207B1 (en) * 1999-04-15 2001-11-20 I2 Technologies Us, Inc. System and method for optimizing the allocation of a resource

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6021402A (en) * 1997-06-05 2000-02-01 International Business Machines Corporaiton Risk management system for electric utilities
US6223101B1 (en) * 1997-06-30 2001-04-24 Kabushiki Kaisha Toshiba District heat supply plant controller
US6185483B1 (en) * 1998-01-27 2001-02-06 Johnson Controls, Inc. Real-time pricing controller of an energy storage medium

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
ROGER BJORGAN ET AL: "Financial Risk Management in a Competitive Electricity Market" IEEE TRANSACTIONS ON POWER SYSTEMS, IEEE SERVICE CENTER, PISCATAWAY, NJ, US, vol. 14, no. 4, November 1999 (1999-11), pages 1285-1291, XP011089520 ISSN: 0885-8950 *
See also references of WO03094414A2 *

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