## 1. Introduction

Understanding the calculation of equivalent full cycles in lithium-ion batteries is essential for accurate monitoring and maintenance. This guide explains how to adjust for capacity degradation and compute the equivalent full cycles over time.

## Adjusting for Capacity Degradation

### Dynamic Full Capacity

**Monitor Capacity:**Continuously estimate the current capacity of the battery, which degrades over time.**Update Calculations:**Use the current (degraded) capacity instead of the original capacity for calculating equivalent full cycles.

## 2. Cycle Calculation with Degraded Capacity

### Method

At each partial cycle, determine the equivalent capacity usage based on the current capacity of the battery.

**Formula:**

Equivalent Full Cycles = Σ (Discharge (or Charge) Amount / Current Full Capacity)

## 3. Steps to Calculate Equivalent Full Cycles with Degradation

### Track and Estimate Capacity Degradation

Use methods such as empirical models, historical data, or state-of-health (SoH) algorithms to estimate the current capacity of the battery at regular intervals.

### Monitor Partial Cycles

Continuously monitor the battery’s state of charge (SoC) to record the amount of charge and discharge in each partial cycle.

### Calculate Equivalent Usage

For each partial cycle, calculate the equivalent full cycle contribution using the current estimated capacity.

#### Example Calculation:

Suppose the initial full capacity is 1000 mAh.

### Aggregate Equivalent Full Cycles

Sum the equivalent cycles over time to get the total equivalent full cycles.

#### Example:

**First Partial Cycle:**Discharged by 200 mAh and recharged by 150 mAh. Equivalent Full Cycle Contribution = 200 mAh / 900 mAh = 0.222 cycles**Second Partial Cycle:**Discharged by 250 mAh and recharged by 200 mAh. Equivalent Full Cycle Contribution = 250 mAh / 900 mAh = 0.278 cycles**Total Equivalent Full Cycles after these two partial cycles:**Total Equivalent Full Cycles = 0.222 + 0.278 = 0.5 cycles

## 4. Practical Implementation

### Capacity Estimation

Implement algorithms within the Battery Management System (BMS) to estimate the current capacity regularly. Methods could include cycle counting, impedance measurement, or machine learning models trained on historical degradation data.

### Cycle Tracking and Aggregation

Use the BMS or monitoring software to track partial charges and discharges. Calculate the equivalent full cycle contribution for each partial cycle based on the current capacity estimate. Sum these contributions over time to get the total equivalent full cycles.

### Example Scenario with Capacity Degradation

#### Initial Capacity

Battery starts with a full capacity of 1000 mAh.

#### First Partial Cycle (Initial Capacity)

Discharged by 200 mAh and recharged by 150 mAh. Equivalent Full Cycle Contribution = 200 mAh / 1000 mAh = 0.2 cycles

#### Capacity Degrades

Estimated current capacity is now 950 mAh.

#### Second Partial Cycle (Degraded Capacity)

Discharged by 300 mAh and recharged by 250 mAh. Equivalent Full Cycle Contribution = 300 mAh / 950 mAh = 0.316 cycles

### Aggregate Cycles

Total equivalent full cycles after these partial cycles: Total Equivalent Full Cycles = 0.2 + 0.316 = 0.516 cycles

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