Parallel AC Optimal Power Flow for Fast Jacobian and Hessian Computation
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Solution Overview
Problem
The complexity of optimal power flow problems in energy and utility operations leads to high computation costs and low solution quality due to the need for explicit computation of Jacobian and Hessian functions, especially with AC power flow constraints, which are typically approximated using direct current models.
Innovation Solution
The method employs multi-threaded parallelism to compute constraints, Jacobian functions, and Hessian of Lagrangian functions, using complex numbers instead of trigonometric functions, allowing for efficient computation and reuse of main burdens, thereby speeding up the process and improving solution quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If AC power flow constraints are considered directly with explicit computation of Jacobian and Hessian functions, then solution quality is improved, but computation complexity and cost increase significantly
Solution Approach 1:
The patent segments the computation of Jacobian and Hessian functions into multiple independent threads that can execute in parallel. The Hessian computation is divided into blocks corresponding to different constraints, with each thread computing a specific block independently. This segmentation reduces the sequential computation burden while maintaining the accuracy of AC power flow constraints.
Solution Approach 2:
The patent introduces parallelism as a new dimension for computation by utilizing multi-threaded architectures. Instead of computing Jacobian and Hessian functions sequentially in a single thread, the invention distributes computations across multiple threads simultaneously, effectively adding a temporal parallelism dimension to the computational process.
2Productivity
If DC power flow approximation is used instead of AC power flow constraints, then computation time is reduced, but solution accuracy deteriorates
Solution Approach 1:
The patent implements dynamic computation strategies where the level of approximation (DC vs AC) can be adjusted based on problem requirements and available computational resources. The system can dynamically switch between exact AC computations with parallel acceleration and approximate DC models, allowing adaptive balancing of speed and accuracy.
3Productivity
If multi-threaded parallelism is implemented for computing constraints, Jacobian functions, and Hessian, then computation speed is improved, but system complexity increases
Solution Approach 1:
The patent segments the computational workload into distinct threads handling different aspects: constraint evaluation, Jacobian computation, and Hessian computation. Each thread operates independently on its assigned tasks, reducing inter-thread dependencies and simplifying the overall system architecture while achieving parallel speedup.
Data Source
AI summary
An exemplary method includes solving on a computing system an optimal power flow formulation for a plurality of generators in a power system. The solving includes computing using multi-threaded parallelism a plurality of constraints for the formulation, computing using multi-threaded parallelism a plurality of Jacobian functions of the constraints, and computing using multi-threaded parallelism a Hessian of Lagrangian functions. The method further includes outputting results of the solving, wherein the results comprise values of generation levels for the plurality of generators. Apparatus and program products are also disclosed.