Power System State Estimation With Inequality Constraint Potentials
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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 and preventing ill-conditioning of the gain matrix.
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 invention extracts 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, allowing the use of efficient WLS algorithms while still enforcing feasibility constraints through the potential function terms that penalize constraint violations.
Solution Approach 2:
The invention introduces parameterized potential functions with adjustable parameters that control the enforcement of inequality constraints. By modifying these parameters, the system can balance between enforcing feasibility constraints and maintaining estimation accuracy, resolving the contradiction between reliability and measurement precision.
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 invention introduces parameterized potential functions as intermediary elements between the inequality constraints and the objective function. These potential functions act as mediators that enforce constraints through their mathematical structure rather than through large weight values, thereby maintaining gain matrix conditioning while still ensuring constraint satisfaction.
Solution Approach 2:
The invention uses parameterized potential functions with adjustable parameters to control constraint enforcement. By changing these parameters appropriately, the system can enforce constraints effectively without resorting to large weight values that would ill-condition the gain matrix, thus resolving the contradiction between constraint satisfaction and numerical stability.
3Adaptability or versatility
If state estimation is performed in distribution systems with lower telemetry redundancy and data quality, then the system can provide state estimation for networks with limited measurements, but the solution is more likely to violate feasibility constraints due to lower data quality
Solution Approach 1:
The invention applies preliminary anti-action by incorporating parameterized potential functions into the objective function before solving the state estimation problem. These potential functions preemptively counteract the tendency of low-quality measurements to produce infeasible solutions by enforcing inequality constraints through the mathematical structure of the objective function, thus preventing constraint violations before they occur.
Solution Approach 2:
The invention uses parameterized potential functions with adjustable parameters that can be tuned based on the quality and redundancy of available measurements. In distribution systems with lower data quality, these parameters can be adjusted to strengthen constraint enforcement, thereby maintaining reliability and feasibility despite limited and noisier measurements.
Data Source
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.