Measurement Device Placement via Spanning Trees for Grid Observability
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Solution Overview
Problem
Existing methods for placing measurement devices in very large power systems face challenges with combinatorial optimization, leading to high computational complexity and difficulty in achieving full observability, especially due to the curse of dimensionality.
Innovation Solution
A method using a hardware processor to determine an optimal placement strategy by identifying a spanning tree, traversing it to generate candidate placement strategies, and selecting the minimum number of measurement devices based on distance and observability criteria, ensuring all nodes are observable.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If combinatorial optimization methods are used to place measurement devices, then full observability of the power system can be achieved, but computational complexity increases exponentially due to the curse of dimensionality
Solution Approach 1:
The patent segments the power system into a spanning tree structure, dividing the complex network into hierarchical levels (root node, intermediate nodes, leaf nodes). This segmentation transforms the exponential combinatorial optimization problem into a polynomial-time greedy algorithm by processing nodes in a structured sequence from root to leaves, ensuring observability without exhaustive search.
Solution Approach 2:
The patent performs preliminary action by pre-identifying the spanning tree structure and determining the hierarchical levels of all nodes before placing measurement devices. The root node and its adjacent nodes are identified in advance as priority locations, allowing the algorithm to make informed placement decisions without real-time complex calculations during the optimization process.
2Reliability
If measurement devices are placed at every bus to ensure full observability, then complete system monitoring is achieved, but cost and communication link requirements become impractical
Solution Approach 1:
The patent applies local quality by placing measurement devices strategically at specific locations (root node and adjacent nodes of the spanning tree) rather than uniformly at every bus. This localized placement exploits the tree structure properties where measurements at key nodes can infer states of multiple downstream nodes through power flow equations, reducing the total number of devices while maintaining full system observability.
Solution Approach 2:
The patent uses partial action by implementing a greedy placement strategy that stops adding measurement devices once the spanning tree observability condition is satisfied. Instead of placing devices at all possible locations or using exhaustive methods, the algorithm places devices incrementally at the most beneficial locations until the minimum sufficient set is achieved, avoiding unnecessary device installations.
3Manufacturing precision
If traditional combinatorial optimization methods are applied to very large power systems, then theoretical optimality can be pursued, but the solution breaks down due to computational intractability
Solution Approach 1:
The patent substitutes the mechanical/combinatorial optimization approach with a mathematical graph theory approach. Instead of using iterative combinatorial algorithms that explore solution spaces, the patent employs a deterministic greedy algorithm based on spanning tree properties, replacing complex optimization mechanics with simpler mathematical relationships that guarantee polynomial-time execution while maintaining optimality for the observability problem.
Data Source
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AI summary
Classical optimization techniques, when applied to the placement of measurement devices in very large power networks, become computationally intractable and are not guaranteed to converge. In contrast, disclosed embodiments guarantee an optimal placement strategy of measurement devices, such as phasor measurement units for measuring voltage and current, across a power network of any size, such that the voltage at each bus is observable, in dramatically less computational time than classical optimization techniques. In particular, embodiments traverse at least one spanning tree of a graph of the power network, and place measurement devices based on distance values of the nodes from the nearest measurement device. The distance values, and potentially the observability status, of all nodes are updated after each placement.