# Assessment of Unintentional Islanding Operations in Distribution Networks with Large Induction Motors

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Test System Description

## 3. Field Measurements

_{1}(node 2), located at the head of feeder A, and node PCC

_{2}(node 8), from which a large IM is supplied. Although, a high number of real events have been recorded, to not excessively extend the document, only three events are analyzed here. A representative sample of these events is listed in Table 1.

_{1}and PCC

_{2}. The fault recorders register voltage and current signals with 32 samples per cycle. The over-current relays are equipped with an oscillography function; in PCC

_{1}the relay registration is set to 400 ms, whilst in PCC

_{2}, this value is set to 600 ms. More information about the relays and their recording characteristics can be obtained from the manufacturer in [16]. The reason why each event is displayed in different figures is the memory limitation of the digital fault recorder; therefore, in each relay and for every event, two files are generated. Note, however, that for brevity purposes, the recordings from the relay located at (PCC

_{1}) will only be shown for the first and third event. Measurements at PCC

_{1}, are plotted to display the type of fault that caused CB operation that precedes the IO.

_{1}during half month and the time of occurrence of some recorded events; namely Events 1, 4, 5, 7, 8, and 9, as numbered in Table 1. Figure 2 and Figure 3 show measurements recorded respectively at PCC

_{1}, and PCC

_{2}, and corresponding to the beginning and the end of Event 1. Figure 4 and Figure 5 show the recordings corresponding to Events 2, and 3, respectively. A short analysis of the three events is presented below.

_{1}and PCC

_{2}, the effect of line impedance from node 2 to 8 (11 Ω) is observable, thus, the voltage sag of 7.1 kV at node 8 becomes 8.89 kV at the PCC

_{1}. The sequence is as follows: (i) SLG fault occurs at node 8; (ii) CB opens; (iii) CB recloses after a prefixed period (820 ms).

- Figure 2 depicts some recordings measured at the source side of PCC
_{1}. The two plots show frequency, voltage and current variations during a period that covers pre-fault, during-fault, and post-fault scenarios, including the post-reclosing period. The beginning of the full event is depicted in Figure 2a; the upper arrows indicate the three parts of the transient process. One can observe voltage and current variations due to CB operation: The measured currents correspond to those flowing through feeder B; the frequency is that of the transmission system and remains constant; voltages are affected by substation grounding, and they exhibit both sags and swells. Take into consideration that this can also affect the unfaulted feeder loads. Figure 2b plots the transient response caused by the reclosing operation: The current due to the re-energization, the effect of the current drawn due to the IM reacceleration, and the effect of the out-of-phase reconnection are observable. - Figure 3 depicts the measurements recorded at the MV side of the transformer at the load-side of PCC
_{2}during the same period that Figure 2. After CB operation, the IM continues connected to the feeder, which does not longer supply active power. Consequently, the frequency in this part of the system steadily decreases until the reclosing instant. Figure 3b also shows that, according to the waveforms measured, after CB reclosing the IM reaccelerates until it recovers its rate speed, although, initially, the frequency (and the IM speed) decreases even more as a consequence of the reclosing transient; see Section 4. Take into account that frequency and voltage mismatches between the two CB terminals at the reclosing time will cause a transient torque that could seriously affect the machine.

_{2}. It is clear from Figure 4b that the IM is acting as a generator after the circuit breaker CB clears the fault. It is also noticeable that the values when the CB recloses are lower when compared with the previous Event 1, due to the higher loads connected into the affected feeder at that instant.

_{1}and PCC

_{2}corresponding to a permanent SLG fault that occurs at node 8, clearly observable by taking a look at the voltage sag magnitude for the faulty phase at the PCC

_{2}; see Figure 5 and Event 3 in Table 1. Moreover, it is worth mentioning that the SLG in Feeder A appears simultaneously with a two-phase-to-ground (LLG) in an MV neighbor feeder. After the CB opening operation, the fault is fed by the IM. Figure 5b shows the measurements of the PCC

_{2}and evidences the untimely tripping operations by the head-CB. For this event, the fault was prolonged 800 ms after the CB aperture. The transient represented in Figure 5b can be divided into parts: the top arrows in this figure indicate the pre-fault situation, the SLG fed by the main grid, and the fault fed by the IM.

## 4. System Components Modeling

#### 4.1. Introduction to Modeling Guidelines

- The saturation effect is considered in transformers.
- Transmission line impedance, for each particular section, is assumed to be equal for the three phases.
- IM is modelled as saturable because of the stator current increment that follows CB opening.
- Typical IEC-IEEE curves are considered for protective devices.

#### 4.2. Transmission System

#### 4.3. Transformers

#### 4.4. Protective Devices

_{0}for a 50/51N earth overcurrent relay can be calculated as follows,

_{0}are adjustable and typically ranged between 0.05 and 1.6, I is the picked up current, I

_{n}is the rated current, I> is an acceptable overload factor, and n is a factor to distinguish between relay curves. In particular, n is 0.02 for SI, 1 for VI and 2 for EI; t is a factor which also depends on the curve, for SI is 0.14, for VI is 13.5, and for EI is 80. For ground faults, I

_{0}is the sum vector of the three picked up currents sensed by the relay, I

_{0}> is the overload factor, between 0.1 and 0.8.

_{6}, oil or air insulation); a study of CB characterization has been presented in [29].

_{1}are summarized in Table 2.

#### 4.5. Induction Motors

_{em}is the electromagnetic torque, Γ

_{b}is the friction torque, Γ

_{load}is the mechanical load torque, θ

_{m}is the angular position, J

_{T}is the total moment of inertia (considering the rotor inertia and mechanical load), and P

_{m}is the mechanical power developed by the IM. Since the IMs considered here are the squirrel cage, the rotor voltages are set to zero.

_{rd}and i

_{rq}are the direct and quadrature components of the rotor currents, i

_{sd}and i

_{sd}are the direct and quadrature components of the IM stator currents, M represents the coupling inductance between stator and rotor and 𝓅 are the pole pairs. The data of the IMs are detailed in Table A2 of Appendix A.

#### 4.6. Loads

_{n}and Q

_{n}are the initial active and reactive powers, V is the initial value of voltage, V

_{n}is the adjusted voltage, P and Q the active and reactive power with the adjusted voltage, Δf is the difference between the rated frequency (50 Hz) and the adjusted frequency, k

_{pv}is the exponential factor that varies from 0 to 2 depending on the load type, and k

_{pf}is the frequency sensitivity factor.

_{o}and Q

_{o}are the active and reactive powers at the initial voltage V

_{o}, P(s) and Q(s) are the active and reactive powers at the rated voltage V, n

_{p}and n

_{q}are constants to model the three type of loads (i.e., if n = 0 the load is modelled as constant power, if n = 1 the load is modelled as constant current, and if n = 2 the load is modelled as constant impedance), tp and tq are time constants that control the dynamics of both active and reactive powers.

#### 4.7. System Model

## 5. Islanding Analysis

#### 5.1. Overview

_{2}(see Figure 7) where the IM are connected. In this figure, it can be seen that, before the fault occurs (t = 0.8 s), the induction machine is acting as a motor (the measured active power is positive), but once the fault is cleared the power becomes negative, which demonstrates the fact that the IM is transiently acting as a generator.

#### 5.2. Dynamic Model Analysis during Islanding

_{Kin_initial}is the initial kinetic energy prior to the CB opening, J

_{T}the total moment of inertia (considering the rotor inertia and mechanical load), and ω

_{pre_islanding}is the mechanical speed before the island is formed.

_{em}is set to zero, and (6) can be rewritten:

_{im}is the IM angular speed, ω

_{im}

_{0}is IM initial angular speed, δ

_{im}is the IM rotor angle, P

_{mIM}is the mechanical power developed by the IM when acting as a generator, P

_{eload}is the power drawn by the feeder loads, and H

_{im}is the inertia constant of the IM, expressed in seconds. In fact, the amount of feeder loads that remain within the island, represent a load torque for the IM when acting as a generator.

_{island}is the frequency during the island. As has been mentioned, load voltage dependence has been considered. If the term P

_{eload}includes constant impedance, constant power and constant current load models, electrical powers are divided into P

_{1}which is assumed to be the sum of all constant impedance loads, P

_{2}the sum of all constant current loads and P

_{3}are the sum of all static constant power loads within the island. Thus, it follows that,

_{1}, P

_{2}, P

_{3}are the sum of all constant impedance, constant current and constant power considering n LV nodes, which are computed as follows:

## 6. Model Validation

#### 6.1. Event 1

#### 6.2. Event 2

#### 6.3. Event 3

#### 6.4. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Internal Parameters | Values | Rated Parameters | Values |
---|---|---|---|

L_{s} | 0.0078 H | P | 160 kW |

L_{r} | 0.0078 H | 𝓅 | 1 |

R_{r} | 0.0077 Ω | f | 50 Hz |

R_{s} | 0.0137 Ω | V | 400 V |

L_{m} | 0.0076 H | J | 2.9 kgm^{2} |

Transformers | |||||||

Transformer Type | V_{p}/V_{s} (kV) | S (MVA) | ε (%) | L_{m}/R_{m} (H/kΩ) | |||

Substation transformer | TR1 | 120/25 kV | 10 | 10.4 | 78; 313 | ||

Distribution transformers | TR2 | 25/0.4 kV | 1 | 6 | 180; 370 | ||

TR3 | 25/0.4 kV | 0.63 | 5.1 | 350; 480 | |||

TR4 | 25/0.4 kV | 0.4 | 4.3 | 404; 694 | |||

TR5 | 25/0.4 kV | 0.25 | 4.1 | 811; 1666 | |||

Distribution Lines | |||||||

Lines | Nodes | Length (km) | Parameters:Z_{1}/Z_{0} (Ω/km); C_{0} (μF/km) | Loadability (A) | |||

L1 | 2–4 | 5 | 0.306 + j0.405/0.38 + j1.62 | 300 | |||

L2 | 4–3 | 3.3 | 1.07 + j0.441/1.3 + j1.76, | 120 | |||

L3 | 4–6 | 4.3 | 0.306 + j0.405/0.38 + j1.62 | 300 | |||

L4 | 6–5 | 4 | 1.07 + j0.441/1.3 + j1.76 | 120 | |||

L5 | 6–7 | 2.5 | 0.306 + j0.405/0.38 + j1.62 | 300 | |||

L6 | 7–8 | 2 | 0.306 + j0.405/0.38 + j1.62 | 300 | |||

L7 | 8–9 | 7 | 0.687 + j0.416/0.8 + j1.66 | 200 | |||

L8 | 2–10 | 3.8 | 0.127 + j0.114/0.17 + j0.45; 0.229 | 389 | |||

L9 | 10–11 | 4.43 | 0.208 + j0.123/0.278 + j0.492; 0.192 | 320 | |||

L10 | 11–12 | 4 | 0.687 + j0.416/0.8 + j1.66 | 200 | |||

L11 | 12–13 | 3.3 | 0.687 + j0.416/0.8 + j1.66 | 200 | |||

L12 | 1–2 | 0.28 | 0.306 + j0.405/0.38 + j1.62 | 300 |

## Appendix B

Load Node | Rated Voltage (V) | Rated P/Q (kW/kVAr) | Load Model * |
---|---|---|---|

Node 15 | 400 | 30/4 | Constant power |

Node 16 | 400 | 100/20 | Constant impedance |

Node 17 | 400 | 300/45 | Constant impedance |

Node 18 | 400 | 600/−157 | Induction motors |

Node 19 | 400 | 100/10 | Constant impedance |

Node 20 | 400 | 30/4 | Constant current |

Node 21 | 400 | 25/10 | Constant impedance |

Node 22 | 400 | 200/80 | Constant impedance |

Node 23 | 400 | 40/18 | Constant impedance |

*****The load model type listed in the table is model type implemented in Matlab/Simulink. Although there is not sufficient evidence (or field measurements) to select a given model, the model selected for each load provides a close enough simulation result to that obtained from measurements.

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**Figure 2.**Event 1—Single-line-to-ground fault at node 8. Measurements recorded in PCC

_{1}. (

**a**) Frequency, RMS phase voltages and current signals before and during the beginning of the event; (

**b**) frequency, RMS voltages and current signals during the end of the event.

**Figure 3.**Event 1—Single-line-to-ground fault at node 8. Measurements recorded in PCC

_{2}. (

**a**) Frequency, RMS phase voltages and current signals before and during the beginning of the event; (

**b**) frequency, RMS voltages and current signals during the end of the event.

**Figure 4.**Event 2—Single-line-to-ground between nodes 6 and 7. Measurements recorded in PCC

_{2}. (

**a**) Frequency, RMS phase voltages and current signals before and during the beginning of the event; (

**b**) frequency, RMS voltages and current signals during the end of the event.

**Figure 5.**Event 3—Permanent fault at node 8. (

**a**) Frequency value, RMS phase voltages and current signals recorded at PCC

_{1}; (

**b**) frequency value, RMS phase voltages and current signals recorded at PCC

_{2}.

**Figure 11.**RMS voltage, active and reactive-powers for each load model-Constant Power = Red line, Constant Current = Blue line; Constant Impedance = Green line.

**Figure 12.**Frequency and voltage comparison between scenarios with different load models-Constant Power = Red line, Constant Current = Blue line; Constant Impedance = Green line.

**Figure 13.**Event 1 validation. (

**a**) Frequency comparison, dashed-black (measurement), solid-black (simulation); (

**b**) RMS Phase voltage comparison, solid (simulation)/dashed (measurements), orange (Phase A), blue (Phase B), and green (Phase C).

**Figure 14.**Event 2 validation. (

**a**) Frequency comparison, dashed-black (measurement), solid-black (simulation); (

**b**) RMS Phase voltage comparison, solid (simulation)/dashed (measurements), orange (Phase A), blue (Phase B), and green (Phase C).

**Figure 15.**Event 3 validation. (

**a**) Frequency comparison, dashed-black (measurement), solid-black (simulation); (

**b**) RMS Phase voltage comparison, solid (simulation)/dashed (measurements), orange (Phase A), blue (Phase B), and green (Phase C).

Event | Beginning | Ending | Fault Type | Fault Current (A) | Fault Location | t_{cl} (ms) | P (MW) | Q (MVAr) | V (kV) |
---|---|---|---|---|---|---|---|---|---|

1 | 17:01:09.776 | 17:01:10.636 | SLG | 218 | Node 8 | 90 | 0.52 | −0.03 | 8.5 |

2 | 06:30:41.305 | 06:30:42.679 | SLG | 367 | L3 | 80 | 1 | −0.1 | 0 |

3 | 04:10:35.580 | 04:10:36.880 | LLG/SLG | 707 | Node 8 | 60 | 0.8 | 0 | 0 |

4 | 18:14:54.263 | 18:14:55.128 | SLG | 215 | Node 8 | 88 | 0.7 | −0.1 | 6.1 |

5 | 17:13:58.246 | 17:13:59.096 | SLG | 350 | Node 7 | 80 | 0.65 | 0.05 | 5.45 |

6 | 09:52:38.440 | 09:52:39.395 | SLG | 300 | Node 7 | 70 | 0.56 | −0.05 | 3.5 |

7 | 11:49:04.702 | 11:49:05.456 | SLG | 367 | Line 5 | 65 | 0.87 | −0.05 | 4.7 |

8 | 16:04:15.667 | 16:04:16.607 | LLG/SLG | 360 | Node 7 | 60 | 1.21 | −0.1 | 2.1 |

9 | 14:30:03.491 | 14:30:04.441 | SLG | 264 | Line 6 | 65 | 0.77 | −0.1 | 6.1 |

_{1}; t

_{cl}: The clearing time of the CB at PCC

_{1}; P, Q: Active and reactive power of feeder loads at the time the event occurs; V: RMS phase-A voltage value one cycle before the reclosing takes place.

ANSI Code | k | n | t | I_{threshold} (A) | I_{of} | ANSI Curve |
---|---|---|---|---|---|---|

50 | 0.05 | 0.02 | 0.14 | 100 | 1.25 | Standard inverse |

50n | 0.05 | 2 | 80 | 20 | − | Extremely inverse |

© 2020 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**

Casals-Torrens, P.; Martinez-Velasco, J.A.; Serrano-Fontova, A.; Bosch, R.
Assessment of Unintentional Islanding Operations in Distribution Networks with Large Induction Motors. *Energies* **2020**, *13*, 345.
https://doi.org/10.3390/en13020345

**AMA Style**

Casals-Torrens P, Martinez-Velasco JA, Serrano-Fontova A, Bosch R.
Assessment of Unintentional Islanding Operations in Distribution Networks with Large Induction Motors. *Energies*. 2020; 13(2):345.
https://doi.org/10.3390/en13020345

**Chicago/Turabian Style**

Casals-Torrens, Pau, Juan A. Martinez-Velasco, Alexandre Serrano-Fontova, and Ricard Bosch.
2020. "Assessment of Unintentional Islanding Operations in Distribution Networks with Large Induction Motors" *Energies* 13, no. 2: 345.
https://doi.org/10.3390/en13020345