Multi-Dimensional Holomorphic Embedding for Power Flow Convergence

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Solution Overview

Problem

Current power system technologies face challenges in accurately and efficiently performing online voltage stability assessment and control, particularly with the increasing integration of distributed energy resources, due to limitations in existing numerical and analytical methods, which can lead to convergence issues and inaccuracies in voltage control.

Innovation Solution

A multi-dimensional holomorphic embedding method (MDHEM) is proposed, which embeds independent variables into power flow equations to derive analytical multivariate power series solutions for voltage control, allowing for non-iterative calculations and improved convergence, and a new remote voltage control approach using participation factor matrices to distribute reactive power effectively.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If iterative numerical methods (Newton-Raphson, Gauss-Seidel) are used for power flow calculation, then the method can handle complex power systems, but convergence issues occur and computational time increases

Engineering Contradiction:

Improveconvergence reliabilityVSAvoidcomputational time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent replaces iterative numerical methods with an analytical power flow method based on holomorphic embedding and Padé approximants. This substitution eliminates the iterative mechanical process by deriving closed-form analytical solutions, thereby resolving the contradiction between convergence reliability and computational time.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent transforms the power flow equations by embedding a complex parameter s and applying Padé approximants to convert the analytical solution into a rational function form. This parameter transformation enables the method to achieve both fast computation and guaranteed convergence by avoiding iterative numerical procedures.

Inventive Principle:

Principle #35Parameter changes

2Reliability

If remote voltage control is implemented using conventional power flow methods, then voltage stability can be maintained, but the Jacobian matrix extension reduces convergence speed

Engineering Contradiction:

Improvevoltage stabilityVSAvoidconvergence speed

Core Design Contradiction:

ReliabilityVSSpeed

Solution Approach 1:

The patent replaces the conventional iterative power flow method with an analytical approach based on holomorphic embedding. This substitution eliminates the need to extend and repeatedly invert the Jacobian matrix, thereby maintaining voltage stability control while achieving fast computation without convergence issues.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

3Measurement precision

If iterative methods are used for online voltage stability assessment, then detailed analysis can be performed, but the method is not suitable for real-time applications

Engineering Contradiction:

Improvevoltage stability assessment accuracyVSAvoidreal-time processing capability

Core Design Contradiction:

Measurement precisionVSProductivity

Solution Approach 1:

The patent substitutes iterative numerical methods with an analytical power flow method that provides closed-form solutions. This enables real-time online voltage stability assessment with high precision by eliminating iterative computation, thereby achieving both measurement precision and real-time processing capability.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

4Ease of operation

If numerical iteration divergence is interpreted as voltage collapse, then a simple criterion is established, but ghost solutions may be converged to

Engineering Contradiction:

Improvevoltage collapse detection simplicityVSAvoidsolution physical existence

Core Design Contradiction:

Ease of operationVSReliability

Solution Approach 1:

The patent replaces iterative numerical methods with an analytical approach using holomorphic embedding and Padé approximants. This substitution eliminates the problem of ghost solutions by providing a unique analytical solution that can be verified for physical existence, while maintaining simple voltage collapse detection criteria.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS11271398B2Voltage stability assessment, control and probabilistic power flow based on multi-dimensional holomorphic embedding techniques

Publication Date: 2022.03.08 UNIVERSITY OF TENNESSEE RESEARCH FOUNDATION

AI summary

A multi-dimensional holomorphic embedding method for voltage control of an AC power system includes embedding multiple independent symbolic variables representing multiple control elements of the AC power system into AC power flow equations that describe the AC power system, analytically solving voltages for targeted buses of the AC power system in a form of multivariate power series or multivariable Padé approximants about the multiple independent symbolic variables such that coefficients of the multivariate power series or multivariable Padé approximants are obtained non-iteratively, and jointly adjusting the multiple control elements according to the multivariate power series or multivariable Padé approximants to control voltages of the targeted buses.