Distributed Power Flow Optimization via Dual Decomposition
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Solution Overview
Problem
Conventional methods for optimizing power flows in electric power networks are inefficient and do not effectively distribute computations, leading to sub-linear convergence and reliance on centralized solutions that do not utilize network topology.
Innovation Solution
The method employs a decomposition and coordination procedure that distributes the optimization problem into smaller, independent sub-problems using dualization of coupled constraints and semi-smooth equation theory for superlinear convergence, along with smoothing methods to ensure global convergence, even from initial parameters far from optimal.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If centralized optimization methods are used, then the optimization problem can be solved in a unified manner, but the computational efficiency and convergence speed are poor
Solution Approach 1:
The patent divides the centralized optimization problem into multiple distributed sub-problems, one for each bus in the power network. Each sub-problem is solved independently using local information and Lagrange multipliers, eliminating the need for a single centralized solver and significantly improving computational efficiency and convergence speed.
2Speed
If conventional subgradient method is used for dual decomposition, then the optimization problem can be distributed, but the convergence is sub-linear
Solution Approach 1:
The patent changes the parameter update rule from the conventional subgradient method to a Newton-based method that uses second-order derivative information (Hessian matrix). This parameter change in the optimization algorithm achieves superlinear convergence while maintaining the distributed structure of the dual decomposition approach.
3Reliability
If distributed optimization is implemented, then network topology can be exploited, but achieving global convergence from arbitrary initial parameters is difficult
Solution Approach 1:
The patent implements a feedback mechanism where Lagrange multipliers are updated based on the residual of the coupling constraints. This feedback loop continuously adjusts the distributed sub-problem solutions to ensure that the overall system constraints are satisfied, guaranteeing global convergence to the optimal solution regardless of initial parameter values.
Data Source
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AI summary
Power flow in an electric power network is optimized by first decomposing an optimization problem into a set of disjoint parameterized optimization problems. The disjoint optimization problems are independent of each other, and the decomposition is based on dualized coupled constraints having corresponding multipliers. Each optimization problem is solved independently to obtain a corresponding solution, and a sensitivity of each solution to changes in the parameter. The parameters are updated using the corresponding solutions and the sensitivities, and iterated until convergence.