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Extended SINDICOMP: Characterizing MV Voltage Transformers with Sine Waves^{ †}

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

## 3. Using Sine Waves for the Measurement of the VT Frequency Behavior

#### 3.1. Preliminary Consideration and Scope of the Technique

- Waveforms composed by a fundamental tone, at 50 Hz and rated amplitude and a harmonic tone with fixed amplitude (1% of fundamental tone) and variable frequency and phase angle (in the following, this kind of test will be referred to as FH1, that stands for Fundamental and one Harmonic tone). Here, SINDICOMP is not yet applied.
- Sine waves with reduced amplitude (40 V) and variable frequency (in the following, this kind of test will be referred to as SFS, which stands for Sinusoidal Frequency Sweep).

- using SINDICOMP to compensate for the non-linearity effects;

#### 3.2. First Step: Non Linearity Compensation

- the subscripts “p” and “s” stand for primary and secondary side respectively;
- the primary quantities are here referred to the primary side of the transformer, so that the transformation ratio does not explicitly appear (that is the quantities at the secondary side are multiplied by the rated ratio of the VT);
- ${\dot{Z}}^{*}$ and ${\overline{I}}_{m,h}$ are, respectively, the equivalent VT leakage series impedance and the h-harmonic component of the magnetization current;
- the superscript “d” and “sin” refer to tests performed under distorted and sinusoidal conditions.

#### 3.3. Second Step: Approximated Voltage Transformer (VT) Frequency Response

- ${k}_{r}=\raisebox{1ex}{${V}_{p,r}$}\!\left/ \!\raisebox{-1ex}{${V}_{s,r}$}\right.$ is the rated transformation ratio (${V}_{p,r}$ and ${V}_{s,r}$ are the rated primary and secondary voltages);
- ${V}_{p,h}$ and ${V}_{s,h}$ are the root mean square (rms) values of the primary and secondary h-order harmonic voltage;
- ${\phi}_{p,h}$ and ${\phi}_{s,h}$ are phase angles of the primary and secondary h order harmonic voltage.

## 4. Measurement Setup

_{s}equal to 50 kHz, the time window chosen is 1 s and ten repetitions are executed for each test. The Discrete Fourier Transform (DFT) is performed on the acquired samples and the phasors of the voltages at VT primary and secondary side are measured.

## 5. Application of E-SINDICOMP to Various Voltage Transformer (VTs)

#### 5.1. Test Description

#### 5.2. Identification of the D_{lim} Value

#### 5.3. VT 1 Characterization

#### 5.4. VT2 Characterization

#### 5.5. VT3 Characterization

#### 5.6. Burden Effect

## 6. Conclusions

- E-SINDICOMP requires two measurement steps for the frequency characterization of MV VTs, the first of which, executed at power frequency, is identical to the standard procedure for VT calibration [20], so that every VT calibration laboratory is able to perform it.
- The second measurement step involves the generation and measurements of sine waves at some tens of volt and up to some kilohertz, again requiring measuring instrumentation generally available in most electrical measurement laboratories.
- E-SINDICOMP has been applied to three different commercial MV VTs, showing a good performance improvement with respect to the use of the widely adopted low voltage sinusoidal frequency sweep technique.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Ratio error of the Voltage Transformer (VT) evaluated performing FH1 (square marker) and SFS (circle marker) characterization tests.

**Figure 2.**Phase error of the Voltage Transformer (VT) evaluated performing FH1 (square marker) and SFS (circle marker) characterization tests.

**Figure 3.**Graphical description of the proposed procedure for the identification of the Voltage Transformer (VT) frequency response.

**Figure 4.**Behavior of the frequency derivative of the Voltage Transformer (VT) ratio error from the SFS test. The point [${f}_{Dlim}$, ${D}_{lim}$] identifies the limit beyond which the linear effects affecting the ratio error are predominant.

**Figure 5.**Setup for the Voltage Transformer (VT) characterization: (

**a**) block diagram, (

**b**) generation and measurement circuit at Italian National Metrology Institute (INRIM).

**Figure 6.**VT1 (square marker), VT2 (circle marker) and VT3 (triangle marker): SFS ratio error up to resonance frequency (inset: zoom up to ${f}_{Dlim}$) (

**a**) and their derivative curves $D$ (

**b**).

**Figure 7.**VT1 ratio error deviation vs frequency with different values for ${D}_{lim}$ and ${f}_{Dlim}$.

**Figure 8.**VT1: FH1 ratio error with linearity compensation (with SINDICOMP) and without linearity compensation (NO SINDICOMP) (

**a**); comparison of ratio errors obtained with REF (FH1 with SINDICOMP), SFS and E-SINDICOMP (

**b**).

**Figure 9.**VT1: FH1 phase error with linearity compensation (with SINDICOMP) and without linearity compensation (NO SINDICOMP) (

**a**); comparison of phase errors obtained with REF (FH1 with SINDICOMP) and SFS (E-SINDICOMP phase error is equal to SFS phase error) (

**b**).

Name | Primary Voltage (kV) | Secondary Voltage (V) | Rated Burden (VA) | Accuracy Class | First Resonance Frequency f_{r} (kHz) |
---|---|---|---|---|---|

VT1 | 20/√3 | 100/√3 | 50 | 0.5 | 5.5 |

VT2 | 11/√3 | 110/√3 | 50 | 0.5 | 9.2 |

VT3 | 20 | 100 | 50 | 0.2 | 2.0 |

**Table 2.**Selected ${D}_{lim}$ and ${f}_{Dlim}$ values of the investigated Voltage Transformer (VTs).

DUT | ${\mathit{D}}_{\mathit{l}\mathit{i}\mathit{m}}$ (0.01/Hz) | ${\mathit{f}}_{\mathit{D}\mathit{l}\mathit{i}\mathit{m}}\phantom{\rule{0ex}{0ex}}\mathbf{\left(}\mathbf{Hz}\mathbf{\right)}$ | ${\mathit{f}}_{\mathit{l}\mathit{i}\mathit{m}}\phantom{\rule{0ex}{0ex}}\mathbf{\left(}\mathbf{Hz}\mathbf{\right)}$ |
---|---|---|---|

VT1 | −0.15 | 2500 | 800 |

VT2 | −0.14 | 4000 | 1600 |

VT3 | −0.14 | 800 | 300 |

Frequency (Hz) | Ratio Error Deviation (%) | Phase Error Deviation (mrad) SFS-REF | |
---|---|---|---|

SFS-REF | E-SINDICOMP-REF | ||

100 | −0.36 | 0.03 | 0.93 |

200 | −0.54 | −0.0039 | −0.19 |

300 | −0.72 | 0.022 | −0.11 |

700 | −1.19 | 0.22 | 1.22 |

1000 | −1.27 | −0.031 | 1.28 |

1250 | −1.28 | −0.38 | 1.26 |

1500 | −1.29 | −0.69 | 1.26 |

1750 | −1.29 | −0.93 | 1.20 |

2000 | −1.27 | −1.0 | 1.21 |

Frequency (Hz) | Ratio Error Deviation (%) | Phase Error Deviation (mrad) SFS-REF | |
---|---|---|---|

SFS-REF | E-SINDICOMP-REF | ||

100 | −0.24 | −0.03 | 0.57 |

500 | −0.47 | −0.01 | −0.31 |

1000 | −0.62 | 0.12 | 0.07 |

1500 | −0.68 | 0.31 | 0.35 |

2000 | −0.69 | −0.01 | 0.41 |

2500 | −0.69 | −0.21 | 0.39 |

3000 | −0.69 | −0.43 | 0.38 |

3500 | −0.67 | −0.56 | 0.34 |

Frequency (Hz) | Ratio Error Deviation (%) | Phase Error Deviation (mrad) SFS-REF | |
---|---|---|---|

SFS-REF | E-SINDICOMP-REF | ||

200 | −0.86 | −0.21 | −0.052 |

300 | −1.14 | 0.120 | −0.27 |

500 | −0.96 | −0.19 | −1.03 |

700 | −0.91 | −0.77 | −0.56 |

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**MDPI and ACS Style**

Crotti, G.; D’Avanzo, G.; Giordano, D.; Letizia, P.S.; Luiso, M.
Extended SINDICOMP: Characterizing MV Voltage Transformers with Sine Waves. *Energies* **2021**, *14*, 1715.
https://doi.org/10.3390/en14061715

**AMA Style**

Crotti G, D’Avanzo G, Giordano D, Letizia PS, Luiso M.
Extended SINDICOMP: Characterizing MV Voltage Transformers with Sine Waves. *Energies*. 2021; 14(6):1715.
https://doi.org/10.3390/en14061715

**Chicago/Turabian Style**

Crotti, Gabriella, Giovanni D’Avanzo, Domenico Giordano, Palma Sara Letizia, and Mario Luiso.
2021. "Extended SINDICOMP: Characterizing MV Voltage Transformers with Sine Waves" *Energies* 14, no. 6: 1715.
https://doi.org/10.3390/en14061715