System and method for ground fault detection and fault type evaluation

The embodiments disclose a circuit for detecting and determining a type of ground fault in a security system. An operational amplifier (OA) having positive and negative inputs and an output may receive AC input signals having different frequencies, f1 and f2 at a positive input and provide an AC output signal at the output. An OA feedback loop may comprise a ground fault equivalent impedance connected at the OA negative input and a feedback resistor connected between the OA output and the OA negative input. A rectifier may convert the AC output signal to a DC signal and a filter to obtain a steady DC voltage from the rectified DC signal. A steady DC voltage for two different AC input signals may be obtained and converted to a relative voltage with respect to a constant input voltage amplitude. The relative voltages may be compared to detect and determine a type of ground fault condition.

BACKGROUND OF THE INVENTION

1. Field of the Invention

Embodiments of the present disclosure relate to security alarm systems and associated methods for protecting residences, businesses and other premises. More particularly, the present disclosure relates to ground fault detection within the circuitry of a security alarm system and identifying the type of ground fault condition once detected.

2. Discussion of Related Art

Security or alarm systems are installed in premises to detect hazardous or potentially hazardous conditions. A security system generally includes a plurality of detectors/sensors, one or more keypads and a control panel which contains much of the system electronics. The control panel may include a communication interface for remote monitoring and two-way communication over telephone or wireless communication paths with a remote monitoring station. Each of the detectors may communicate with the control panel to provide its current status as well as notification of an alarm condition. Examples of possible alarm conditions may include unauthorized entry or the unexpected presence of a person who may be an intruder, fire, smoke, toxic gas, high/low temperature conditions (e.g., freezing), flooding, power failure, etc. In other words, an alarm condition may represent a detectable condition that might lead to personal hazard or property damage. Audible and/or visible alarm notification devices such as sirens, lights, etc., may also be utilized to notify occupants of the existence of an alarm condition. The control panel may be located in a utility room, basement, etc., and may communicate with the detectors and notification devices over wired or wireless signal paths. A keypad, which may also communicate with the control panel over a wired or wireless connection, may be used to arm/disarm the system as well as providing a means to display various system messages via a status display screen.

Maintaining the integrity of electrical connections between and among the various detectors/sensors, notification devices, keypads and control panel is of great importance to ensure that these devices are functioning properly. Ground fault conditions may present a breakdown in system integrity. A ground fault condition is generated when a minimum leakage current is flowing to earth ground; in particular if any wire connected to the alarm system is shorted or heavily coupled to earth ground. In the case of an alarm system, if any wire connected to the alarm system should touch or create a leakage to earth-ground, a ground fault should be indicated. Thus, it is desirable to detect, identify and notify of a ground fault condition in the control panel that may compromise the integrity of a system. If left unaddressed, ground fault conditions may render the security system inoperable.

One type of ground fault condition is a non-isolated panel connection to earth ground. A non-isolated panel connection may include certain of the wired control panel connections to other system components such as, for example, the detectors, keypads and notification devices. One common approach to detecting such a ground fault condition involves injecting a steady DC current to earth ground and measuring the voltage drop between earth ground and circuit ground. The voltage drop is proportional to the ratio of earth ground to circuit ground resistance. This may typically involve a current generator to supply the DC current that may be coupled to the higher voltage of the circuit to drive the ground resistance. The voltage drop between earth ground and circuit ground is then evaluated to detect whether a ground fault has occurred. For example, a detected resistance that is smaller than a specific expected value may indicate an unspecified ground fault condition in the system. The above solution, however, is not immune to DC level shifting. Generally, DC level shifting may occur when interfacing different types of circuits to each other, such as when interfacing circuits operating at one particular voltage level to circuits operating at another voltage level. The above solution cannot categorize, identify, or distinguish between a capacitive coupling induced ground fault condition and a resistance induced ground fault condition. In addition, a capacitive coupling type of ground fault condition may increase the probability of a control panel malfunction due to possible component coupling to a noise source. It is with respect to these and other considerations that the present improvements have been needed.

SUMMARY

In view of the foregoing, a ground fault detection and notification system is needed that can reliably identify the type of a detected ground fault condition. Accordingly, exemplary embodiments of the present disclosure are directed to a process of detecting and identifying ground fault conditions for security systems.

In an exemplary embodiment, a circuit for detecting and determining a type of ground fault in a security system is disclosed. An AC function generator may generate at least two separate AC input signals of different frequencies, f1and f2. An operational amplifier (OA) having positive and negative inputs and an output may receive the AC input signals at the positive input and provide an AC output signal at the output. An OA feedback loop may comprise a ground path impedance coupled between the OA output and the OA negative input. The AC output signal may be coupled with the ground path impedance and applied to the OA negative input. A rectifier may convert the AC output signal to a DC signal and a filter to obtain a steady DC voltage from the rectified AC signal.

In another exemplary embodiment, a method of determining a type of ground fault is disclosed. A first AC input signal having a first frequency (f1) may be applied to a positive input of an operational amplifier (OA). A feedback signal derived from a first AC output signal of the OA coupled to a ground path impedance may be applied to a negative input of the OA. The first AC output signal may be rectified to convert the first AC output signal to a first DC signal and then filtered to obtain a first steady DC voltage. A second AC input signal having a second frequency (f2) may be applied to the positive input of the operational amplifier (OA). A feedback signal derived from a second AC output signal of the OA coupled to a ground path impedance may be applied to the negative input of the OA. The second AC output signal may be rectified to convert the second AC output signal to a second DC signal and then filtered to obtain a second steady DC voltage. The ratio of the second steady DC voltage to the first steady DC voltage may be determined and used to characterize a type of ground fault.

DESCRIPTION OF EMBODIMENTS

FIG. 1is a block diagram of a typical security system10capable of implementing the embodiments of the present disclosure. The security system10may be installed in a building or premises. Security system10includes a control panel20which generally controls operation of the system. A number of detection devices181. . .18nare utilized to monitor an area. Detection devices may include, for example, motion detectors, door contacts, glass break detectors, smoke detectors, water leakage detectors, etc. Detection devices181. . .18ncommunicate with panel20by a wired interconnect18A, wirelessly18B, through the electric wiring of the premises18C, or otherwise. One or more user interfaces, such as keypad25is used to communicate with control panel20to arm, disarm, notify and generally control system10. The security system10may further include other notification devices such as sirens, emergency lights, etc., referenced generally as19.

Control panel20communicates with each of the detection devices181. . .18n, keypad25and notification devices19as well as communicating with a monitoring facility30which is typically geographically remote from the premises in which system10is installed. Control panel20may include a CPU34, memory35and communicator36. CPU34functions as a controller to control the various communication protocols within system10. Memory35stores system parameters, detection device information, address information etc. Communicator36sends and receives signals to/from the monitoring facility30via communications link31. Alternatively, communicator36may be a separate device that communicates with controller20via a hardwired or wireless connection.

When an alarm condition occurs based on the operation of one or more detection devices181. . .18n, a signal is transmitted from the respective detection device to control panel20. Depending on the type of signal received from the one or more detection devices, communicator36communicates with monitoring facility30via link31to notify the monitoring facility that an alarm notification has occurred at the premises. Communication link31may be a POTS (Plain Old Telephone System), a broadband connection (e.g., internet), a cellular link such as GSM (Global System for Mobile communications) transmission, a voice-over-IP (VoIP) connection, etc. In certain security systems, keypad25, control panel20and communicator36may be housed within a single unit.

As noted above, keypad25is used to communicate with control panel20to arm, disarm, notify and generally control system10. Keypad25includes a status display which may include either individual indicators, such as discrete light emitting diodes or may include an LCD or LED display, capable of displaying messages regarding the status of particular detection devices181. . .18nand/or operation of the system.

Each security system is given at least one unique access code (sometimes referred to as a PIN), which is generally a sequence of symbols (e.g. numbers, letters, characters, etc.) entered via keypad25used to arm and disarm system10. When arming system10, a user enters their access code and an exit delay time is provided before the detection devices181. . .18nare activated so that a user may exit the premises before system10becomes armed. Conversely, upon entering the premises, the user enters the access code to disarm the system10. An entry delay time period may be programmed into the system10to allow the user to enter the access code before the system goes into alarm mode.

Maintaining the integrity of electrical connections throughout the security system is of great importance to ensure that the detection devices181. . .18n, control panel20, keypad25and notification device(s)19are all functioning properly. Ground fault conditions may indicate a breakdown in system integrity. As noted above, a ground fault condition is a type of short circuit that may exist when a hot wire touches or leaks to an earth ground wire or other earth grounded conductor. If left unaddressed, ground fault conditions may render the security system inoperable and/or create hazardous voltages to anyone touching the equipment.

Quickly and accurately determining the type of a ground fault may aid in troubleshooting and remedying the problem causing the ground fault condition. There are typically three types of ground fault conditions that may lead to undesirable leakage conditions in the control panel20, those that are resistive in nature, those that are capacitive in nature, and those that stem from an AC fault. An AC fault, for instance, may result when one of the AC wires from an AC power source such as, for example, a main transformer within the control panel20is shorted to or closely coupled to earth ground. If the type of ground fault condition is identifiable, the source of the problem may be easier to pinpoint and fix by an electrical technician.

The embodiments described herein present an operational amplifier (OA) based circuit that may be implemented within the control panel20. The circuit may assist in detecting and identifying multiple types of ground fault conditions. In general, the circuit makes use of the ground impedance of the panel as part of a feedback loop to measure the gain of the OA when driven by particular AC input signals. As further detailed below, OA gains (as converted to and measured in DC voltage levels) between particular OA input signals and the OA output signal may be compared to detect and determine a type of ground fault condition. The circuit may allow for impedance calculations that may indicate capacitive coupling ground fault conditions, resistive ground fault conditions, and AC faults or perturbances from earth ground. Once a ground fault condition has been detected and identified, remedial steps may be taken to correct the underlying problem that caused the ground fault condition.

FIG. 2illustrates an exemplary ground fault detection circuit200in accordance with an embodiment of the present disclosure. The circuit200ofFIG. 2may be incorporated into a control panel20of a security system10to detect and identify undesirable ground fault conditions that may occur within the system10. A ground fault condition may be indicative of a short or a close coupling of a connection to earth ground. Such a condition may undesirably disturb the functionality of the security system to the point of rendering the system inoperable.

The circuit200may include an AC function generator210to ensure good amplitude stability and control such as, for example, a direct digital synthesis (DDS) sine wave generator. An AC function generator is a generic signaling device adapted to generate a variety of test signals. For example, AC function generator210may generate sinusoidal waveforms of different frequencies as set by frequency control input FCTRL214. For illustrative purposes, a first waveform may be generated having a frequency of f1while a second waveform may be generated having a frequency of f2in which f2is half of f1. The first and second AC signals may be engineered to have the same amplitude. The AC function generator210may be disabled using On/Off input212.

In operation, the first and second AC signals may be alternately applied to an operational amplifier (OA)220at input215in which the input voltage (vin) for each of the first and second AC signals is the same (e.g., the same amplitude). A DC blocking capacitor (CB)216ensures that no DC signals pass to the OA220. A ground fault impedance path232may also be incorporated into a ground fault feedback loop230of the OA220that feeds the OA output signal at227back to the OA negative input to the OA220through a feedback resistor (RFB)234. Thus, the OA AC signal output amplitude at227will be correlated to the ground fault impedance (ZG)232. The ground fault feedback loop230may be modeled as an RC series circuit comprised of an impedance ZG232and capacitor CG233which forms a ground fault equivalent impedance231that is coupled in series with feedback resistor (RFB)234. For the frequency of generated reference voltages, the impedance of the capacitor CGis very low and can be considered ZG=ZG+Z(CG). Because ZG>>Z(CG), the OA220operates as a variable gain stage to generate an AC output signal at227having a voltage level (vout) that may be determined according to

Since the output signal at227is an AC signal, it is supplied to a rectifier240to convert it to a DC signal. The rectifier240is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC) which flows in only one direction. While rectification can deliver unidirectional current, it does not produce a steady voltage. In order to produce steady DC voltage level from a rectified AC signal, a filter250may be used. In its simplest form the filter250may be a capacitor placed at the DC output of the rectifier240. Thus, after rectification and filtering, the AC output signal of OA220is converted to a steady DC voltage260. This process is performed for each of the AC input signals (f1and f2) generated by AC function generator210resulting in a steady DC voltage260for each of the AC input signals (f1and f2).

If the ground impedance ZG232is infinite, the OA220will act as a repeater meaning that the OA output signal level at227(vout) will be the same as the OA positive input signal at215(vin). This will yield the minimum rectified result and is indicative of no ground fault condition. Any other ground impedance that is not infinite will create a gain at the output of the OA220at227when an AC input signal is applied at the positive input215of OA220. Thus, a gain at the output of the OA220at227will yield a steady DC voltage at260and may be indicative of a ground fault condition.

If the steady DC voltages260(e.g., vout1and vout2) are the same after rectification and filtering of the output signal at227for both AC input signals (f1and f2), the fault may be characterized as resistive. If the steady DC voltages260(vout1and vout2) are different after rectification and filtering of the output signal at227for both AC input signals (f1and f2), the fault may be characterized as reactive (e.g., due to capacitive coupling).

For example, given a frequency characteristic of f2=½f1, a vrelratio (i.e., vrel—2/vrel—1) of 1:1 indicates a pure resistive ground fault condition and a ratio of 2:1 indicates a pure reactive ground fault condition. A vrelratio between 1 and 2 indicates a degree to which the ground fault condition is reactive meaning there may be a capacitive coupling problem though not necessarily a total breakdown. If the AC function generator210is off and the output level (vout) of OA220is high, the ground fault condition may be characterized as an AC coupling issue.

Returning to circuit200ofFIG. 2, the earth ground connection may be AC coupled such that any DC level shifting (e.g., a change in the DC voltage level) that may result from I/0 biasing between circuit ground and earth ground will not affect the ground fault condition evaluation process. Biasing in electronics refers to the establishing of predetermined voltages or currents at various points of an electronic circuit to set an appropriate operating point. Thus, circuit200has been designed to be immune from any such DC level shifting effects because of the AC coupled earth ground connection through CG233.

The circuit200may further include a test loop225adapted to perform device integrity checking and resistive fault calibration. For instance, the resistor (R_TEST)226may be substituted for the ground fault impedance path ZG232. Since the resistor (R_TEST)226is a known value, the results for each of the AC input signals generated by AC function generator210can be calculated ahead of time and then compared to the actual results to calibrate the circuit based on the expected results.

The measurement cycle used to obtain the steady DC voltages260(vout1and vout2) for the AC input signals characterized by f1 and f2is repetitive according to the following process. The circuit200is initially set such that the AC function generator210is off and the test loop225is off. The output (vout) of the OA220at227is recorded. Next, the AC function generator210is switched on via On/Off input212. The frequency control (FCTRL)214is set for frequency f1and a first sine wave of frequency f1is generated and applied to the positive input of OA220at215. The circuit200will rectify the OA220output at227using rectifier240then filter the rectified output using filter250to yield a first measurement (vout1) at260that is recorded and vrel—1(as vout1−vin) is evaluated. The frequency control (FCTRL)214is then set for frequency f2in which f2is ½ of f1, for example, and a second sine wave of frequency f2is generated and applied to the positive input of OA220at215. The circuit200will rectify the OA220output at227using rectifier240then filter the rectified output using filter250to yield a second measurement (vout2) at260that is also recorded and vrel—2(as vout2−vin) is evaluated. The AC function generator210is then switched off using On/Off input212concluding one measurement cycle. The process is repeated on a continual basis to monitor the overall security system10status with respect to ground fault conditions.

FIG. 3illustrates one embodiment of a logic flow300of an exemplary ground fault detection method in accordance with an embodiment of the present disclosure. The logic flow300may be representative of some or all of the operations executed by one or more embodiments described herein.

In the illustrated embodiment shown inFIG. 3, the logic flow300may initiate a measurement cycle at block305. The logic flow300may take a measurement to determine an AC ground fault condition at block310as is described in more detail with reference toFIG. 4. The logic flow300may then take the measurements to determine a resistive or reactive ground fault condition at block315as is described in more detail inFIG. 5. The logic flow300may then evaluate the measurements to determine a type of ground fault condition at block320as is described in more detail inFIG. 6. The logic flow300may react to a ground fault condition at block325and create a ground fault condition notification alert at block330.

For example, upon detection of a ground fault condition, the control panel20may create a notification alert. The notification alert may include one or more of an audible chime, a steady or blinking light, and a signal to a remote monitoring location. The audible chime may be sounded by a notification device19such as a speaker. The steady or blinking light may be displayed by a notification device19such as a light bulb or light emitting diode (LED) visible on the keypad25and/or the control panel20. In addition, the notification alerts may be configured to indicate the type of ground fault condition. For example, the audible alert may sound differently depending on the type of ground fault condition that was detected. Thus, a speaker may emit sounds in a particular pattern to indicate the type of ground fault condition. An AC ground fault condition may be associated with a single intermittent chirp. A pure resistive ground fault condition may be associated with a double intermittent chirp. A reactive ground fault condition may be associated with a triple intermittent chirp. Similarly, a light may blink in a particular pattern to indicate the type of ground fault condition. The embodiments are not limited to these examples.

FIG. 4illustrates one embodiment of a logic flow400for taking the measurement to determine an AC ground fault condition referenced in block310ofFIG. 3in accordance with an embodiment of the present disclosure. The logic flow400may be representative of some or all of the operations executed by one or more embodiments described herein.

In the illustrated embodiment shown inFIG. 4, the logic flow400the AC function generator210and test loop225are switched off at block405. With the AC function generator210and test loop225switched off, the output of OA220is measured and recorded at operating point227of circuit200at block410. The embodiments are not limited to this example.

FIG. 5illustrates one embodiment of a logic flow500for taking a measurement to determine a resistive/reactive ground fault condition referenced in block315of the logic flow300shown inFIG. 3in accordance with an embodiment of the present disclosure. The logic flow500may be representative of some or all of the operations executed by one or more embodiments described herein.

In the illustrated embodiment shown inFIG. 5, the logic flow500sets the AC function generator210to “On” and the test loop225to “Off” at block505. The logic flow500may then apply a first input signal generated by AC function generator210to the positive input215of OA220at block510. The first input signal generated by AC function generator210may be characterized by a frequency of f1. The OA220will produce an output signal at227. The output signal at227will be a function of the input signal at215and a negative input signal at217. The negative input signal at217may be derived from a feedback loop comprising the output signal at227coupled with the ground fault impedance path232. The ground fault equivalent impedance231may be modeled as an RC series circuit comprised of the impedance ZG232and capacitor CG233. The ground fault feedback loop230may be modeled as the ground fault equivalent impedance231and the feedback resistor (RFB)234.

The logic flow500may then rectify the output of OA220at block515. The output of OA220at227will be an AC signal. The AC signal output of OA220at227may be input to the rectifier240to convert it to a DC signal. The logic flow500may then filter the output of rectifier240by applying the output of rectifier240to the filter250at block520. The output of rectifier240will be a DC signal but not one of steady voltage. The filter250may produce a steady DC voltage260for the first input signal generated by AC function generator210. The steady DC voltage260for the first input signal may be referred to as vout1. The same steps may then be performed for a second input signal generated by AC function generator210.

The logic flow500may apply the second input signal generated by AC function generator210to the positive input215of OA220at block530. The second input signal generated by AC function generator210may be characterized by a frequency of f2which may be, for example, ½ of f1. The OA220will produce an output signal at227. The output signal at227will be a function of the input signal at215and a negative input signal at217. The negative input signal at217may be derived from a feedback loop comprising the output signal at227coupled with the ground fault impedance232. The ground fault equivalent impedance231may be modeled as an RC series circuit comprised of the impedance ZG232and capacitor CG233. The ground fault feedback loop230may be modeled as the ground fault equivalent impedance231and the feedback resistor (RFB)234.

The logic flow500may then rectify the output of OA220at block535. The output of OA220at227will be an AC signal. The AC signal output of OA220at227may be input to the rectifier240to convert it to a DC signal. The logic flow500may then filter the output of rectifier240by applying the output of rectifier240to the filter250at block520. The output of rectifier240will be a DC signal but not one of steady voltage. The filter250may produce a steady DC voltage260for the second input signal generated by AC function generator210. The steady DC voltage260for the second input signal may be referred to as vout2. The embodiments are not limited to this example.

FIG. 6illustrates one embodiment of a logic flow600for evaluating the measurements referenced in block320of logic flow300shown inFIG. 3in accordance with an embodiment of the present disclosure. The logic flow600may be representative of some or all of the operations executed by one or more embodiments described herein.

In the illustrated embodiment shown inFIG. 6, the logic flow600may evaluate voutat block605. voutmay be indicative of the presence of an AC ground fault. If voutis equal to zero (0) volts when AC function generator (e.g., DDS)210is turned OFF, then no AC ground fault condition is determined at block610. If, however, voutis not equal to zero (0) volts when AC function generator (e.g., DDS)210is turned OFF, then an AC ground fault condition is determined at block615. This may cause the OA220to act as an inverted amplifier for any AC perturbation present at earth ground when the AC function generator (e.g., DDS)210is turned OFF.

Three (3) different states may be tested to evaluate whether there is an AC ground fault. The first test is for an AC fault as just described in blocks605-615. If there is no AC fault as determined at block610, the AC function generator (e.g., DDS)210may be turned ON to evaluate whether there may be other types of ground faults. The AC function generator (e.g., DDS)210may utilize two (2) different input frequencies to evaluate whether there may be other types of ground faults. In this example, the ratio of the input frequencies is 2:1. Other frequency ratios for f1and f2may be implemented such that a ground fault type may be determined based on a chosen ratio (e.g., n:1).

Fault Type Evaluation

As previously mentioned, there can be three types of ground fault conditions: an AC fault type, and two types of low impedance fault types—resistive or reactive. The circuit200ofFIG. 2may assist in detecting and identifying the type of the ground fault condition which can significantly aid in troubleshooting and fixing the problem causing the ground fault condition. As described above, the circuit200repetitively cycles taking measurements for vout, evaluates vrel—1and vrel—2and recording the results. The results are then analyzed to determine what type of ground fault has occurred.

An AC fault may occur, for instance, if one of the AC wires from the main transformer secondary is shorted or is closely coupled with earth ground. The value of voutmay detect this situation. For example, if AC function generator210is off, the positive input215of the OA220will be coupled to ground since it is not being driven by the AC function generator210and the OA output227will follow the AC level at the negative input217of OA220. If considering, for example, the ground impedance ZG232, the OA220output signal at227will be amplified according to the ratio of the ground impedance to the feedback resistance (−RFB/ZG). In this case ZG232is the impedance of AC perturbation source. The OA220output signal at227may then be rectified by rectifier240and filtered by filter250. A higher level AC negative input signal at217may saturate the OA220output at227and generate a fault. The OA220voltage output level at227will be set according to (−RFB/ZG)*vinwhere vinis the perturbative input voltage and ZG232represents the internal resistance of perturbative source. Usually an AC fault will saturate the OA at output227. In this example, if voutat227yields 0V when AC function generator210is off then no AC fault has occurred. This fault condition may be determined over a few measurement cycles.

A low impedance fault type may occur, for instance, if one of the available control panel inputs is touching or is coupled to earth ground. The values for vrel—1, and vrel—2may provide information about earth ground impedance and the fault type (resistive or reactive). A reactive result may be characterized as a capacitive coupling issue.

An AC fault type is first excluded by performing the first step of the cycle (described above) and analyzing voutat227. The circuit200then obtains values for vrel—1, and vrel—2which may be interpreted as follows.

If voutrepresents the OA220output voltage at227and vinthe carrier level at215, then the dependency may be described as:

vout=vi⁢⁢n⁡(1+RFBZG)(Eq.⁢1)
if vrel=vout−vin, then

vrel=vout-vi⁢⁢n=vi⁢⁢n·RFBZG(Eq.⁢2)
if the ground impedance is modeled as an RC series circuit, the complex impedance becomes:

ZCOMPLEX=R+1j⁢⁢ω⁢⁢c=R-j⁢1ω⁢⁢c(Eq.⁢3)
where ZG232at a specific carrier frequency may be determined as:

ZG=ZCOMPLEX=R2+1ω2⁢c2(Eq.⁢4)
The impedances that result for two different frequencies, f1and f2are:

ZG⁢⁢1=R2+1(2⁢⁢π⁢⁢f1)2⁢c2(Eq.⁢7)ZG⁢⁢2=R2+1(π⁢⁢f1)2⁢c2(Eq.⁢8)
In this case two possible extreme conditions may be considered. The first condition is indicative of a pure resistive fault in which

vrel_⁢2=vrel_⁢1(Eq.⁢9)Δ⁢⁢vrel=vrel_⁢2vrel_⁢1=1(Eq.⁢10)
The second condition is indicative of a pure capacitive fault in which R=0 and

For two different frequencies with a defined ratio of 2:1 (e.g., f1and ½ f1), Δvrelwill swing from 1 to 2 depending on the ground fault type. Thus, by evaluating Δvrel(vrel—2/vrel—1) it can be decided whether a ground fault condition exists and if so characterize the type of that ground fault condition.