Planning economic energy dispatch in electrical grid under uncertainty

• US 9,058,444 B2
• Filed: 01/03/2013
• Issued: 06/16/2015
• Est. Priority Date: 07/17/2012
• Status: Expired due to Fees

• Current Assignee: GlobalFoundries, Inc.
• Original Assignee: International Business Machines Corporation
• Inventors: Ghosh, Soumyadip, Phan, Dung T.
• Primary Examiner(s): Shah, Kamini S
• Assistant Examiner(s): PIERRE LOUIS, ANDRE
• Application Number:
  US13/733,431
• Publication Number:
  US 20140025352A1
• Time in Patent Office: 894 Days
• Field of Search: 703/18, 700/28, 700/33, 700/36, 700/295
• US Class Current: 1/1
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544
• CPC Class Codes: G06F 2113/04 Power grid distribution networks
• CPC Class Codes: G06F 2119/06 Power analysis or power optimisation
• CPC Class Codes: G06F 30/13 Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
• CPC Class Codes: G06F 30/18 Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling circuit design at the physical level G06F30/39; network planning tools for wireless communication networks H04W16/18
• CPC Class Codes: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30
• CPC Class Codes: Y02E 40/70 Smart grids as climate change mitigation technology in the energy generation sector
• CPC Class Codes: Y02E 60/00 Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
• CPC Class Codes: Y04S 10/50 Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
• CPC Class Codes: Y04S 40/20 Information technology specific aspects, e.g. CAD, simulation, modelling, system security

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. Under certain conditions the sequence of optimal solutions obtained under both alternatives has a limit point that is a globally-optimal solution to the original two-stage nonconvex program. A further decomposition approach derived from the Alternating Direction Method of Multipliers algorithm is implemented.

Claims

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 alternating current 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 nonconvex optimization problem modeling an economic dispatch problem under renewable-generation uncertainty using said finite number of scenarios;

solving said nonconvex 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 immediately successive 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, wherein said solving includes solving a two-stage minimization problem by;

decomposing said non-convex optimization problem based on an iterative outer approximation technique, said decomposing including solving a sequence of lower-approximation problems for a first-stage minimization problem with each iteration improving a piecewise-linear outer-approximation for a recourse function that represents the second time interval stage costs of the spot market access,

wherein one or more processor units in communication with a memory storage device performs said receiving said modeling power flow and uncertainty data, said formulating and solving.

2. The method of claim 1 further providing solving said nonconvex optimization problem to determine:

optimal power output levels of said active generators and energy levels exchanging with a spot market for each scenario, and

how the produced energy is routed through the grid to consumption nodes, such that an expected cost for energy generation and spot market access is minimized.

3. The method of claim 1 wherein said two-stage minimization problem solves minimizing said optimization function subject to Alternating Current power balance operational constraints at said first time interval to obtain optimal energy dispatch levels of active generation units and energy levels exchanging with a spot market for each scenario for said immediate successive second time interval.

4. The method of claim 3 wherein said iterative outer approximation technique comprises:

constructing said piecewise-linear outer-approximation of the recourse function by iteratively approximating an intersection of a collection of affine inequalities.

5. The method of claim 3, wherein said solving a sequence of lower-approximation problems includes a second stage solution comprising:

iteratively solving, for each renewable energy generation scenario, n=1, . . . , N, a subproblem (Sⁿ) associated with said optimal energy levels exchanging with a spot market for each scenario during said immediate successive second time interval; and

iterative solving the k-th lower-approximation to said optimization problem to obtain an optimal solution and an augmented lower approximation.

6. The method of claim 5 further comprising:

in said 2^nd stage solution, adding all linear inequalities generated from solving optimization problem as new constraints to the 1st stage problem for solving at a next outer-approximation iteration.

7. The method of claim 5 further comprising:

in 2^nd stage solution, aggregating all linear inequalities from solving optimization problem, and adding a single unique linear inequality as a new constraint to the 1st stage problem for solving at a next outer-approximation iteration.

8. The method of claim 5 wherein said optimal energy dispatch levels includes optimal energy level exchanged with a spot market for each said scenario.

9. The method of claim 5 further comprising:

obtaining subgradients of the optimization function generated from the solution of the second stage subproblems (Sⁿ).

10. The method of claim 1 further comprising:

decomposing nonconvex sample-average approximation problem by alternating direction method of multipliers approach.

11. The method of claim 1, wherein said optimization problem modeling of said economic dispatch problem receives input data comprising:

a network topology, branch and nodal admittance matrices, voltage limits on every node, thermal limits on every branch, and real power and reactive power generation limits.

12. The method of claim 1, wherein said nonconvex optimization problem to be minimized includes a function Ψ

(g) modeled according to;