# FPGA-Based Smart Sensor to Detect Current Transformer Saturation during Inrush Current Measurement

^{*}

## Abstract

**:**

## 1. Introduction

## 2. CT Saturation Detection Algorithm

#### 2.1. CT Model and Saturation

_{2}, and the inductance L

_{2}. In R

_{2}are included the secondary winding resistance and the burden resistance, while L

_{2}comprises the secondary leakage inductance and the burden inductance.

_{2}, is given by

_{2}is the current through the secondary winding, which using the nodal rule can be expressed as a function of the primary current, i

_{1}, and the magnetizing current, i

_{m}, as

_{1}and N

_{2}are the primary (commonly equal to 1) and secondary winding turns, respectively.

_{m}, which has different values of inductance for different states of operation. It has a high value under normal conditions (it tends to behave as if it is similar to an open-circuit) and a low value (it tends to behave as if it is similar to a short-circuit) when the CT is saturated. The magnetizing current i

_{m}is related to the flux by the saturation curve, a nonlinear function that characterizes the nonlinearity of L

_{m}. For the saturation detection algorithm developed in this section, it is not necessary to know the CT saturation curve in detail, because the detection is based only on the shape of the measured secondary current. However, it is necessary to know the information about the core flux and its behavior.

_{2}because under application of modern numerical relays the burden can be considered fully resistive [9], the magnetic flux in the core is given by

#### 2.2. Time-Domain Features

_{2}at the n instant, can be obtained as

_{3}, of a time-discrete series x(k) is defined as [30]

#### 2.3. Start of Saturation

- Set an initial threshold value, TH, equal to 0.05 pu;
- Set a third-moment threshold value, m
_{3TH}, equal to 0.003 pu; - Calculate in real time the two time-domain features (di
_{2}and m_{i}_{2,3}), with Equations (5) and (7), for the secondary CT current. To calculate m_{i}_{2,3}, it must be considered an overlap L equal to 10 samples; - Detect maximum or minimum local peaks in m
_{i}_{2,3}and compare them with the threshold value TH. If the absolute peak value is greater than the absolute value of existing TH, the latter will be updated with the peak value; - To detect the first CT saturation inception at n instant, it must be fulfilled that:
- If TH is positive, di
_{2}(n) must be negative with an absolute value greater than the threshold value; - If TH is negative, di
_{2}(n) must be positive and greater than the absolute threshold value;

- 6.
- The TH value is updated with the third part of di
_{2}(n) value, corresponding to the first CT saturation; - 7.
- The subsequent CT saturation inceptions are detected if:
- If TH is positive, di
_{2}(n) must be positive and greater than the threshold. In addition, m_{i}_{2,3}(n) or m_{i}_{2,3}(n − 1) must be different from zero and with an absolute value greater than m_{3TH}; - If TH is negative, di
_{2}(n) must be negative and lower than the threshold value. Furthermore, m_{i}_{2,3}(n) or m_{i}_{2,3}(n − 1) must be different from zero and with an absolute value greater than m_{3TH}.

#### 2.4. End of Saturation

_{2}values to obtain the CT flux. Because ${\mathsf{\varphi}}_{R}$ only displaces the flux about the vertical axis and R

_{2}scales the flux waveform, a pseudo-flux proportion to the actual flux can be obtained at the n time using the trapezoidal rule as

## 3. Smart Sensor

#### FPGA-Based Processor

## 4. Validation and Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Typical waveforms of different saturated secondary currents (dotted lines) against primary currents (solid line): large symmetrical current (

**top**), fault current (

**center**), and inrush current (

**bottom**).

**Figure 3.**Second-order difference function (di

_{2}) of a saturated inrush current (i

_{2}), and an enlargement of both signals during the first two saturation intervals.

**Figure 4.**Moving third-order central moment (m

_{i}

_{2,3}) of a saturated inrush current (i

_{2}), and an enlargement of both signals during the first two saturation intervals.

**Figure 5.**Flowchart of the CT saturation detection algorithm. (TH: threshold value, m

_{3TH}: third moment threshold value, i

_{2}: secondary CT current, m

_{i}

_{2,3}: moving third-order central moment, d

_{i}

_{2}: second-order difference function, n: sample number).

**Figure 12.**Performance of proposed algorithm on inrush currents for different resistive CT burdens: (

**a**) 0.8 Ω, (

**b**) 1 Ω, (

**c**) 1.5 Ω, (

**d**) 3 Ω.

**Figure 13.**Performance of proposed algorithm on fault currents for different resistive CT burdens: (

**a**) 0.8 Ω, (

**b**) 1 Ω, (

**c**) 1.5 Ω, (

**d**) 3 Ω.

**Figure 14.**Performance of proposed algorithm against Gaussian noise. Signal to noise ratio: (

**a**) 35 dB, (

**b**) 50 dB, (

**c**) 35 dB, (

**d**) 50 dB.

Processing Core | Logic Elements | Registers | 9-Bit Multipliers | Memory Bits | Clock Cycles |
---|---|---|---|---|---|

Second-order difference | 480 | 56 | 2 | 0 | 2 |

Third central moment | 1900 | 430 | 8 | 0 | 2L + 2(e + f) + 1 |

Integral | 494 | 74 | 2 | 0 | 2 |

Decision stage | 254 | 80 | 0 | 0 | 3 |

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## Share and Cite

**MDPI and ACS Style**

Martínez-Figueroa, G.d.J.; Córcoles-López, F.; Bogarra, S. FPGA-Based Smart Sensor to Detect Current Transformer Saturation during Inrush Current Measurement. *Sensors* **2023**, *23*, 744.
https://doi.org/10.3390/s23020744

**AMA Style**

Martínez-Figueroa GdJ, Córcoles-López F, Bogarra S. FPGA-Based Smart Sensor to Detect Current Transformer Saturation during Inrush Current Measurement. *Sensors*. 2023; 23(2):744.
https://doi.org/10.3390/s23020744

**Chicago/Turabian Style**

Martínez-Figueroa, G. de J., Felipe Córcoles-López, and Santiago Bogarra. 2023. "FPGA-Based Smart Sensor to Detect Current Transformer Saturation during Inrush Current Measurement" *Sensors* 23, no. 2: 744.
https://doi.org/10.3390/s23020744