# A New Method to Monitor the Primary Neutral Integrity in Multi-Grounded Neutral Systems

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## Abstract

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## 1. Introduction

## 2. The Proposed Primary Neutral Monitoring Method

#### 2.1. Establishment of the Equivalent Analysis Circuit

_{T}represents the transformer grounding resistance, and R

_{gc}represents the customer grounding resistance. Under normal operating conditions, the current flowing in the neutral line of the MGN system is mainly caused from the unbalanced utility loads and customer loads, and the flow of current is shown in Figure 1. In Figure 1, the green line represents the unbalanced current caused by the unbalanced customer loads, and the red line represents the unbalanced current caused by the unbalanced utility loads.

_{P}and Z

_{S}, where V

_{P}is the phase to neutral voltage and Z

_{S}is the equivalent impedance for the primary system. Z

_{MGN}represents the equivalent impedance of the primary multiple groundings. The derivation process for the value of Z

_{MGN}will be discussed in the next subsection. Z

_{an}represents the equivalent customer loads between the hot wire a and neutral; Z

_{bn}represents the equivalent customer loads between the hot wire b and neutral; Z

_{ab}represents the equivalent customer loads between the hot wire a and b. Z

_{sn}is the impedance of the neutral line in the transformer secondary side, and Z

_{sp}is the distribution line impedance. In Figure 2, the current flowing in the primary neutral is labeled as I

_{np}, and the current flows in the secondary neutral are labeled as I

_{ns}. I

_{a}, V

_{a}and I

_{b}, V

_{b}represent the phase current and voltage of the secondary side. I

_{P}represents the current in the transformer primary side, and ${I}_{{R}_{T}}$represents the grounding current of the transformer. The unbalanced current in the transformer secondary side is labeled as I

_{ub_S}in Figure 2.

_{gc}and then flows from the earth to the transformer grounding R

_{T}and primary grounding Z

_{MGN}. This neutral current further circulates back to the transformer secondary neutral.

_{U}is determined by the unbalanced voltage V

_{U}and the equivalent load impedance Z

_{U}, which is caused by the imbalance of the two single-phase loads (Z

_{an}and Z

_{bn}). The analytical formulas to calculate Z

_{U}and I

_{U}are given in Equations (1) and (2).

_{U}is the equivalent unbalanced voltage source, which can be calculated based on the transformer secondary rated voltage V

_{N}.

_{sn_C}represents the current flowing through the secondary neutral line, and I

_{ns_C}represents the current flowing into the ground through the customer grounding impedance R

_{gc}. The current I

_{ns_C}is split into two parts as I

_{RT_C}and I

_{np_C}. The subscript C in each variable represents that the neutral currents are caused only by the customer. Based on Figure 3, it can be seen that the current flowing in the neutral of the primary system I

_{np_C}can be calculated by Equation (4).

_{T}and the primary neutral equivalent impedance Z

_{MGN}. For an MGN system, the transformer grounding resistance R

_{T}is usually constant. Therefore, the value of g is mainly determined by the equivalent neutral impedance Z

_{MGN}of the primary system. If the primary system neutral is broken, the equivalent impedance Z

_{MGN}should increase, and the value of parameter g should decrease. Therefore, the variation for the value of parameter g can be used to reflect the primary neutral condition.

#### 2.2. Impedance Determination under Normal Operating Conditions

_{T}can be estimated based on the substation database. The value of impedance Z

_{MGN}can be determined based on the following procedures.

_{pn}is the primary neutral conductor impedance between two grounding poles. R

_{gn}represents the pole grounding resistance. Z

_{lad}

_{(k)}and Z

_{lad}

_{(k+1)}represent the equivalent impedance for the multiple grounding system with k or (k + 1) grounding poles, respectively. The equivalent impedance of a ladder network with (k + 1) grounding poles can be calculated according to Equation (6) [18].

_{lad}

_{(k)}≈ Z

_{lad}

_{(k+1)}.

_{lad}is the equivalent impedance of the ladder network; thus, Equation (9) is derived.

_{lad}

_{1}and Z

_{lad}

_{2}. The equivalent impedance of each network can be estimated by Equation (10). Additionally, the equivalent primary system impedance seen from the transformer connection point can be calculated by the parallel connection of Z

_{lad}

_{1}and Z

_{lad}

_{2}according to the analytical formula shown in Equation (11).

#### 2.3. Impedance Determination Based on the Measurement Data

_{np}can be divided into two parts, as shown in Equation (12).

_{np_U}is the primary neutral current caused by the utility, and I

_{np_C}is the primary neutral current caused by the customer. Similarly, the neutral current in the secondary system I

_{ns}is also composed of two parts, I

_{ns_U}and I

_{ns_C}.

_{1}and t

_{2}, Equation (14) can be rewritten as Equations (15) and (16).

_{1}and t

_{2}, respectively. Subtracting Equation (15) from Equation (16), then Equation (17) can be obtained.

_{np_U}and ΔI

_{ns_U}will both equal zero. Equation (17) can be further simplified to Equation (18); therefore, parameter g can be calculated by Equation (19).

_{np}and I

_{ns}can be used to estimate the value of parameter g. Furthermore, based on the estimated parameter g, the primary neutral impedance Z

_{MGN}can be estimated from Equation (20) according to Equation (5).

#### 2.4. Determination of the Primary Neutral Condition

_{MGN}of the primary neutral system can be calculated according to Equation (11). The actual value of Z

_{MGN}can be estimated based on the procedures shown in Section 2.3. When the primary neutral line is loosened or broken, the equivalent impedance of the primary neutral conductor Z

_{MGN}should increase. Therefore, by monitoring the value of Z

_{MGN}, the condition of the primary neutral integrity can be known.

_{np}and I

_{ns}can be monitored continuously. Therefore, parameter g can be estimated according to Equation (19) based on the variation of the neutral current. The transformer grounding impedance can be known based on the substation data, and then Z

_{MGN}can be estimated by Equation (20).

_{MGN}and theoretical Z

_{MGN}.

_{MGN_t}is the theoretical value of Z

_{MGN}obtained from Equation (11), which represents the primary neutral impedance of a normal operating system; Z

_{MGN_m}is the monitored value of Z

_{MGN}based on Equation (20), which can reflect the actual condition of the primary neutral groundings. Under normal operating conditions, the monitored parameter Z

_{MGN_m}should equal its theoretical value Z

_{MGN_t}, and SC should be of a value nearly of zero. If there is a neutral broken problem happening at the primary side, the value of Z

_{MGN_m}will increase. Referring to Figure 1, it is known that the nearer the neutral broken point to the monitored transformer, the larger Z

_{MGN}and the larger SC. Therefore, the value of SC not only reflects the primary neutral condition, but also reflects the distance of the primary neutral broken point to the monitored service transformer.

## 3. Data Selection Criteria

_{a}and P

_{b}should be large enough in order to guarantee that enough neutral current disturbances can be generated by the customer load. Moreover, the time interval between two consecutive sampled data should be short enough in order to further assure that the current variation caused by the primary side is small. The data that can satisfy the above criterion are selected out, and then, the time instants corresponding to these data are determined. Since the estimation of parameter g is based on the variation of neutral current in the primary and secondary neutral, the neutral current data corresponding to the above time instants are further selected out and used for the parameter estimation according to Equation (19).

_{np}and ΔI

_{ns}can be selected out according to the above data selection criterion. Assume that there are N groups of neutral current that can meet the above requirements, such as $(\Delta {I}_{ns,1},\Delta {I}_{np,1})$, $(\Delta {I}_{ns,2},\Delta {I}_{np,2})$, …, $(\Delta {I}_{ns,i},\Delta {I}_{np,i})$, …,$(\Delta {I}_{ns,N},\Delta {I}_{np,N})$. According to the least square method, parameter g can be estimated based on the selected datasets as shown in Equation (22).

_{MGN_m}can be estimated, and the sensitivity coefficient SC can be determined according to Equation (21). Parameter Z

_{MGN_m}can be estimated at a certain time interval based on the continuously monitored data, and thus, the value of SC can be updated for each time period. The broken or loosened problems happening in the primary neutral line can be reflected by the variation of SC. A threshold value (TV) to evaluate the variation of SC should be set beforehand based on the parameters of the power system. If SC is less than TV, this indicates that the condition of the primary neutral system is good. Otherwise, one should check the primary neutral condition near the monitored transformer.

## 4. Simulation Verification

_{MGN}are estimated, and SC is calculated based on the proposed method; and the results are compared with their theoretical values. Finally, in the third part, the broken primary neutral situations are simulated, and the proposed method is used to reflect the primary neutral condition.

#### 4.1. Validity Verification of Parameter g

_{MGN}and the transformer grounding impedance R

_{T}. In order to verify the proposed method for systems under different neutral integrity conditions, the following three scenarios are simulated.

- Scenario 1:
- A normal operating condition of the system with R
_{T}= 15 Ω and Z_{MGN}= 0.4404 Ω. - Scenario 2:
- A broken primary neutral condition with R
_{T}= 15 Ω and Z_{MGN}= 7.5 Ω. - Scenario 3:
- A transformer neutral broken condition with R
_{T}= 150 Ω and Z_{MGN}= 0.4404 Ω.

_{np}and I

_{ns}. Additionally, the parameter calculation should be under the assumption that the neutral current variation is caused only by the customer. Therefore, by adjusting the individual load power in the two hot wires of the customer and at the same time maintaining the total load power to be constant, many cases have been generated. Due to space limitation, the results for four cases of each scenario are shown in Table 2. Based on the variation of the neutral current, parameter g can be calculated based on Equation (19), and the estimation results of g are compared with their theoretical value.

_{MGN}becomes larger, and the value of g should be less than its normal value. Correctly, the estimation result of g based on the variation of the neutral currents reflects this situation. In Scenario 3, when the transformer grounding is broken, R

_{T}becomes larger, and the value of g should become larger than its normal value. Again, the estimated result correctly reflects this situation. Moreover, the estimation values of parameter g for all cases nearly overlap with their theoretical values. Therefore, analysis in this section reveals that the proposed parameter g can correctly reflect the neutral condition in the MGN system, and the method to estimate g based on the variation of neutral current is valid and accurate.

#### 4.2. Verification of the Proposed Method Based on a Typical MGN Network

_{gs}is the substation grounding resistance (less than 1 Ω), R

_{gn}is the pole grounding resistance, Z

_{line}

_{1}is the primary phase conductor impedance, z

_{pn}is the primary neutral conductor impedance, R

_{T}is the transformer grounding resistance, R

_{gc}is the customer grounding resistance, Z

_{line}

_{2}is the secondary phase conductor impedance and Z

_{sn}is the secondary neutral conductor impedance.

_{a}and P

_{b}represent the phase a and phase b loads in the transformer secondary side, respectively. (P

_{a}+ P

_{b}) is the total load in this phase of the transformer. S

_{p}represents the total three-phase power for the whole transformer. The quantitative data selection criterion for this system is summarized as shown in Equation (25).

_{MGN_m}can be obtained, and the results of Z

_{MGN_m}and SC are shown in Table 4.

_{MGN_m}matches the theoretical Z

_{MGN_t}very well, and the value of SC is very small. This means that the quantitative data selection criterion is proper and the proposed method is accurate to estimate the equivalent primary neutral impedance Z

_{MGN}under normal operating conditions.

#### 4.3. Monitoring of the Primary Neutral Broken Condition

_{MGN}to reflect the primary neutral condition is studied, and the threshold value of SC is proposed.

#### 4.3.1. Broken Primary Neutral at Two Sides

_{MGN}is shown in Table 5. The theoretical value Z

_{MGN_t}under normal operating conditions can be used as a reference to check the estimated Z

_{MGN_m}value. Then, the sensitivity coefficient SC can be calculated according to Equation (21), which is an indicator that can be used to reflect the primary neutral integrity.

#### 4.3.2. Broken Primary Neutral at One Side

_{MGN_t}and SC are given in Table 6.

_{MGN_m}is larger than its normal value, and the sensitivity parameter SC can reach a value of 87.64%, which can correctly reflect the broken neutral condition in the primary system near this transformer. However, SC is smaller than the two-broken-point case; this is reasonable since the neutral broken at two sides of the transformer is more serious than the neutral broken at only one side of the transformer. By changing the distances between the neutral broken point and the service transformer, the relationship between the broken distance and parameter SC is analyzed, whose results are shown in Figure 18. Additionally, from the results, it can be seen that, when the broken neutral is close to the transformer, SC is large. As the distance between the broken neutral and the transformer increases, SC becomes smaller. This is reasonable since the sensitivity of SC will get lower for the broken neutral happening far away from the monitored transformer.

#### 4.3.3. Broken Transformer Grounding

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**The equivalent analysis circuit for the unbalanced current totally caused by the customer.

**Figure 13.**The powers and neutral currents of the transformer for the two-side broken neutral condition.

**Figure 16.**The powers and neutral currents of the transformer for the single-point neutral-broken condition.

# | Parameters | Values |
---|---|---|

Primary System | Z_{S} (Ω) | 0.00249 |

Z_{MGN} (Ω) | 0.4404 | |

R_{T} (Ω) | 15 | |

Secondary System | R_{gc} (Ω) | 1.0000 |

Z_{sn}, Z_{sp} (Ω) | 0.0498, 0.0249 | |

Z_{an}, Z_{bn}, Z_{ab} (Ω) | 20, 12, 10 |

# | Parameters | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|---|

Equivalent customer loads | Z_{an} (Ω) | 17 | 18 | 19 | 20 |

Z_{bn} (Ω) | 13.4 | 12.9 | 12.4 | 12 | |

Z_{ab} (Ω) | 10 | 10 | 10 | 10 | |

Scenario 1 | I_{ns} (A) | 0.06277 | 0.08725 | 0.1113 | 0.1324 |

I_{np} (A) | 0.06098 | 0.08476 | 0.1081 | 0.1286 | |

Scenario 2 | I_{ns} (A) | 0.01533 | 0.02131 | 0.02717 | 0.03233 |

I_{np} (A) | 0.01022 | 0.01420 | 0.01812 | 0.02156 | |

Scenario 3 | I_{ns} (A) | 0.06230 | 0.08659 | 0.1104 | 0.1314 |

I_{np} (A) | 0.06212 | 0.08633 | 0.1101 | 0.1310 |

Parameter | Value |
---|---|

R_{gs} (Ω) | 0.15 |

R_{gn} (Ω) | 15 |

Z_{line}_{1} (Ω/km) | 0.2494 + 0.8782 |

z_{pn} (Ω) | 0.04271 + j0.09609 |

R_{T} (Ω) | 15 |

R_{gc} (Ω) | 1 |

Z_{line}_{2} (Ω/km) | 0.2028 + j0.0936 |

Z_{sn} (Ω/km) | 0.5500 + j0.3650 |

Parameter | Value |
---|---|

Z_{MGN_m} (Ω) | 0.5227 + j0.3616 |

Z_{MGN_t} (Ω) | 0.5265 + j0.3422 |

SC (%) | 3.15% |

Parameter | Value |
---|---|

Z_{MGN_m} (Ω) | 13.0590 + j0.6512 |

Z_{MGN_t} (Ω) | 0.5265 + j0.3422 |

SC (%) | 2002.1% |

Parameter | Value |
---|---|

Z_{MGN_m} (Ω) | 1.0216 + j0.5826 |

Z_{MGN_t} (Ω) | 0.5265 + j0.3422 |

SC (%) | 87.64% |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xie, X.; Sun, Y.; Long, X.; Zhang, B.
A New Method to Monitor the Primary Neutral Integrity in Multi-Grounded Neutral Systems. *Energies* **2017**, *10*, 380.
https://doi.org/10.3390/en10030380

**AMA Style**

Xie X, Sun Y, Long X, Zhang B.
A New Method to Monitor the Primary Neutral Integrity in Multi-Grounded Neutral Systems. *Energies*. 2017; 10(3):380.
https://doi.org/10.3390/en10030380

**Chicago/Turabian Style**

Xie, Xiangmin, Yuanyuan Sun, Xun Long, and Bingwei Zhang.
2017. "A New Method to Monitor the Primary Neutral Integrity in Multi-Grounded Neutral Systems" *Energies* 10, no. 3: 380.
https://doi.org/10.3390/en10030380