Parameterized Potential Functions for Feasible Power State Estimation
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Solution Overview
Problem
Conventional state estimation methods for power systems often result in numerical ill-conditioning and violate feasibility constraints, particularly in distribution systems with lower telemetry redundancy and data quality, leading to inaccurate estimates of nodal metrics.
Innovation Solution
Convert the constrained optimization problem into an unconstrained convex optimization problem using parameterized potential functions for equality constraints, with center-of-attraction parameters to ensure that the solution satisfies all constraints within a tolerance, and iteratively update these parameters to enforce feasibility.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If conventional unconstrained non-linear weighted least squares method is used for state estimation, then the solution process is simple and fast, but the solution violates feasibility constraints on power injection (e.g., DER output exceeding maximum capacity)
Solution Approach 1:
The patent transforms the static constrained optimization problem into a dynamic unconstrained optimization problem by introducing time-varying center-of-attraction parameters that evolve during the solution process. The parameterized potential function creates a dynamic landscape that guides the solution toward feasibility while maintaining computational efficiency.
Solution Approach 2:
The patent changes the parameters of the optimization problem by introducing center-of-attraction parameters that modify the potential function. These parameters are updated iteratively to enforce constraints, transforming the problem from constrained to unconstrained while maintaining constraint satisfaction through parameter evolution.
2Stability of the object's composition
If equality-constrained non-linear weighted least squares method is used to avoid numerical ill-conditioning, then numerical stability is improved, but the method still does not enforce feasibility constraints on power injection
Solution Approach 1:
The patent introduces a parameterized potential function as an intermediary mechanism that bridges numerical stability and feasibility enforcement. The center-of-attraction parameters act as mediators that guide the solution toward feasible regions while maintaining numerical stability through the unconstrained optimization framework.
Solution Approach 2:
The patent performs preliminary action by transforming the constrained problem into an unconstrained form before solving, using the parameterized potential function to pre-encode constraint information. This preliminary transformation enables subsequent iterative refinement of center-of-attraction parameters to enforce feasibility.
3Reliability
If parameterized potential functions with center-of-attraction parameters are used to enforce feasibility constraints, then constraint satisfaction is improved, but the solution process requires iterative parameter updates
Solution Approach 1:
The patent implements feedback through iterative updates of center-of-attraction parameters based on constraint violation measurements. The solution process continuously monitors constraint satisfaction and adjusts parameters accordingly, creating a closed-loop system that converges to feasible solutions.
Solution Approach 2:
The patent employs periodic action through iterative optimization cycles where the parameterized potential function is repeatedly evaluated and center-of-attraction parameters are updated at discrete intervals. This periodic refinement process gradually enforces constraints while maintaining solution progress.
Data Source
AI summary
Prior methods of state estimation, based on a constrained optimization problem with equality and/or inequality constraints, rely on penalty-based heuristics which can produce very large weight values, resulting in ill-conditioning of the gain matrix. Disclosed embodiments of state estimation convert the constrained optimization problem into an unconstrained convex optimization problem in which violated equality and/or inequality constraints are represented as parameterized potential functions, each comprising a center-of-attraction parameter. This unconstrained convex optimization problem can be iteratively formed, using successively updated values for the center-of-attraction parameters, and solved, until no equality and/or inequality constraints are violated, to produce a final estimated state. This final estimated state may then be used to control the system being monitored, such as a power system.