# Electrical Grounding Using the Isolated (or Ungrounded) Method

## Learn about the isolated or ungrounded method of system grounding, its main characteristics, advantages, disadvantages, and areas of application.

System grounding is fundamental in any electrical system. Properly selected system grounding improves the operating characteristics, provides a source of ground-fault current relaying, and increases the safety of personnel.

This article is part of a series discussing the various methods of system grounding, emphasizing its respective advantages, disadvantages, and areas of application. With this information, an individual may evaluate a grounding system qualitatively, assess whether it is appropriately selected and applied, and advise improvements if needed. The forms of grounding discussed in this article focus on alternating current (AC) systems.

Power system engineers have made significant steps in the way they control fault rates to improve service continuity by detecting and separating trouble or fault areas promptly. In this process, they analyze the behavior of the power systems under normal and faulted (both balanced and unbalanced) conditions.

The earliest power systems were ungrounded for two key reasons: to provide continuity of service in the event of a temporary ground and to reduce expenditures in grounding equipment and conductors. However, engineers kept running into many difficulties resulting from fault conditions. The fault statistics showed that most of them involved the ground, so they developed ways to connect energized parts to it. This practice allows for a higher fault current to go back to the source and lets the protective devices pick it up and operate.

## What is System Grounding?

System grounding connects a current-carrying component of an electrical system to the ground: neutrals of transformers, neutrals of rotating equipment, transmission, and distribution lines. A choice of methods is available that, if thoughtfully applied, enables significant improvements to be obtained even under challenging circumstances. Among the best-known methods are ungrounded, ground fault neutralizer, resistance grounded, reactance grounded, and solid or effectively grounded. All of these terms refer to the nature of the external circuit from the system neutral to the ground.

From one extreme to the other, there are several degrees of grounding that depend on the ratio of zero-sequence reactance to positive-sequence subtransient reactance (Xₒ/X1) and the ratio of zero-sequence resistance to positive-sequence subtransient reactance (Rₒ/X1), as viewed from the fault location. According to ANSI standards, when Xₒ/X1≤3.0 and Rₒ/X1≤1, the system is effectively grounded, which means there is no impedance between the system neutral and ground and we label it as solid ground.

Opinions and subjects associated with system grounding show a diversity that ranges from dogmatic belief to open-minded consideration of alternatives, from patient satisfaction to a wish for perfection. The method chosen depends on applicable code requirements, voltages, plant specifications, and an engineer’s experience and personal preferences.

## Review of the Method of Symmetrical Components

Although a thorough analysis of the method of symmetrical components is beyond the scope of this article, a quick refresher is useful for examining unbalanced conditions.

When there is no symmetry in the three phases of a power system — as the result of unbalanced loads, unbalanced faults, or short-circuits — the use of the method of symmetrical components in performance calculations is helpful. This method provides a means to transform an unbalanced system into three balanced systems by first obtaining the symmetrical components of the current at the fault location. Analyzing them as single-phase, it achieves accurate predictions of the values of current and voltage throughout the system.

The first paper indicating the possibilities of resolving an unbalanced system of currents into positive and negative sequence components as they are now known was published by L.G. Stokvis in 1912. These components were a by-product of Stokvis's attempt to find a method of determining the magnitude of the third-harmonic voltage produced by unbalanced line-to-load lines.

In 1913, C.L. Fortescue started researching a way to resolve an unbalanced system of n related phasors into n systems of balanced phasors called the symmetrical components of the original phasors. He referred to the overall framework with the term Symmetrical Coordinates. The n phasors of each set of components have the same length, and the adjacent phasors have equal angles between them. His conclusions were presented in an AIEE paper titled Method of Symmetrical Coordinates Applied to the Solution of Polyphase Networks in 1918. This work introduced the concept of zero-sequence voltages and currents.

Other systems developed are the positive-plus-negative, positive-minus negative, and zero sequence system, and the α, β, 0 components.

## Assessing this Method

The method assessed in this article will be symmetrical components because of its widespread use. The sequence components resulting from the transformation are positive-sequence, negative-sequence, and zero-sequence. Each set will have three quantities, one per phase.

With the original phasors labeled as a, b, and c, the three positive-sequence phasors are equal in magnitude and displaced 120° with phase sequence as the original phasors (abc). The negative-sequence phasors have the same characteristics, but the phase sequence is opposite to that of the original phasors (acb). The in-phase zero-sequence phasors are equal in magnitude. The three sets of phasors revolve at the same angular velocity, commonly counterclockwise.

The subscript for the positive-sequence components is 1, for the negative-sequence is 2, and for the zero-sequence is 0. Therefore, the positive-sequence voltage phasor of phase a will be Va1, the negative-sequence Va2, and the zero-sequence Va0 as seen in Figure 1.

*Figure 1. Symmetrical components of three unbalanced phasors*

Adding the positive-sequence, negative-sequence, and zero-sequence components result in the original unbalanced phasors seen in Figure 2.

*Figure 2. Addition of the symmetrical components*

The current of any one sequence flows in an independent circuit known as the sequence network, which comprises the source, if any, and the sequence impedance.

The voltage drop in a sequence network equals the sequence impedance multiplied by the sequence current. The positive-sequence (Z1), negative-sequence (Z2), and zero-sequence (Z0) impedances may have different values as seen in Figure 3.

*Figure 3. Sequence networks*

Impedance is a complex number involving the ratio of two phasors: voltage and current (Z=V/I). It has a real component, the resistance (R), and an imaginary component, the reactance (X). Then, the series circuit impedance is

Z=R+jX

for inductive reactance or

Z=R-jX

for capacitive reactance.

The sequence impedances, in terms of resistance and reactance, are

Z1=R1+jX1

Z2=R2+jX2

Z0=R0+jX0

The interconnection of the sequence networks depends on the fault examined.

## Isolated or Ungrounded Systems

It is a fact of nature that all power systems are grounded in some way or another. In terms of an electrical system, isolated or ungrounded refers to the notion that there is no intention of grounding. However, the conductors of all electrical equipment have a distributed natural capacitance between them and the ground. There are also capacitors used for power factor correction and voltage support, but these are not the ones we are examining. *An ungrounded system is a system grounded through capacitance.*

This natural capacitance is the result of electric charges traveling between energized conductors, through a dielectric medium including the ground. In overhead lines, the dielectric medium is the encircling air, and in cables, it is the insulation. Under normal conditions, a symmetrical set of three-phase capacitive currents flows in the lines, no matter the connected load: the *charging current*. Figures 4 and 5 illustrate these concepts.

*Figure 4. Distributed natural capacitance to ground and capacitive (charging) currents*

*Figure 5. Voltages and capacitive (charging) currents under normal conditions*

Usually, the charging current is smaller in aerial lines than in cables because of the higher capacitance of the latter.

When a line faults to ground, the fault current (denoted by If in the diagram below) goes back to the source through the distributed natural capacitances. This current is low in magnitude and not enough to actuate the protective devices, leaving the system in operation. This property means fewer interruptions in transmission and distribution lines, continuity of service in factories, and critical systems.

*Figure 6. Single line-to-ground fault in phase a.*

Imagine a cross-country distribution line with undulating movement close to tree branches on a windy day. If one of the branches contacts a line conductor, this is a line-to-ground fault. As previously pointed out, a low fault current will look for the source through the system's distributed natural capacitances, and no protective device will pick it up. As likely as not, the fault will be momentary and the line will continue in service.

Now visualize a factory with a high downtime cost. Rodents gain access to cable insulation, eat it, and start a line-to-ground fault. The power system won't stop (rodents will!). Clear the fault when the machinery is not in use — no need for downtime or loss of production.

These two examples show why many engineers claim ungrounded systems as an advantage. But real-life operation is not always that easy and there are some drawbacks, as we'll see in the following paragraphs.

### Drawbacks of Ungrounded Systems

Experience shows that as transmission and distribution systems grow in length and voltage, a large share of transient grounds — momentary grounds and lightning — are no longer self-clearing. This happens because the increase in capacitance boosts the fault current to significant values.

Before the ground-fault, the neutral of the ungrounded system remains close to ground potential, blocked there by the balanced capacitance of the three phases. The fault causes the neutral to shift in potential, and a line-to-line voltage appears throughout the system between the ground and the two unfaulted lines — a 73% increase — until clearing the fault. An example of this can be seen below in Figure 7.

*Figure 7. Neutral voltage shift with line-to-ground fault*

If the insulation coordination is not adequate and the fault is allowed to persist for a long time, the insulation may see a dramatic reduction in its lifespan or completely fail. It will initiate failures of rotating equipment, transformers, cables, and miscellaneous electrical equipment, thus disrupting normal operations. The National Electrical Code (NEC) requires the use of ground detectors to indicate when a fault occurs, and qualified maintenance personnel must trace and remove the ground as soon as possible.

From an economic perspective, higher insulation levels equal higher costs. For example, cables are available in three insulation levels: 100% for when it takes less than one minute to clear the fault, 133% for less than one hour, and 173% for an indefinite time. The higher percentage, the higher the price tag.

Another inconvenience is that tracing faults revealed by ground detectors requires time and money. If a second line-to-ground fault coincides in a different phase (which is very common) it results in high short circuit current. This current will trip one or two protective devices, cause considerable damage to equipment, and pose a shock hazard to personnel.

Figure 5 shows the phasor diagram of the source voltage and capacitive currents in normal conditions, and Figure 8 shows the phasor diagram of voltages and capacitive currents under a single line-to-ground fault in phase a. Notice the effects of the line-to-line voltages driving the capacitances of the unfaulted lines: the voltage to ground and the charging currents increase by √3, and the phase relationship of the currents changes from 120° to 60°.

*Figure 8. Voltages and capacitive currents under single line-to-ground fault in phase a*

Other issues of ungrounded systems are found in the transient overvoltages from *arcing-ground faults* and the *ferroresonant effects*.

Arcing-ground is a form of sequential clearing and restriking that can create overvoltages of more than five times the standard voltage. The fault current, although small, may be sufficient to support this arc. Ferroresonance is a nonlinear phenomenon caused by the system capacitance resonating with the exciting reactance of transformers, which creates very high amplitude and distorted waveforms. These two events are essential factors acting against the practice of operating power systems ungrounded.

### Studying System Behavior with the Method of Symmetrical Components

Let's examine the behavior of a system with a delta-delta connected transformer during a line-to-ground fault with the method of symmetrical components. First, we interconnect the three sequence networks in series (Figure 9).

*Figure 9. Sequence networks for line-to-ground fault*

Second, notice the values of the distributed capacitive reactances X_{1}c, X_{2}c, and X_{0}c, are large in comparison with the series impedance values Z_{1}s, Z_{2}s, ZTx, Z_{1}line, Z_{2}line, and Zₒline. For a rough calculation, consider that Z_{1}s and ZTx short-circuit X_{1}c in the positive-sequence network and that Z_{2}s and ZTx short-circuit X_{2}c in the negative sequence network. Also, the sum of the source, transformer, and line series impedances approaches zero relative to X_{0}c. Therefore, the key component to calculate the fault current is the zero-sequence capacitive reactance X_{0}c.

Then, source voltage Vs = Vւո (line-to-neutral)

I1 = I2 = Iₒ = Vւո/Xₒc.

Fault current If = Ia = 3Iₒ = 3Vւո/Xₒc = √3Vււ/Xₒc, where Vււ = √3Vւո = line-to-line source voltage.

Get the currents in phases b and c using the phasor diagram from Figure 8.

Let Ia = -1 per unit, then Ib = 0.577 Ia∠+30° pu and Ic = 0.577 Ia∠-30° pu.

Observe that Iₒ = charging current and the absolute value of Ia = √3Ib = √3Ic = 3xcharging current.

To calculate the charging current and the fault current during the design phase it is common practice to use typical charging capacities (Cₒ) from tables for all power system components and add them to find the total charging capacitance in microfarad (µF) per phase. Then, Xₒc = 1/2πꬵ Cₒ = 1/120πCₒ Ω/phase for a frequency of 60 Hz.

In installed low voltage systems, the best way to determine the amount of the charging current is a test by intentionally grounding one phase with a special device. However, observe caution since this is a risky operation.

### Example 1

Calculate the charging current and the single-line-to-ground fault current for a 13.8 kV ungrounded power system whose total charging capacitance has been estimated, by tables, in 0.658 µF per phase.

First, calculate zero-sequence capacitive reactance = Xₒc = 10⁶/(120x3.14x0.658) = 4,031 Ω/phase.

Then, the charging current =** Iₒ** = Vւո/Xₒc = 13,8kV/(√3x4,031) = **1.98 A/phase.**

Finally, the fault current** If **= 3Iₒ = 3x1.98 = **5.94 A**

### Example 2

A 69 kV ungrounded power system undergoes a single-line-to-ground fault in phase a. The charging current per phase is 19.7A. Calculate the zero-sequence capacitive reactance, the fault current, and currents in phases b and c while the fault is active.

First, from Iₒ = Vւո/Xₒc, the capacitive reactance **Xₒc **= Vւո/Iₒ = 69kV/√3x19.7 = **2,022 Ω/phase.**

Then, the fault current **If** = Ia =3Iₒ = 3x19.7 = **59.1 A.**

Finally, from Figure 8, **Ib** = 0.577Ia∠+30° = 0.577x59.1∠+30° = **34.1∠+30° A.**

**Ic** = 0.577Ia∠-30° = 0.577x59.1∠-30° = **34.1∠-30° A.**

The values used in these examples are from actual power systems. Typical charging currents for distribution systems in industrial plants range from less than 1A to 20A. Utility distribution systems would exhibit higher values because of the greater length of the conductor involved.

### Favorable Performance Traits and Drawbacks

The core advantage of an ungrounded system in industrial plants lies in the possibility of maintaining service of the entire network, including the faulted section, while repairing the fault during a maintenance shutdown, thereby reducing downtime. In transmission and distribution lines, service is not interrupted during temporary faults like lightning or occasional contact with vegetation or animals.

Against this benefit must be balanced disadvantages such as the difficulty of relaying the fault automatically, the complexity of locating it, the long-continued overstressing of the insulation of the unfaulted phases, the hazard of multiple grounds in different phases, the transient overvoltages due to arcing grounds, the ferroresonance effects, and the increased cost of insulation in all electrical components.

## Areas of Application

Choosing a grounding method depends on the power system usage and the degree of power interruption tolerated. Power systems in most older factories were ungrounded, three-phase, three-wire, delta, and many of these are still in use today. They based the choice on three factors: continuity of operations, less use of copper (fewer conductors are needed), and no need for grounding equipment. However, it has a high additional cost of insulation.

Nowadays, the general recommendation in industrial systems is to not use the ungrounded method unless in need of service continuity or certain code requirements. Neither is it recommended for transmission and distribution systems in utilities.

## Summary

System grounding is a crucial factor for the correct operation of any power system. It consists in the connection of current-carrying conductors, such as the neutrals, to ground either solidly or with a current limiting device.

All electrical components have a distributed natural capacitance to the ground. When an AC voltage is applied, a small current (the charging current) flows to the ground through the capacitance.

The connection of the isolated or ungrounded systems to the ground is through distributed natural capacitance. When a line-to-ground fault occurs, the ground shorts out the capacitance of that phase, and the voltage to ground and charging currents of the ungrounded phases increase by √3.

Consideration of this system should only occur when the consequences of an abrupt shutdown are more severe than those of a small ground-fault current flowing for some time. However, downsides in the use of ungrounded systems act against its practice, the most significant drawbacks being arcing-ground overvoltages and ferroresonant conditions.th

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