Planning economic energy dispatch in electrical grid under uncertainty
First Claim
1. A method for determining a generator dispatch plan for a power grid under uncertain conditions comprising:
- receiving data modeling power flow of active generation units over nodes of a power grid network of multiple local buses interconnected via transmission lines, said active generation units including conventional energy generators producing energy;
receiving during a first time interval data of a set of forecast scenario modeling uncertainty in renewable energy output, said set capturing a finite number of scenarios generation for an immediately successive 2nd time interval;
formulating a two-stage nonconvex optimization problem modeling economic dispatch problem under renewable-generation uncertainty using said finite number of scenarios;
solving said non-convex optimization problem during said first time interval to obtain power dispatch levels for said generators and energy levels exchanging with a spot market for each scenario at said 2nd time interval that minimizes expected cost of power generation and cost of exchanging energy with a spot market modeled for each said modeled uncertainty, said solving including decomposing said non-convex optimization problem based on an alternating direction method of multipliers (ADMM) approximation, said solving based on said ADMM approximation comprising;
reformulating said non-convex optimization problem by splitting the power grid into a number of separate regions, and specifying variables representing a new power flow duplicated in an overlap between regions; and
solving the optional power flow for each region, as an associated subproblem, wherein the optimal power flow is solved in a distributed fashion;
forming a modified Lagrangian function of the re-formulated non-convex optimization problem based on the reformulation, wherein said solving based on said ADMM approximation comprises an iterative method, wherein each iteration comprises;
applying a joint optimization and an updating multiplier step; and
controlling the dispatching of active generation units over a network of multiple local buses interconnected via transmission lines based on a result of said solving of said non-convex optimization problem,wherein said reformulated non-convex optimization problem comprises;
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Abstract
A method for solving a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Certain generation decisions are made only in the first stage and fixed for the subsequent (second) stage, where the actual renewable generation is realized. The uncertainty in renewable output is captured by a finite number of scenarios. Any resulting supply-demand mis-match must then be alleviated using high marginal-cost power sources that can be tapped in short time frames. The solution implements two outer approximation algorithms to solve this nonconvex optimization problem to optimality including the application of a decomposition approach derived from the Alternating Direction Method of Multipliers (ADMM) algorithm.
9 Citations
16 Claims
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1. A method for determining a generator dispatch plan for a power grid under uncertain conditions comprising:
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receiving data modeling power flow of active generation units over nodes of a power grid network of multiple local buses interconnected via transmission lines, said active generation units including conventional energy generators producing energy; receiving during a first time interval data of a set of forecast scenario modeling uncertainty in renewable energy output, said set capturing a finite number of scenarios generation for an immediately successive 2nd time interval; formulating a two-stage nonconvex optimization problem modeling economic dispatch problem under renewable-generation uncertainty using said finite number of scenarios; solving said non-convex optimization problem during said first time interval to obtain power dispatch levels for said generators and energy levels exchanging with a spot market for each scenario at said 2nd time interval that minimizes expected cost of power generation and cost of exchanging energy with a spot market modeled for each said modeled uncertainty, said solving including decomposing said non-convex optimization problem based on an alternating direction method of multipliers (ADMM) approximation, said solving based on said ADMM approximation comprising; reformulating said non-convex optimization problem by splitting the power grid into a number of separate regions, and specifying variables representing a new power flow duplicated in an overlap between regions; and solving the optional power flow for each region, as an associated subproblem, wherein the optimal power flow is solved in a distributed fashion; forming a modified Lagrangian function of the re-formulated non-convex optimization problem based on the reformulation, wherein said solving based on said ADMM approximation comprises an iterative method, wherein each iteration comprises; applying a joint optimization and an updating multiplier step; and controlling the dispatching of active generation units over a network of multiple local buses interconnected via transmission lines based on a result of said solving of said non-convex optimization problem, wherein said reformulated non-convex optimization problem comprises; - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A system for determining a generator dispatch plan for a power grid under uncertain conditions comprising:
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a memory storage device; a processor coupled to the memory device, the processor configured to; receive data modeling power flow of active generation units over nodes of a power grid network of multiple local buses interconnected via transmission lines, said active generation units including conventional energy generators producing energy; receive during a first time interval data of a set of forecast scenario modeling uncertainty in renewable energy output, said set capturing a finite number of scenarios generation for an immediately successive 2nd time interval; formulate a two-stage nonconvex optimization problem modeling economic dispatch problem under renewable-generation uncertainty using said finite number of scenarios; solve said non-convex optimization problem during said first time interval to obtain power dispatch levels for said generators and energy levels exchanging with a spot market for each scenario at said 2nd time interval that minimizes expected cost of power generation and cost of exchanging energy with a spot market modeled for each said modeled uncertainty, said solving including decomposing said non-convex optimization problem based on an alternating direction method of multipliers (ADMM) approximation, wherein during said solving based on said ADMM approximation, the processor is configured to; reformulate said non-convex optimization problem by splitting the power grid into a number of separate regions, and specifying variables representing a new power flow duplicated in an overlap between regions; and solve the optional power flow for each region, as an associated subproblem, wherein the optimal power flow is solved in a distributed fashion; form a modified Lagrangian function of the re-formulated non-convex optimization problem based on the reformulation, wherein said solving based on said ADMM approximation comprises an iterative method, wherein in each iteration the processor is configured to; apply a joint optimization and an updating multiplier step; and control the dispatching of active generation units over a network of multiple local buses interconnected via transmission lines based on a result of said solving of said non-convex optimization problem, wherein said reformulated non-convex optimization problem comprises; - View Dependent Claims (9, 10, 11, 12, 13)
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14. A computer program product for determining a generator dispatch plan for a power grid under uncertain conditions, the computer program product comprising a non-transitory computer readable storage medium, the computer readable storage medium not a propagating signal, the computer readable storage medium readable by a processing circuit and storing instructions run by the processing circuit for performing a method comprising:
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receiving data modeling power flow of active generation units over nodes of a power grid network of multiple local buses interconnected via transmission lines, said active generation units including conventional energy generators producing energy; receiving during a first time interval data of a set of forecast scenario modeling uncertainty in renewable energy output, said set capturing a finite number of scenarios generation for an immediately successive 2nd time interval; formulating a two-stage nonconvex optimization problem modeling economic dispatch problem under renewable-generation uncertainty using said finite number of scenarios; solving said non-convex optimization problem during said first time interval to obtain power dispatch levels for said generators and energy levels exchanging with a spot market for each scenario at said 2nd time interval that minimizes expected cost of power generation and cost of exchanging energy with a spot market modeled for each said modeled uncertainty, said solving including decomposing said non-convex optimization problem based on an alternating direction method of multipliers (ADMM) approximation, said solving based on said ADMM approximation comprising; reformulating said non-convex optimization problem by splitting the power grid into a number of separate regions, and specifying variables representing a new power flow duplicated in an overlap between regions; and solving the optional power flow for each region, as an associated subproblem, wherein the optimal power flow is solved in a distributed fashion; forming a modified Lagrangian function of the re-formulated non-convex optimization problem based on the reformulation, wherein said solving based on said ADMM approximation comprises an iterative method, wherein each iteration comprises; applying a joint optimization and an updating multiplier step; and controlling the dispatching of active generation units over a network of multiple local buses interconnected via transmission lines based on a result of said solving of said non-convex optimization problem, wherein said reformulated non-convex optimization problem comprises; - View Dependent Claims (15, 16)
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Specification