# Influence of Background Voltage Distortion on Operation of Passive Harmonic Compensation Devices

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Method for Determination the Share Contribution of Harmonic Sources

_{S}at the point of common coupling (PCC) in Figure 1. Several consumers can be connected at this point. Typically, an industrial consumer is connected through its own supply transformer (T) to the PCC. Load 1 and load 2 of consumer 1 can include nonlinear and linear loads. Current harmonics injected by consumer 1 affect the voltage quality at the PCC (at the high voltage side of the transformer) and at the consumer buses. This nonlinear load refers to the internal distortion source (connected at the low voltage side of the transformer). Other consumers with nonlinear loads connected to the PCC are considered as external distortion sources. These consumers are sources of background voltage harmonics at the PCC and at the consumer buses. Also, harmonic currents flow through the transformer of consumer 1 from the nonlinear load of other consumers. These currents will be called background harmonic currents.

_{3h}is the background voltage harmonic distortion, U

_{PCCh}is the voltage harmonic distortion at the PCC, U

_{Ch}is the voltage harmonic distortion at the consumer bus, I

_{01h}is the nonlinear load harmonic current of Load 1, I

_{02h}is the nonlinear load harmonic current of Load 2, I

_{Ch}is the supply feeder harmonic current of the consumer, I

_{1h}is the total harmonic current of Load 1, I

_{2h}is the total harmonic current of Load 2, I

_{Z1h}is the linear load harmonic current of Load 1, I

_{Z2h}is the linear load harmonic current of Load 2, I

_{Fh}is the harmonic current of the passive filter, Z

_{Sh}is the energy system equivalent of harmonic impedance, Z

_{1h}is the equivalent harmonic impedance of Load 1, Z

_{2h}is the equivalent harmonic impedance of Load 2, Z

_{Fh}is the equivalent harmonic impedance of the shunt passive filter, Z

_{Th}is the harmonic impedance of the supply transformer and S is the switch.

_{Σh}is the equivalent harmonic impedance of the scheme; U

_{01h}is the harmonic voltage, which is obtained when current I

_{01h}flows through Z

_{Σh}; U

_{02h}Is the harmonic voltage, which is obtained when current I

_{02h}flows through Z

_{Σh}. Based on Equation (1), the following equations can be obtained:

_{01h}and I

_{02h}onto the total harmonic current vector (I

_{01h}+ I

_{02h}), the Equations (2) and (3) can be written as follows:

_{1Dh}, K

_{2Dh}are the contributions of distortion sources to the total voltage distortion at the consumer bus; ψ

_{01h}, ψ

_{02h}are the phase angles of nonlinear load harmonic currents I

_{01h}and I

_{02h}, respectively; ψ

_{012h}is the phase angle of the total harmonic current of nonlinear loads (I

_{01h}+ I

_{02h}).

_{01h}and I

_{02h}, as well as their summation, seems difficult, especially in the presence of external distortion sources. This paper proposes the application of a shunt passive harmonic filter to solve this problem. Consider the following case.

^{th}harmonic frequency is zero. In this case, harmonic currents I

_{Z1h}and I

_{Z2h}become zero. The harmonic currents of the nonlinear load I

_{01h}and I

_{02h}flow entirely through the filter circuit, as follows:

_{1h}and I

_{2h}) and the passive filter I

_{Fh}, it is possible to determine the contributions of distortion sources to the total voltage distortion at the consumer bus. It should be noted that if there is an external source of distortion and an ideal passive filter (with zero impedance at the h

^{th}harmonic frequency) is connected, the harmonic current arising from the source U

_{3h}flows entirely through the passive filter circuit at the h

^{th}harmonic frequency and there is no problem in determining the contribution of the external distortion source.

_{1h}and I

_{2h}corresponds to a certain error of the currents I

_{01h}and I

_{02h}. An estimation of such an error is given in [38,39] and is insignificant due to the fact that the harmonic impedance of the filter at the h

^{th}harmonic frequency is significantly less than the harmonic impedance of Load 1 and Load 2 of the consumer at the same frequency. Then harmonic currents I

_{1h}and I

_{2h}flow through the supply feeder circuit and the passive filter circuit at the h

^{th}harmonic frequency. So, the equivalent harmonic current, equal to the sum of harmonic currents I

_{1h}and I

_{2h}, can be determined by measuring the harmonic currents in the supply feeder circuit I

_{Ch}and the passive filter circuit I

_{Fh}. Thus, the contributions of consumer loads can be determined by measuring the currents I

_{Ch}, I

_{Fh}, I

_{1h}and I

_{2h}. The Equations (4) and (5) can be written as follows:

_{1h}, ψ

_{2h}are the phase angles of harmonic currents I

_{1h}and I

_{2h}, respectively; ψ

_{12h}is the phase angle of the harmonic current obtained by summing the supply feeder harmonic current I

_{Ch}and the passive filter harmonic current I

_{Fh}.

_{3h}(background harmonic current) will reduce the harmonic current I

_{Ch}to I’

_{Ch}according to the superposition principle. Further, flowing through the passive filter circuit at the h

^{th}harmonic frequency, the background harmonic current will increase the harmonic current I

_{Fh}to I’

_{Fh}. But the sum of these harmonic currents will remain practically unchanged (I

_{Ch}+ I

_{Fh}≈ I’

_{Ch}+ I’

_{Fh}). This property of the proposed method allows one consumer, regardless of external conditions (presence of background distortions), to determine the most significant load connections in order to further compensate for distortions.

_{3h}. Based on Figure 2, in accordance with the indicated current directions, the harmonic voltage U

_{3h}and the contribution of the external distortion source K

_{3Dh}can be determined by Equations (9) and (10):

_{3Dh}will determine the maximum current addition to the passive harmonic filter overload. When using shunt active harmonic filters, which eliminate the influence of internal distortion sources, the contribution identified by Equation (10) is also important. It shows the maximum possible value of the harmonic voltage that will remain on the consumer buses if the influence of internal distortion sources is completely eliminated.

#### 2.2. Description of Simulation Model and Parameters

_{UR}, R

_{TPR}and R

_{TR}, respectively. The inductor Ls1 with internal resistance Rs1 represents the energy system impedance. The inductor Ls2 with internal resistance Rs2 represents the impedance of the supply transformer through which the consumer is connected to the PCC.

_{TR}and the parameters of the supply feeder Z

_{S2}were varied by changing the step of regulation (step 1–step 4).

_{TR}and the parameters of the supply feeder Z

_{S2}were varied by the changing step of regulation (step 1–step 4).

_{TR}and the parameters of the supply feeder Z

_{S2}were varied by changing the step of regulation (step 1–step 4). For different load compositions (mode 1—all consumer loads are connected, mode 2—all consumer loads are connected except UR, mode 3—all consumer loads are connected except TPR), the following values of the SPHF harmonic currents were measured:

- -
- The SPHF harmonic current when external distortion source TR is disconnected and all consumer loads are connected for the corresponding mode (I
_{Fh_0}); - -
- The SPHF harmonic current when external distortion source TR is connected and all consumer loads are connected for the corresponding mode (I
_{Fh_1}); - -
- The SPHF harmonic current when external distortion source TR is connected and all consumer loads (except SPHF) are disconnected (I
_{Fh_2}).

_{F1h}= I

_{Fh_1}/I

_{Fh_0}shows the real addition to the SPHF harmonic current from an external distortion source, since the total SPHF harmonic current is a geometric summation of the components from all distortion sources. The value ΔI

_{F2h}= I

_{Fh_2}/I

_{Fh_0}shows the maximum addition to the SPHF harmonic current from an external distortion source, since there are no components from internal distortion sources.

## 3. Results and Discussion

#### 3.1. Simulation Results

#### 3.1.1. Contribution of Internal Distortion Sources Depending on the Parameters of the External Source and the Supply Feeder

_{S2}was varied by changing the regulation step (Step 1 to Step 4) according to the values in Table 1.

_{Dh}for UR and TPR were calculated using the following expression:

_{Dh1}is the share contribution of the consumer load when TR is disconnected and K

_{Dh2}is the share contribution of the consumer load when TR is connected.

_{TR}= 20 Ω).

#### 3.1.2. Contribution of External Distortion Sources Depending on the Parameters of the Supply Feeder

_{3Dh}depending on the resistance R

_{TR}and the impedance of the supply feeder. All electrical loads are connected to the PCC. The share contribution was determined by Equation (10).

_{T}is the transformer impedance taking into account the transformation ratio, Z

_{Trated}is the transformer impedance for the rated voltage, N is the number of transformer taps and β is the voltage change when moving the tap switch to the next position, p.u.

#### 3.1.3. Assessment of SPHF Overload by Currents from an External Distortion Source

_{Fh}on the resistance of the external distortion source TR for different electrical load compositions specified in Section 2.2. The dependences in Figure 6 correspond to the supply feeder impedance in Step 1.

_{F1h_0}, I

_{F1h_1}and I

_{F1h_2}were assessed for Step 1 and Step 4 supply feeder impedance. The error values δ

_{1}for Step 1 supply feeder impedance and δ

_{4}for Step 4 supply feeder impedance were calculated by using the following expression:

_{max}and the real addition I

_{real}to the RMS current for different load composition and supply feeder impedance values.

_{TR}= 11 kVA, S

_{UR}= 2.8 kVA, S

_{TPR}= 2.7 kVA and S

_{sc1}/S

_{sc2}= 2 (for Step 1 supply feeder impedance). For mode 1 parameters, close to low-voltage electrical grids (S

_{sc1}/S

_{sc2}= 10, for Step 4 supply feeder impedance), the RMS current ratio is about 1.1.

#### 3.2. Analytical Calculation of SPHF Overload by Background Harmonic Currents

- -
- Power of the external distortion source;
- -
- Short circuit power at the consumer buses;
- -
- Short circuit power at the point of external nonlinear load connection;
- -
- Parameters of the passive harmonic filter.

_{3h}is the voltage source of background harmonic distortion, I

_{3h}is the current source of background harmonic distortion, U

_{Ch}is the voltage harmonic distortion at the consumer bus, I

_{Ch}is the supply feeder harmonic current of the consumer, X

_{Sh}is the energy system harmonic inductive reactance, X

_{Fh}is the equivalent harmonic inductive reactance of the shunt passive filter and X

_{Th}is the harmonic inductive reactance of the supply transformer. The circuits in Figure 8 are presented for the h

^{th}harmonic frequency, which is close to (slightly below) the resonant frequency of the passive harmonic filter (the equivalent impedance of the passive filter is inductive).

- -
- The parameters of the linear load connected in parallel to the passive filter are not taken into account at the h
^{th}harmonic because the equivalent impedance of the passive filter at the h^{th}harmonic (near the resonant frequency) is very low; - -
- The parameters of the power system and the supply transformer are assumed to be inductive;
- -
- The resistance of the SPHF is not taken into account.

_{sc1}at point 1 and S

_{sc2}at point 2. The filter parameters can be represented through the detuned factor f

_{r}and the reactive power of the filter capacitor bank Q

_{CB}at the fundamental frequency. For example, if the resonance frequency of the passive filter is 237.5 Hz and the harmonic frequency is 250 Hz (5% filter detuning), then f

_{r}is equal to 0.95. As a result, the following expressions were obtained:

_{h}= I

_{1}/h. Then, Equation (15) is transformed into Equation (18) as follows:

_{UR}is the power of the uncontrolled rectifier, h is the order of the harmonic and U

_{rated}is the nominal voltage of the uncontrolled rectifier.

_{Ch}and U

_{Ch}:

_{TR}= 20 Ω. The value K

_{SC}was calculated according to Equation (17). The values I

_{3h_meas}and I

_{Fh_meas}were obtained based on simulation results by measuring harmonic currents at the TR connection to the PCC and at the passive filter feeder, respectively. The value I

_{Fh_calc}was calculated according to Equation (15). The error value δ

_{I}was calculated by using the followingequation:

_{I}| = 4.49% in Table 5). Thus, based on the identified equations that allow one to calculate the SPHF background harmonic current, it is possible to evaluate the influence of external distortion sources depending on the short circuit ratio, reactive power and detuned factor of the passive filter, the harmonic order and value of the external source harmonic current.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Bagheri, A.; de Oliveira, R.A.; Bollen, M.H.J.; Gu, I.Y.H. A Framework Based on Machine Learning for Analytics of Voltage Quality Disturbances. Energies
**2022**, 15, 1283. [Google Scholar] [CrossRef] - Kanálik, M.; Margitová, A.; Beňa, Ľ.; Kanáliková, A. Power System Impedance Estimation Using a Fast Voltage and Current Changes Measurements. Energies
**2020**, 14, 63. [Google Scholar] [CrossRef] - Bogdanov, I.; Abramovich, B. Improving the efficiency of autonomous electrical complexes of oil and gas enterprises. J. Min. Inst.
**2021**, 249, 408–416. [Google Scholar] [CrossRef] - Morenov, V.; Leusheva, E.; Lavrik, A.; Lavrik, A.; Buslaev, G. Gas-Fueled Binary Energy System with Low-Boiling Working Fluid for Enhanced Power Generation. Energies
**2022**, 15, 2551. [Google Scholar] [CrossRef] - Khalifa, A.; Bazhin, V.; Ustinova, Y.; Shalabi, M. Study of the Kinetics of the Process of Producing Pellets from Red Mud in a Hydrogen Flow. J. Min. Inst.
**2022**, 254, 261–270. [Google Scholar] [CrossRef] - Ustinov, D.A.; Aysar, A.R. Development of a New Working Algorithm for Improving the Efficiency of the Remote Protection in the Distributed Generation Networks. Occup. Saf. Ind.
**2023**, 5, 20–27. [Google Scholar] [CrossRef] - Bhattacharyya, S.; Cobben, S.; Ribeiro, P.; Kling, W. Harmonic Emission Limits and Responsibilities at a Point of Connection. IET Gener. Transm. Distrib.
**2012**, 6, 256–264. [Google Scholar] [CrossRef] - Crepaldi, J.; Amoroso, M.M.; Ando, O.H. Analysis of the Topologies of Power Filters Applied in Distributed Generation Units—Review. IEEE Lat. Am. Trans.
**2018**, 16, 1892–1897. [Google Scholar] [CrossRef] - Belsky, A.; Glukhanich, D.; Sutikno, T.; Hatta Jopri, M. Estimation of Hourly Solar Irradiation on Tilted Surfaces. Bull. Electr. Eng. Inform.
**2023**, 12, 3202–3214. [Google Scholar] [CrossRef] - Ustinov, D.A.; Aysar, A.R. Analysis of the Impact of the Distributed Generation Facilities on Protection Systems and Voltage Mode: Review. Occup. Saf. Ind.
**2023**, 2, 15–20. [Google Scholar] [CrossRef] - Buslaev, G.; Lavrik, A.; Lavrik, A.; Tcvetkov, P. Hybrid System of Hydrogen Generation by Water Electrolysis and Methane Partial Oxidation. Int. J. Hydrogen Energy
**2023**, 48, 24166–24179. [Google Scholar] [CrossRef] - Fujita, H.; Yamasaki, T.; Akagi, H. A Hybrid Active Filter for Damping of Harmonic Resonance in Industrial Power Systems. IEEE Trans. Power Electron.
**2000**, 15, 215–222. [Google Scholar] [CrossRef] - Bai, H.; Wang, X.; Loh, P.C.; Blaabjerg, F. Harmonic Analysis and Mitigation of Low-Frequency Switching Voltage Source Inverter with Series LC Filtered VSI. In Proceedings of the 2017 IEEE Applied Power Electronics Conference and Exposition (APEC), Tampa, FL, USA, 26–30 March 2017; pp. 3299–3306. [Google Scholar] [CrossRef]
- Srivastava, M.; Goyal, S.K.; Saraswat, A.; Shekhawat, R.S.; Gangil, G. A Review on Power Quality Problems, Causes and Mitigation Techniques. In Proceedings of the 2022 1st International Conference on Sustainable Technology for Power and Energy Systems (STPES), Srinagar, India, 4–6 July 2022; pp. 1–6. [Google Scholar] [CrossRef]
- Kazmierkowski, M.P. Power Quality: Problems and Mitigation Techniques [Book News]. IEEE Ind. Electron. Mag.
**2015**, 9, 62. [Google Scholar] [CrossRef] - Zhukovskiy, Y.; Korolev, N.; Malkova, Y. Monitoring of Grinding Condition in Drum Mills Based on Resulting Shaft Torque. J. Min. Inst.
**2022**, 256, 686–700. [Google Scholar] [CrossRef] - Karadeniz, A.; Balci, M.E. Comparative Evaluation of Common Passive Filter Types Regarding Maximization of Transformer’s Loading Capability under Non-Sinusoidal Conditions. Electr. Power Syst. Res.
**2018**, 158, 324–334. [Google Scholar] [CrossRef] - Gimenes, T.K.; da Silva, M.P.C.; Ledesma, J.J.G.; Ando, O.H. Impact of Distributed Energy Resources on Power Quality: Brazilian Scenario Analysis. Electr. Power Syst. Res.
**2022**, 211, 108249. [Google Scholar] [CrossRef] - Jopri, M.H.; Ghani, M.A.; Abdullah, A.; Sutikno, T.; Manap, M.; Too, J. Naïve Bayes and Linear Discriminate Analysis Based Diagnostic Analytic of Harmonic Source Identification. Indones. J. Electr. Eng. Comput. Sci.
**2020**, 20, 1626–1633. [Google Scholar] [CrossRef] - Martinez, R.; Castro, P.; Arroyo, A.; Manana, M.; Galan, N.; Moreno, F.S.; Bustamante, S.; Laso, A. Techniques to Locate the Origin of Power Quality Disturbances in a Power System: A Review. Sustainability
**2022**, 14, 7428. [Google Scholar] [CrossRef] - Shcherbakova, P.; Senderovych, G.; Abramovitz, A. Revisiting the Active Power Direction Method. IET Gener. Transm. Distrib.
**2021**, 15, 1056–1069. [Google Scholar] [CrossRef] - Mohamed, I.F.; Abdel Aleem, S.H.E.; Ibrahim, A.M.; Zobaa, A.F. Optimal Sizing of C -Type Passive Filters under Non-Sinusoidal Conditions. Energy Technol. Policy
**2014**, 1, 35–44. [Google Scholar] [CrossRef] - Abdel Aleem, S.H.E.; Elmathana, M.T.; Zobaa, A.F. Different Design Approaches of Shunt Passive Harmonic Filters Based on IEEE Std. 519-1992 and IEEE Std. 18-2002. Recent Patents Electr. Electron. Eng.
**2013**, 6, 68–75. [Google Scholar] [CrossRef] - Ko, W.; Tuomainen, M. Design and Application of a Single-tuned Passive Harmonic Filter to Suppress Harmonic Distortion and Resonance for Railway Traction Power Systems—A Case Study. IET Electr. Syst. Transp.
**2022**, 12, 153–164. [Google Scholar] [CrossRef] - AbdelAziz, M.M.; AbouEl-Zahab, E.E.-D.; Ibrahim, A.M.; Zobaa, A.F. Practical Considerations Regarding Power Factor for Nonlinear Loads. IEEE Trans. Power Deliv.
**2004**, 19, 337–341. [Google Scholar] [CrossRef] - Aziz, M.M.A.; Zobaa, A.F.; Ibrahim, A.M.; Monem, A.M.A. Effect of Time Variation of System Impedance and Voltage Harmonics on LC Compensation for Nonlinear Loads. In Proceedings of the 2004 11th International Conference on Harmonics and Quality of Power (IEEE Cat. No.04EX951), Lake Placid, NY, USA, 12–15 September 2004; pp. 77–82. [Google Scholar] [CrossRef]
- Azebaze Mboving, C.S.; Hanzelka, Z.; Firlit, A. Analysis of the Factors Having an Influence on the LC Passive Harmonic Filter Work Efficiency. Energies
**2022**, 15, 1894. [Google Scholar] [CrossRef] - Aleem, S.H.E.A.; Balci, M.E.; Zobaa, A.F.; Sakar, S. Optimal Passive Filter Design for Effective Utilization of Cables and Transformers under Non-Sinusoidal Conditions. In Proceedings of the 2014 16th International Conference on Harmonics and Quality of Power (ICHQP), Bucharest, Romania, 25–28 May 2014; pp. 626–630. [Google Scholar] [CrossRef]
- Abdul Kahar, N.H.B.; Zobaa, A.F. Application of Mixed Integer Distributed Ant Colony Optimization to the Design of Undamped Single-Tuned Passive Filters Based Harmonics Mitigation. Swarm Evol. Comput.
**2019**, 44, 187–199. [Google Scholar] [CrossRef] - Nassif, A.; Xu, W.; Freitas, W. An Investigation on the Selection of Filter Topologies for Passive Filter Applications. In Proceedings of the IEEE PES General Meeting, Minneapolis, MN, USA, 25–29 July 2010; p. 1. [Google Scholar] [CrossRef]
- Almutairi, M.S.; Hadjiloucas, S. Harmonics Mitigation Based on the Minimization of Non-Linearity Current in a Power System. Designs
**2019**, 3, 29. [Google Scholar] [CrossRef] - Filho da Costa Castro, J.; Lima, L.R.; Belchior, F.N.; Ribeiro, P.F. A Novel Approach to the Design of Passive Filters in Electric Grids. Int. J. Emerg. Electr. Power Syst.
**2016**, 17, 693–701. [Google Scholar] [CrossRef] - Menti, A.; Zacharias, T.; Milias-Argitis, J. Optimal Sizing and Limitations of Passive Filters in the Presence of Background Harmonic Distortion. Electr. Eng.
**2009**, 91, 89–100. [Google Scholar] [CrossRef] - Benaouadj, M.; Boumous, Z.; Boumous, S. Active Harmonic Filtering for Improving Power Quality of an Electrical Network. J. Eur. Syst. Autom.
**2022**, 55, 397–403. [Google Scholar] [CrossRef] - Hoon, Y.; Mohd Radzi, M.; Hassan, M.; Mailah, N. Control Algorithms of Shunt Active Power Filter for Harmonics Mitigation: A Review. Energies
**2017**, 10, 2038. [Google Scholar] [CrossRef] - Davi Curi Busarello, T.; Vendrusculo, E.A.; Pomilio, J.A.; da Silva, N. Analysis of a Derivative Hybrid Power Filter in Distorted Voltage Grid. In Proceedings of the 2013 IEEE PES Conference on Innovative Smart Grid Technologies (ISGT Latin America), Sao Paulo, Brazil, 15–17 April 2013; pp. 1–5. [Google Scholar] [CrossRef]
- Mahmoud, M.O.; Mamdouh, W.; Khalil, H. Source Current Harmonic Mitigation of Distorted Voltage Source by Using Shunt Active Power Filter. Int. J. Electr. Comput. Eng.
**2020**, 10, 3967–3977. [Google Scholar] [CrossRef] - Skamyin, A.; Belsky, A.; Dobush, V.; Gurevich, I. Computation of Nonlinear Load Harmonic Currents in the Presence of External Distortions. Computation
**2022**, 10, 41. [Google Scholar] [CrossRef] - Zhukovskiy, Y.L.; Vasilev, B.Y.; Korolev, N.A.; Malkova, Y.M. Analysis of the behavior of asynchronous electric drive with a closed scalar control system when changing the inductance of the magnetizing circuit. Indones. J. Sci. Technol.
**2022**, 8, 65–78. [Google Scholar] [CrossRef]

**Figure 4.**The dependence of consumer load contributions on the supply feeder impedance (R

_{TR}= 20 Ω).

**Figure 5.**The dependence of the external source contribution TR on the resistance of the nonlinear load TR for different supply feeder impedance values.

**Figure 6.**The dependences of the relative value of SPHF harmonic currents ΔI

_{Fh}on R

_{TR}for different modes of electrical load and supply feeder impedance in Step 1.

**Figure 7.**The dependence of the RMS current ratio, taking into account the maximum and real addition, on the power of the external distortion source TR.

**Figure 8.**The simplified equivalent electrical schemes with connected SPHF and background harmonic distortions represented as a current harmonic source (

**a**) and a voltage harmonic source (

**b**).

Elements of the Scheme | Parameters and Values |
---|---|

Grid | U_{0} = 0.4 kV, R_{S1} = 0.18 Ω, L_{S1} = 1.75 mH |

Supply feeder Z_{S2} (step 1) | Step 1: R_{S2} = 0.22 Ω, L_{S2} = 1.71 mHStep 2: R _{S2} = 0.83 Ω, L_{S2} = 4.8 mHStep 3: R _{S2} = 1.0 Ω, L_{S2} = 10.96 mHStep 4: R _{S2} = 1.49 Ω, L_{S2} = 14.73 mH |

Induction motor (M) | U_{M} = 0.38 kV, P_{M} = 1.5 kW, η = 76%, cosφ = 0.74 |

Thyristor rectifier (TR) | U_{TR} = 0.38 kV, R_{TR} = [20; 200] Ω |

Thyristor power regulator (TPR) | U_{TPR} = 0.38 kV, R_{TPR} = 32.3 Ω |

Uncontrolled rectifier (UR) | U_{UR} = 0.38 kV, R_{UR} = 96.8 Ω |

Capacitor banks (CB) | 4 step of regulation, Q_{CB1} = 0.5 kvar, f_{tuned} = 134 Hz |

Passive harmonic filter (SPHF) | L_{F} = 14.1 mH, C_{F} = 31 μF, f_{tuned} = 241 Hz |

Stage Number | TR | UR | TPR | M | CB | Variation Parameters | |
---|---|---|---|---|---|---|---|

Z_{S2} | R_{TR}, Ω | ||||||

1 and 2 | + | + | + | + | + | Step 1–Step 4 | [20; 200] |

3 (mode 1) | + | + | + | + | + | ||

3 (mode 2) | + | − | + | + | + | ||

3 (mode 3) | + | + | − | + | + |

**Table 3.**The error values of the UR and TPR share contribution calculated according to Equation (11).

R_{TR} | δK_{Dh} (UR), % | δK_{Dh} (TPR), % | ||||||
---|---|---|---|---|---|---|---|---|

Step 1 | Step 2 | Step 3 | Step 4 | Step 1 | Step 2 | Step 3 | Step 4 | |

20 | 3.0 | 3.6 | 0.8 | 0.2 | 9.7 | 0.6 | 1.4 | 1.1 |

80 | 0.4 | 0.8 | 0.2 | 0.1 | 2.1 | 0.3 | 0.1 | 0.2 |

140 | 0.2 | 0.4 | 0.1 | 0.1 | 1.2 | 0.2 | 0.1 | 0.1 |

200 | 0.1 | 0.3 | 0.1 | 0.1 | 0.9 | 0.2 | 0.1 | 0.1 |

R_{TR} | I_{Fh_0}, A | I_{Fh_2}, A | I_{Fh_0} + I_{Fh_2}, A | I_{Fh_1}, A | δ_{1}, % | δ _{4}, % | ||||
---|---|---|---|---|---|---|---|---|---|---|

Step 1 | Step 4 | Step 1 | Step 4 | Step 1 | Step 4 | Step 1 | Step 4 | Step 1 | Step 4 | |

20 | 1.611 | 1.751 | 1.761 | 0.446 | 3.372 | 2.197 | 3.271 | 2.016 | 3.00 | 8.24 |

40 | 0.902 | 0.23 | 2.513 | 1.981 | 2.450 | 1.860 | 2.51 | 6.11 | ||

80 | 0.457 | 0.117 | 2.068 | 1.868 | 2.031 | 1.787 | 1.79 | 4.34 | ||

140 | 0.263 | 0.067 | 1.874 | 1.818 | 1.851 | 1.764 | 1.23 | 2.97 | ||

200 | 0.185 | 0.047 | 1.796 | 1.798 | 1.779 | 1.758 | 0.95 | 2.22 |

K_{SC} | S_{sc1}, kVA | I_{3h_meas}, A | f_{r} | I_{Fh_meas}, A | I_{Fh_calc}, A | δ_{I}, % |
---|---|---|---|---|---|---|

2.00 | 250 | 4.82 | 0.966 | 1.855 | 1.938 | −4.48 |

3.97 | 4.78 | 1.092 | 1.083 | 0.83 | ||

7.19 | 4.76 | 0.601 | 0.628 | −4.49 | ||

9.40 | 4.75 | 0.470 | 0.488 | −3.84 |

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## Share and Cite

**MDPI and ACS Style**

Skamyin, A.; Shklyarskiy, Y.; Gurevich, I.
Influence of Background Voltage Distortion on Operation of Passive Harmonic Compensation Devices. *Energies* **2024**, *17*, 1342.
https://doi.org/10.3390/en17061342

**AMA Style**

Skamyin A, Shklyarskiy Y, Gurevich I.
Influence of Background Voltage Distortion on Operation of Passive Harmonic Compensation Devices. *Energies*. 2024; 17(6):1342.
https://doi.org/10.3390/en17061342

**Chicago/Turabian Style**

Skamyin, Aleksandr, Yaroslav Shklyarskiy, and Ilya Gurevich.
2024. "Influence of Background Voltage Distortion on Operation of Passive Harmonic Compensation Devices" *Energies* 17, no. 6: 1342.
https://doi.org/10.3390/en17061342