Single-Step Perturbation Initialization for Battery DAE Solvers
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Solution Overview
Problem
Conventional methods for initializing consistent initial conditions (ICs) in battery charging/discharging systems are inefficient, often requiring iterative processes and small step sizes, which can lead to solver inefficiencies and failures, especially when dealing with lithium-ion batteries, due to non-physical approximations and significant computational efforts.
Innovation Solution
A single-step method that uses a perturbation initialization and a switch function to estimate ICs for algebraic variables, allowing explicit solvers to solve differential algebraic equations (DAEs) directly without iterations, thereby reducing system stiffness and increasing robustness by enabling larger perturbation values and faster calculation of ICs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional initialization routines are used to calculate consistent initial conditions, then the DAE solver can obtain accurate ICs, but the computational time increases significantly and specific solvers are required
Solution Approach 1:
The patent applies preliminary action by performing a perturbation analysis before the main DAE solution to estimate consistent initial conditions. The method introduces a small perturbation parameter ε and solves a simplified system of equations first to obtain approximate ICs, which are then used as starting points for the main solver. This preliminary step avoids the need for complex iterative initialization routines during the main computation.
Solution Approach 2:
The patent uses parameter changes by transforming the original DAE system into a perturbed system with a small parameter ε. By solving the system for different values of ε and taking the limit as ε approaches zero, the method obtains consistent initial conditions. This parameter transformation approach converts a difficult initialization problem into a more tractable form that can be solved efficiently.
2Ease of operation
If non-physical approximations are used to estimate initial conditions, then the calculation is simpler, but the solver may fail when the true ICs differ significantly from the approximation
Solution Approach 1:
The patent introduces an intermediary perturbation parameter ε that acts as a bridge between the simplified non-physical approximation and the true physical system. By solving the perturbed system with small ε values, the method generates intermediate solutions that gradually approach the true physical initial conditions. This intermediary approach maintains simplicity while improving reliability by systematically correcting the non-physical approximations.
3Measurement precision
If very small step sizes are used in Euler backward step to calculate ICs, then the values are very near the initial time, but significant computational effort is required
Solution Approach 1:
The patent applies partial action by using a perturbation parameter ε that is small but not extremely small. Instead of using the极限 case of ε=0 or requiring multiple steps with very small step sizes, the method uses a single step with a moderate small value of ε to obtain sufficiently accurate initial conditions. This partial approach achieves the necessary precision without the excessive computational effort of using extremely small step sizes.
Data Source
AI summary
Battery models using robust fail-safe iteration free approach for solving Differential Algebraic Equations, and associated systems and methods are disclosed. In one embodiment, a method includes generating a model of the rechargeable battery; determining one or more initial conditions for one or more algebraic variables of the model using a solver; holding differential variables of the model static by a switch function while determining the one or more initial conditions; applying the initial conditions to the model by the switch function; and determining one or more parameters for the rechargeable battery by solving the algebraic and differential equations.