Logarithmic Interpolation for Over-Excitation Curve Modeling
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Solution Overview
Problem
Existing electric power system modeling methods, particularly for generator and transformer over-excitation, rely on linear interpolation which can lead to inaccuracies due to the non-linear nature of over-excitation damage curves, resulting in potential equipment damage from magnetic saturation and eddy currents.
Innovation Solution
Implementing logarithmic interpolation based on data provided by equipment manufacturers to model over-excitation curves more accurately, using equations such as Eq. 3 and Eq. 4 for slope calculation and interpolation, to determine operating times and prevent damage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If linear interpolation is used to model over-excitation damage curves, then the modeling process is simple, but the accuracy of operating time calculation deteriorates
Solution Approach 1:
The patent changes the mathematical parameter used for interpolation from linear to logarithmic. Specifically, it uses logarithmic interpolation of the V/Hz product values rather than linear interpolation, which better captures the non-linear relationship between over-excitation levels and damage curves. This parameter change resolves the contradiction by improving accuracy while maintaining reasonable computational complexity.
2Measurement precision
If logarithmic interpolation is used to model over-excitation damage curves, then the accuracy of operating time calculation is improved, but the modeling complexity increases
Solution Approach 1:
The patent applies logarithmic transformation to the V/Hz product values during interpolation. The process calculates the logarithm of V/Hz values, performs linear interpolation on the logarithmic values, and then exponentiates the result. This parameter transformation approach improves accuracy by better representing the physical relationship while the structured algorithm keeps the implementation complexity manageable.
3Measurement precision
If the number of point pairs is increased to improve curve accuracy, then the modeling precision is improved, but the ease of operation deteriorates
Solution Approach 1:
The patent changes the interpolation method from linear to logarithmic, which allows for accurate curve representation using fewer point pairs. The logarithmic transformation naturally captures the exponential relationship in over-excitation damage curves, meaning that critical inflection points can be represented with minimal data points while maintaining high accuracy throughout the curve.
Solution Approach 2:
The patent applies a curved (logarithmic) interpolation approach rather than straight-line (linear) interpolation. This curvature in the mathematical model better fits the physical reality of over-excitation damage curves, allowing accurate representation with fewer control points and simplifying the configuration process.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces operating time errors in protective relays, ensuring generators and transformers are protected from over-excitation by accurately identifying prohibited operation regions and preventing damage.
Implementation Method 1
Over-excitation causes magnetic saturation. Iron is commonly used in generators and transformers, and one physical property of iron is the flux it can support per cross-sectional area or flux density. When the maximum flux density is reached, the iron becomes saturated
Implementation Method 2
Once saturation is reached, excess flux travels via alternate paths. Excess flux traveling via alternative paths will induce circulating currents, known as eddy currents in nonlaminated components that are not designed to carry flux and may generate heat
Data Source
AI summary
The present disclosure relates to systems and methods for protecting against and mitigating the effects of over-excitation of elements in electric power systems. In one embodiment, a system consistent with the present disclosure may comprise a point pair subsystem to receive a plurality of point pairs that define an over-excitation curve for a piece of monitored equipment. The system may receive a plurality of measurements corresponding to electrical conditions associated with the piece of monitored equipment. A logarithmic interpolation subsystem may determine a logarithmic interpolation corresponding to one of the plurality of measurements based on the plurality of point pairs. An over-excitation detection subsystem may detect an over-excitation condition based on the logarithmic interpolation, and a protective action subsystem may implement a protective action based on the over-excitation condition.