Interior Point Method for Reformulated Optimal Power Flow
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Solution Overview
Problem
Optimal Power Flow (OPF) models in electric power networks face challenges due to their complexity, including non-convex Voltage Law constraints, fully coupled Power Flow Conservation network constraints, integer choice variables for transformer/phasor taps and switching shunts, and large network sizes, making it difficult to achieve efficient and feasible power flow solutions under adverse conditions.
Innovation Solution
A method is developed to approximate the optimal power flow in smart electric power grids by formulating a cost function that minimizes power losses, using a reduced set of linear equations, and decomposing them into block matrix equations to yield conditions for the lowest cost per kilowatt-hour delivered, while handling bus and branch control variables and dependent variables based on physical and operational constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional OPF models are used to ensure feasible power flow solutions under adverse conditions, then reliability is improved, but device complexity increases due to non-convex constraints and fully coupled network equations
Solution Approach 1:
The patent segments the complex OPF problem by introducing a slack bus that decouples the power flow equations. The network is divided into independent zones where each zone can be analyzed separately, reducing the fully coupled non-convex constraints into manageable segments while maintaining solution feasibility through the slack bus that absorbs power imbalances.
Solution Approach 2:
The patent transforms the traditional OPF formulation by changing the parameter representation from voltage-angle coordinates to a slack-bus-based coordinate system. This parameter transformation converts non-convex constraints into convex forms, making the problem computationally tractable while preserving the physical feasibility of solutions.
2Reliability
If traditional OPF models with full coupling are used to handle all network components, then reliability is improved, but productivity decreases due to computational burden
Solution Approach 1:
The patent applies segmentation by dividing the fully coupled network into independent zones using the slack bus approach. Each zone can be analyzed separately for contingency cases, dramatically reducing computational complexity while maintaining comprehensive coverage of all network components through systematic zone decomposition.
Solution Approach 2:
The patent uses partial action by focusing computational efforts on specific zones rather than analyzing the entire network simultaneously. The slack bus allows selective analysis of critical zones while simplifying or skipping analysis in less critical areas, improving solution speed without sacrificing essential reliability checks.
3Productivity
If decoupling is applied to reduce computational complexity, then productivity is improved, but reliability worsens due to loss of monotonicity properties in contingency analysis
Solution Approach 1:
The patent introduces the slack bus as an intermediary element that mediates between decoupled zones. This intermediary maintains the monotonicity property by ensuring that power imbalances are systematically accounted for, preserving the logical consistency of contingency analysis even when zones are analyzed separately.
Solution Approach 2:
The patent implements feedback mechanisms where solutions from decoupled zone analyses are aggregated and verified against overall network constraints. The slack bus provides feedback on power balance, ensuring that decoupled solutions maintain global feasibility and monotonicity properties through iterative correction.
4Adaptability or versatility
If traditional OPF models are used to control multiple network components, then adaptability is improved, but device complexity increases due to integer choice variables
Solution Approach 1:
The patent transforms the mixed-integer formulation into a continuous optimization problem by changing parameters from discrete switch positions to continuous control variables. This parameter transformation maintains the adaptability to control transformers, shunts, and other components while eliminating the computational complexity of integer programming.
Data Source
AI summary
A method for approximating an optimal power flow of a smart electric power grid includes providing a cost function that models a smart electric power grid having buses connected by branches, deriving a set of linear equations that minimize the cost function subject to constraints from an expression of an extremum of the cost function with respect to all arguments, reducing a dimension of the linear equations by solving for a subset of the linear equations, re-organizing the reduced dimension linear equations into primal and dual parts, and decomposing the re-organized reduced dimensional linear equations into two systems of block matrix equations which can be solved by a series of back substitutions. A solution of the two systems of block matrix equations yields conditions for a lowest cost per kilowatthour delivered through the smart electric power grid.