Power System State Estimation Using Potential Functions
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional state estimation methods for power systems often fail to enforce feasibility constraints, leading to unrealistic power output estimates, particularly in distribution systems with lower telemetry redundancy and data quality.
Innovation Solution
The method employs parameterized potential functions, specifically quadratic functions, to convert constrained optimization problems into unconstrained convex optimization problems, ensuring that nodal metrics in power systems are constrained to feasible values by updating center-of-attraction parameters to satisfy equality and inequality constraints within a tolerance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional state estimation methods (unconstrained WLS or equality-constrained WLS) are used, then the solution can be obtained efficiently, but the feasibility constraints on power injection are not enforced, leading to unrealistic estimates
Solution Approach 1:
The patent extracts the equality constraints from the constrained optimization problem and incorporates them into the objective function through parameterized potential functions. This transforms the constrained problem into an unconstrained one, maintaining feasibility while simplifying the solution approach.
Solution Approach 2:
The patent introduces parameterized potential functions with adjustable parameters that transform the constrained optimization problem into an unconstrained one. By changing the problem formulation from constrained to unconstrained while embedding constraint satisfaction within the objective function, the method achieves both feasibility and computational efficiency.
2Manufacturing precision
If equality constraints are enforced in state estimation, then power injection feasibility is improved, but the optimization problem becomes more complex and harder to solve
Solution Approach 1:
The patent replaces the mechanical constraint enforcement mechanism (equality constraints in optimization) with a potential field-based approach. By substituting the constraint structure with parameterized potential functions, the method maintains constraint satisfaction while enabling the use of simpler unconstrained optimization algorithms.
3Adaptability or versatility
If distribution systems with lower telemetry redundancy are used, then system deployment is more feasible, but state estimation accuracy deteriorates due to lower data quality
Solution Approach 1:
The patent changes the problem formulation from constrained to unconstrained optimization with parameterized potential functions. This transformation makes the method more adaptable to distribution systems with limited telemetry while maintaining estimation accuracy by embedding constraint satisfaction within the objective function, preventing unrealistic estimates even with lower data quality.
Data Source
Figure 1
Figure 2
Figure 3
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.