Power System State Estimation Using Potential Functions for Feasibility
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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 power output estimates, particularly in distribution systems with lower telemetry redundancy and data quality.
Innovation Solution
The method employs parameterized potential functions to convert constrained optimization problems into unconstrained convex optimization problems, using center-of-attraction parameters to ensure that estimated states satisfy inequality constraints within a tolerance, thereby avoiding the need for large weight values that cause ill-conditioning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional state estimation is solved as an unconstrained or equality-constrained non-linear WLS problem, then the solution avoids numerical ill-conditioning for nodes with zero power injection, but the solution does not enforce feasibility constraints on power injection (e.g., a DER with maximum output of 10 KW may be estimated to produce 12 KW)
Solution Approach 1:
The patent extracts the inequality constraints from the constrained optimization problem and incorporates them into the objective function through parameterized potential functions. This transformation converts the constrained problem into an unconstrained one, where the constraints are enforced through the mathematical structure of the potential functions rather than explicit constraint boundaries.
Solution Approach 2:
The patent introduces dynamic center-of-attraction parameters that are updated during the solution process. These parameters dynamically adjust the attraction points of the potential functions to guide the solution toward feasible regions, allowing the system to adaptively enforce constraints while maintaining numerical stability.
2Reliability
If large weight values are used to enforce inequality constraints in the objective function, then the feasibility constraints are enforced more strictly, but the gain matrix becomes ill-conditioned
Solution Approach 1:
The patent changes the parameterization of the constraint enforcement mechanism by introducing center-of-attraction parameters instead of using fixed large weight values. This parameter change allows the constraints to be enforced through the geometric structure of the potential functions rather than through magnitude-based weighting, thereby maintaining numerical stability.
Solution Approach 2:
The parameterized potential functions act as intermediaries between the objective function and the inequality constraints. Instead of directly applying large weights to enforce constraints, the potential functions mediate the constraint enforcement through their mathematical structure, distributing the constraint influence smoothly and avoiding ill-conditioning.
3Adaptability or versatility
If state estimation is performed in distribution systems with lower telemetry redundancy and data quality, then the system can operate with limited measurements, but the likelihood of obtaining unrealistic power output estimates increases
Solution Approach 1:
The patent performs preliminary action by incorporating feasibility constraints into the optimization objective function before solving the state estimation problem. The parameterized potential functions are constructed in advance to attract the solution toward feasible regions, ensuring that even with limited measurements, the estimated state will satisfy physical constraints.
Data Source
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AI summary
Prior methods of state estimation rely on penalty-based heuristics to enforce inequality constraints, which can produce very large weight values, resulting in ill-conditioning of the gain matrix. Disclosed embodiments of state estimation convert the inequality-constrained optimization problem into an unconstrained optimization problem in which violated inequality constraints are represented as parameterized potential functions, each comprising a center-of-attraction parameter. This unconstrained convex optimization problem can be iteratively prepared, using successively updated values for the center-of-attraction parameters, and solved, until no 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.