# Laboratory Calibration of Energy Measurement Systems (EMS) under AC Distorted Waveforms

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## Abstract

**:**

## 1. Introduction

## 2. Calibration Setups

- power source that should generate high voltages and high currents as required in the current standard EN 50463-2;
- reference measurement system (voltage, respectively current sensors, digitizers and data treatment algorithm to determine the requested quantities);
- device under test.

#### 2.1. LNE Calibration Set-Up

#### 2.1.1. Current Generation with Arbitrary Waveforms

#### 2.1.2. Reference Measuring System

^{20}repetitions).

#### 2.1.3. Characterization and Corrections Implementation

_{0}, H

_{k}—the modules of the continuous component, respectively of the harmonics order k, φ

_{k}—the arguments of the harmonics k with respect to the fundamental, T—the period of the fundamental component.

^{Corrected}.

#### 2.2. FFII-LCOE Calibration Set-Up

#### 2.2.1. Scheme of the Calibration Set-Up

#### 2.2.2. Calibration Setup Implementation

## 3. Uncertainty Estimation

#### 3.1. Model Functions for Uncertainty Estimation of Active and Reactive Power and Energy

- V
_{rms}(t_{j}), I_{rms}(t_{j}), P(t_{j})—the RMS voltage, current and, respectively active power at t_{j}instant; - S(t
_{j}), N(t_{j})—the apparent, respectively the non-active power for a period starting at t_{j}instant; - E
_{p}, N_{Q}—the active energy, respectively the non-active energy in the measuring interval; - δ
_{x}factors represent the relative errors introduced by the devices composing the setups.

#### 3.2. Uncertainty Budget

_{ref}is the power indicated by the reference system; P

_{DUT}is the power indicated by the Device Under Test.

_{DUT})—the standard uncertainty of the power indicated by the DUT. This component is given by the standard deviation of the number of performed repetitions for a given power; u(P

_{Ref})—the standard uncertainty of the power indicated by the reference system. Its estimation is performed according to the description of Section 3.1.

_{Ref}, I

_{Ref}are the RMS values of the u(t), respectively i(t) signals and φ

_{Ref}represent their phase shift. These three quantities are independent.

_{Ref}. The probability density function of all input quantities was considered as normal thus representing the same input uncertainties as used in the GUF method. The calculation itself used the same equations as for the GUF method. The Monte Carlo method works by repeating the calculation of output uncertainties many times with input uncertainties randomized according probability density functions. The number of repetitions (cycles) has to be found out in every particular case. The value of relative uncertainty of u(P

_{Ref})/S was stable to 1% for the number of Monte Carlo cycles greater than 10

^{5}. For all final calculations, the number of Monte Carlo cycles was set to 10

^{6}.

_{Ref})/S calculated by Monte Carlo method follows a normal distribution and is very similar to the value calculated by GUF as outlined in Table 3.

_{Ref})/S calculated by Monte Carlo for both sine wave and 90° phase-fired current waveform at different values of $cos\left({\phi}_{Ref}\right)$. While the uncertainties calculated using GUF (or Monte Carlo with sine waveform) are linearly dependent on the $cos\left({\phi}_{Ref}\right)$, the dependence of uncertainties calculated for phase fired waveform shows very nonlinear behaviour. The smaller uncertainties can be contributed to the nonlinear character of the equations manifesting in the case of complex waveform. Up to it, the special shape of phase fired waveform causes the output uncertainty is decreasing faster for higher values of $cos\left({\phi}_{Ref}\right)$.

## 4. Calibration Procedure

- Before carrying out any test, both voltage and current waveforms have to be synchronized to control the phase displacement between both signals.
- Accuracy test without harmonic content: Voltage and current waveforms at the fundamental frequency of the EMS are applied to the current loop.

_{EMS}) shall not exceed the limits given in Table 4 due to variations in input quantities (current, voltage and power factor or sinφ) given in this table. U

_{n}and I

_{n}are the rated primary voltage, respectively current of the EMF. These error limits shall apply to the measurement of energy in each direction (generated or consumed).

_{min2}, U

_{min1}, and U

_{max2}voltage values are given in EN 50163 [13], depending on the rated voltage of the EMS under calibration.

- 3.
- Accuracy test with harmonics in the voltage circuit: This test is carried out applying different harmonic contents in the voltage waveform. The ε
_{EMS}error with harmonic components in the voltage waveform shall also be measured at the points indicated in Table 5.

- 4.
- Accuracy test with harmonics in the current circuit: this test is carried out applying different harmonic contents in the current waveform. The ε
_{EMS}error with harmonic components in the voltage waveform shall also be measured at the points indicated in Table 6.

- 5.

- 6.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**Low voltage circuits used for generating both voltage u(t) and current i(t) waveforms using a programmable for arbitrary waveforms and the other one for the fundamental waveform.

**Figure 7.**Lay-out of the high current circuit and the high voltage circuit when an EMS is under calibration.

**Figure 8.**(

**a**) Limits for voltage harmonic components, (

**b**) Limits for current harmonic components. Note: HRM = Harmonic.

**Figure 10.**Active power uncertainties relative to the apparent power computed with Monte Carlo method.

$\mathit{c}\mathit{o}\mathit{s}\left({\mathit{\phi}}_{\mathit{R}\mathit{e}\mathit{f}}\right)$ | Uncertainty Sources | Standard Uncertainty | Sensitivity Coefficient | Contribution to the u(P_{ref}) | $\frac{\mathit{u}\left({\mathit{P}}_{\mathit{R}\mathit{e}\mathit{f}}\right)}{\mathit{S}}$ (k = 1) |
---|---|---|---|---|---|

1 | $\frac{u\left({U}_{Ref}\right)}{{U}_{Ref}}$ | 52.7 µV/V | 1 | 52.7 | 539.2 µW/VA |

$\frac{u\left({I}_{Ref}\right)}{{I}_{Ref}}$ | 536.6 µA/A | 1 | 536.6 | ||

$u\left({\phi}_{Ref}\right)$ | 175.2 µrad | 0 | 0 | ||

0.8 | $\frac{u\left({U}_{Ref}\right)}{{U}_{Ref}}$ | 52.7 µV/V | 0.8 | 42.2 | 444.0 µW/VA |

$\frac{u\left({I}_{Ref}\right)}{{I}_{Ref}}$ | 536.6 µA/A | 0.8 | 429.3 | ||

$u\left({\phi}_{Ref}\right)$ | 175.2 µrad | 0.6 | 105.1 | ||

0.5 | $\frac{u\left({U}_{Ref}\right)}{{U}_{Ref}}$ | 52.7 µV/V | 0.5 | 26.35 | 309.4 µW/VA |

$\frac{u\left({I}_{Ref}\right)}{{I}_{Ref}}$ | 536.6 µA/A | 0.5 | 268.3 | ||

$u\left({\phi}_{Ref}\right)$ | 175.2 µrad | 0.87 | 152.4 |

Waveform | Expanded Uncertainty |
---|---|

90° phase-fired waveform with phase shift of 0° with voltage | 0.23% |

45° phase-fired waveform with phase shift of 0° with voltage | 0.20% |

135° phase-fired waveform with phase shift of 0° with voltage | 0.47% |

Burst-fired waveform with phase shift of 0° with voltage | 0.20% |

**Table 3.**Mean values of u(P

_{Ref})/S for one standard uncertainty (equivalent to a coverage factor of 1).

$\mathit{c}\mathit{o}\mathit{s}\left({\mathit{\phi}}_{\mathit{R}\mathit{e}\mathit{f}}\right)$ | 1 | 0.8 | 0.5 |
---|---|---|---|

Monte Carlo | 541.32 | 447.38 | 311.96 |

GUF | 539.2 | 444.0 | 309.4 |

**Table 4.**EMS error limits according to EN 50463-2 [4].

Current Range | Voltage Range | Power Factor Sin φ | Error Limit, Active Energy | Error Limit, Reactive Energy |
---|---|---|---|---|

10% I_{n} ≤ I < 120% I_{n} | U_{min1} ≤ U < U_{max2} | PF ≥ 0.85 sinφ = 1 | 1.5% | 3.0% |

Value of Voltage | Value of Current | Phase Shift | Additional Percentage Error | |
---|---|---|---|---|

For Active Energy | For Reactive Energy | |||

U_{0} = U_{n} with U_{5} = 10% U_{n} and U_{5} = 10% U_{n} + [U_{11} = 3% U_{n}^{(1)}] or [U_{3}=3% U_{n}^{(2)}] | I_{0} = 50% I_{n}without harmonic | Cos φ = 1 for active; sen φ = 1 for reactive | According to the manufacturer specification (not defined in the standard for EMS) |

^{(1)}and 16.7 Hz

^{(2)}in railway systems.

Value of Voltage | Value of Current | Phase Shift | Additional Percentage Error | |
---|---|---|---|---|

For Active Energy | For Reactive Energy | |||

U_{0} = U_{n} without harmonic | I_{0} = 50% I_{n} with I_{5} = 40%I_{n} and I_{0} = 50% I_{n} with I_{13} = 5%I_{n} + [I_{11} = 13%I_{n}^{(1)}] or [I_{4} = 9%I_{n}^{(2)}] | Cos φ = 1 for active; sin φ = 1 for reactive | According to the manufacturer specification (not defined in the standard for EMS) |

^{(1)}and 16.7 Hz

^{(2)}in railway systems.

Value of Voltage | Value of Current | Phase Shift | Additional Percentage Error | |
---|---|---|---|---|

For Active Energy | For Reactive Energy | |||

U_{0} = U_{n} without harmonic | I_{0} = 50% I_{n}Phase-fired waveform | Cos φ = 1 for active; sin φ = 1 for reactive | According to the manufacturer specification (not defined in the standard for EMS) |

Value of Voltage | Value of Current | Phase Shift | Additional Percentage Error | |
---|---|---|---|---|

For Active Energy | For Reactive Energy | |||

U_{0} = U_{n} without harmonic | I_{0} = 50% I_{n}Burst-fired waveform | Cos φ = 1 for active; sen φ = 1 for reactive | According to the manufacturer specification (not defined in the standard for EMS) |

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**MDPI and ACS Style**

Istrate, D.; Khamlichi, A.; Soccalingame, S.; Rovira, J.; Fortune, D.; Sira, M.; Simon, P.; Garnacho, F.
Laboratory Calibration of Energy Measurement Systems (EMS) under AC Distorted Waveforms. *Sensors* **2020**, *20*, 6301.
https://doi.org/10.3390/s20216301

**AMA Style**

Istrate D, Khamlichi A, Soccalingame S, Rovira J, Fortune D, Sira M, Simon P, Garnacho F.
Laboratory Calibration of Energy Measurement Systems (EMS) under AC Distorted Waveforms. *Sensors*. 2020; 20(21):6301.
https://doi.org/10.3390/s20216301

**Chicago/Turabian Style**

Istrate, Daniela, Abderrahim Khamlichi, Soureche Soccalingame, Jorge Rovira, Dominique Fortune, Martin Sira, Pascual Simon, and Fernando Garnacho.
2020. "Laboratory Calibration of Energy Measurement Systems (EMS) under AC Distorted Waveforms" *Sensors* 20, no. 21: 6301.
https://doi.org/10.3390/s20216301