Two-Stage Power Grid Optimization for Path-Independent Resource Valuation
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Solution Overview
Problem
Optimization processes in power grid systems face indeterminacy issues due to non-binding fully loaded constraints, leading to path-dependent results and nebulous resource values, which affect the accuracy and reliability of energy resource valuation.
Innovation Solution
A two-stage optimization process is implemented, where a first optimization process identifies optimal resource values based on a primary objective function, and a second optimization process assigns non-zero values to non-binding fully loaded constraints using a secondary objective function, ensuring path-independent results and maintaining the optimality of the first optimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a single optimization process is used to determine resource values in a power grid, then the computational process is simple and fast, but the results become path-dependent and indeterminate when non-binding fully loaded constraints are present
Solution Approach 1:
The optimization process is divided into two distinct stages: a first optimization process that determines optimal resource values subject to constraints, and a second optimization process that assigns shadow values to constraints. This segmentation resolves the indeterminacy problem by separating the determination of resource values from the assignment of constraint values, ensuring path-independent results while maintaining computational efficiency.
Solution Approach 2:
The first optimization process is executed beforehand to establish the optimal resource values and identify which constraints are fully loaded. This preliminary action provides the foundation for the second optimization process, which then assigns shadow values based on the results of the first process. This sequence ensures that shadow values are assigned only after the optimal solution is known, eliminating path-dependency.
2Ease of manufacture
If shadow values of non-binding fully loaded constraints are set to zero, then the optimization process is straightforward, but the resource values become nebulous and path-dependent
Solution Approach 1:
The patent changes the parameter assignment for shadow values of non-binding fully loaded constraints from zero (conventional approach) to non-zero values determined by a second optimization process. This parameter change transforms the shadow value from an arbitrary zero to a precisely calculated value that reflects the true marginal value of the constraint, thereby improving measurement precision without sacrificing implementation simplicity.
Solution Approach 2:
The second optimization process acts as an intermediary between the first optimization process and the final resource valuation. It takes the results of the first process (optimal resource values and constraint statuses) and produces refined shadow values that eliminate nebulousness. This intermediary step ensures accurate resource valuation while maintaining the overall simplicity of the optimization framework.
3Measurement precision
If a two-stage optimization process is implemented to resolve indeterminacy, then path-independent and consistent resource values are achieved, but the computational complexity and processing time increase
Solution Approach 1:
The two-stage optimization process maintains continuity of useful action by ensuring that the second process builds directly upon the results of the first process without redundant calculations. The shadow value assignment in the second stage is performed efficiently using the constraint identification from the first stage, minimizing additional processing time while achieving path-independent results.
Solution Approach 2:
The second optimization process focuses only on the specific subset of constraints that are fully loaded, rather than re-optimizing the entire system. This partial action approach assigns shadow values only where needed (to fully loaded constraints) while leaving other constraints unchanged, thereby reducing the computational burden and time loss associated with a complete re-optimization.
Data Source
AI summary
A method for delivering an energy resource on a network includes receiving constraints, a first objective function, and a second objective function. The constraints represent electrical load capacities of elements of the network. The constraints and the first objective function are used to identify (i) a load matrix embodying a set of optimal electrical loads for each of the plurality of elements of the power grid and (ii) a corresponding first feature matrix. The load matrix and the first feature matrix optimize the first objective function and satisfy the constraints. If the load matrix and first feature matrix indicate a non-binding fully loaded (NBFL) constraint, the second objective function is used to identify a second feature matrix which optimizes both the first and second objective functions while satisfying the constraints. The second feature matrix assigns a non-zero value to at least one previously identified NBFL constraint.