# Solving Power System Differential Algebraic Equations Using Differential Transformation

## TL;DR

This paper introduces a non-iterative differential transformation method to efficiently solve power system DAEs, including both state and non-state variables, demonstrating improved speed and reliability over traditional numerical approaches.

## Contribution

The paper develops a novel non-iterative analytical approach using differential transformation for solving power system DAEs, including non-state variables, with demonstrated efficiency.

## Key findings

- Faster solution times compared to traditional methods.
- Reliable and accurate results on a large-scale power system.
- Effective handling of nonlinear coupled equations without iteration.

## Abstract

This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules instead of calculating high order derivatives and has proved to be effective in solving state variables of nonlinear differential equations in our previous study. This paper further solves non-state variables, e.g. current injections and bus voltages, directly with a realistic DAE model of power grids. These non-state variables, nonlinearly coupled in network equations, are conventionally solved by numerical methods with time-consuming iterations, but their differential transformations are proved to satisfy formally linear equations in this paper. Thus, a non-iterative algorithm is designed to analytically solve all variables of a power system DAE model with ZIP loads. From test results on a Polish 2383-bus system, the proposed method demonstrates fast and reliable time performance compared to traditional numerical methods.

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Source: https://tomesphere.com/paper/1903.00935