State estimation for a power system using parameterized potential functions for equality constraints
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Solution Overview
Problem
Conventional state estimation methods for power systems fail to enforce feasibility constraints on nodal metrics, leading to unrealistic estimates, particularly in distribution systems with lower telemetry redundancy and data quality, necessitating a solution that constrains solutions to feasible values.
Innovation Solution
Employing parameterized potential functions, specifically quadratic functions, to convert constrained optimization problems into unconstrained convex optimization problems, using center-of-attraction parameters to ensure that equality and inequality constraints are satisfied within a tolerance, thereby ensuring feasible estimates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional unconstrained state estimation methods are used, then computational simplicity is maintained, but feasibility constraints on nodal metrics are not enforced, leading to unrealistic estimates
Solution Approach 1:
The invention extracts the feasibility constraints from the constrained optimization problem and incorporates them into the objective function through parameterized potential functions. This transforms the constrained optimization problem into an unconstrained one, maintaining computational simplicity while ensuring feasibility of estimates.
Solution Approach 2:
The invention changes the parameters of the optimization problem by introducing parameterized potential functions with center-of-attraction parameters. These parameters are updated during the solution process to guide the estimation toward feasible values while maintaining the unconstrained nature of the problem.
2Reliability
If equality constraints are enforced in state estimation, then solution feasibility is improved, but numerical ill-conditioning occurs for nodes with zero power injection
Solution Approach 1:
The invention removes the explicit equality constraints from the optimization problem and embeds them within the objective function through parameterized potential functions. This extraction eliminates numerical ill-conditioning while preserving the feasibility requirements through the potential function formulation.
3Productivity
If distributed energy resource output is estimated without constraints, then computational speed is maintained, but unrealistic estimates exceeding maximum output occur
Solution Approach 1:
The parameterized potential functions with center-of-attriction parameters automatically guide the estimation process toward feasible values. The system self-corrects unrealistic estimates by the mathematical structure of the potential functions, maintaining both computational speed and estimation accuracy without requiring external constraint enforcement.
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.