Linear Optimal Power Flow for Grid Stability
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Solution Overview
Problem
The power grid faces instability due to differences in resistive and reactive load behaviors, surges, brownouts, and natural disasters, with existing monitoring systems making simplifying assumptions that limit their accuracy and responsiveness.
Innovation Solution
A computer-implemented tool and method that employs a processor to execute a solver algorithm, generating piecewise linear constraints for both real and reactive power terms, allowing for linear programming optimization of the power grid, modeling both real and reactive power flow components, and accounting for transmission line losses.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If existing monitoring systems make simplifying assumptions about power grid modeling, then computational speed is improved, but measurement precision and reliability deteriorate
Solution Approach 1:
The patent transforms the non-linear power flow equations into linear form by changing the mathematical parameters and variables used in the model. This linearization technique maintains computational speed while improving measurement precision by accurately representing both real and reactive power components without requiring simplifying assumptions.
Solution Approach 2:
The patent replaces traditional non-linear optimization methods with a linear programming approach. This substitution of the mathematical methodology allows the system to achieve both fast computational speed and high modeling accuracy by using linear constraints and objective functions that can be solved efficiently while capturing the true behavior of the power grid.
2Loss of time
If traditional optimization methods are used, then computational time is reduced, but reliability and predictive capability deteriorate
Solution Approach 1:
The patent changes the mathematical formulation from non-linear to linear by transforming the power flow equations and using linearized constraints. This parameter transformation enables the use of efficient linear programming solvers that provide both fast computational time and reliable predictive capability for power grid optimization.
Solution Approach 2:
The patent substitutes traditional non-linear optimization algorithms with linear programming methods. This methodological replacement maintains computational efficiency while significantly improving reliability by providing accurate predictions of power flow, losses, and system stability under various operating conditions.
3Device complexity
If only real power components are considered, then device complexity is reduced, but manufacturing precision and optimization accuracy deteriorate
Solution Approach 1:
The patent creates a unified linear optimization model that simultaneously handles both real and reactive power components, transmission line losses, and various operational constraints. This multi-functional approach maintains model simplicity while achieving high optimization accuracy by comprehensively considering all relevant power system parameters in a single linear framework.
Solution Approach 2:
The patent merges the consideration of real power, reactive power, and transmission losses into a single integrated linear optimization model. This combination allows the system to maintain low device complexity by using one unified model rather than separate complex models, while achieving high optimization accuracy through comprehensive parameter inclusion.
Data Source
AI summary
An electric power system or power grid is optimized using a computer-implemented tool the represents in computer memory the optimization function and at least one constraint, which the processor operates upon using a linear programming solver algorithm. The constraints are represented in memory as data structures that include both real and reactive power terms, corresponding to at least one of a power flow model and a transmission line model. The transmission line model is represented using a piecewise linear representation. The power flow model may also include for each node in the power system a real power loss term representing transmission line loss allocated to that node.