In North America, more than 70% of circuit miles below 69kV are
three phase, four-wire multi-grounded distribution circuits.
In the event of a single phase-to-ground fault, circuit breakers at the
substation open. If the DR is of sufficient size to support the loads,
an unintentional island could be created. Based upon the method of
symmetrical components, the phase-to-ground voltages on the
unfaulted phases could increase up to 173% of the pre-fault voltage
level. This can damage single phase customers or utility surge
Source: Johnson et al.
IEEE C62.92.1: a system is effectively grounded if the Coefficient of
Grounding is less than 0.8 where the COG is the ratio of max phase to
ground voltage divided by phase-to-phase voltage.
IEEE I42: “…for all points on the system the ratio of zero-sequence
reactance to the positive-sequence reactance is less than 3 and the
ratio of zero sequence resistance to positive sequence reactance is less
than 1 for any condition of operation and for any amount of connected
The X0/X1 and R0/X1 ratios are conditions that usually provide
compliance with the actual definition. The Industrial Application Society
of IEEE took the sequence ratios as the definition when they made their
"color books”, therefore many use the 142 definition, but it is a logical
consequence, not an a priori definition.
A Quick Word on Symmetrical Components
The methodology introduced in 1913 by Charles Fortescue, who
demonstrated that any set of unbalanced three-phase quantities
could be expressed as the sum of three symmetrical sets of balanced
In this diagram, representing a SLG fault, the generator is represented
by a balanced positive sequence voltage phasor. This is not accurate for
an inverter! If a current source is used, it is of vital importance to also
consider the topology of the load.
Source: Johnson et al.
Traditionally, generators are modeled as a voltage behind a sub-
transient, transient and steady state reactances. These are physical
values that can be verified with proper test procedures. In their grid-
tied behavior the inverters modulate the switching of their transistor
bridges to inject current from their DC bus based upon the AC output
current. That is emphatically not a voltage source.
Compliance Issues for Inverters
The inverter does have an AC line inductor, but the impedance to
sequence currents vary with time as the switches open and close.
A PWM Switching PatternInverter H-Bridge
Transformer Based Solutions
For DER plants which install a new transformer, a Delta/Wye(g)
[gen/grid] transformer presents a grounded source to the utility and is
generally accepted as effectively grounded. This, may, however,
desensitize the ground fault relays (51N) at the substation.
For customers with an existing transformer Wye(g)/Delta or Wye(g)/
Wye, a grounding bank must be installed, which adds cost, project
delays, desensitizes the substation relay, and ignores other
mechanisms for TOV which may be more relevant to a given
Controls Based Approaches
Based upon the IEEE C62.92.1 definition, if a generator limits over
voltages to less than 140% L-N it is effective grounded. Therefore,
any mechanism that achieves this should be valid.
Inverters have fast microprocessors onboard.
Fast gate blocking an extra high-voltage fast-trip setting is included by
most manufacturers for self-protection purposes.
Spain and Australia require TOV tests that determine the reaction to a
loss of load. They resemble the CBEMA/ITIC curve.
The inverter shuts down upon seeing a high terminal voltage. Typically,
1.4 p.u., in 50 ms. Note: these are single phase tests and do not
account for different transformer configurations.
Problem: There are many ways to accomplish the
aforementioned behavior. Therefore, it is challenging to
generalize a given inverter’s behavior.
“Rotating machines are 90% physics and 10% engineering
design. Inverters are the exact opposite.”- Reigh Walling
This is the main issue in predicting the behavior of an
inverter during a TOV event.
1. Current Sense: RMS or instantaneous in control loop, sequence
measurements, phasor average or independent control loops,
2. Voltage Sensing: 1 or 3 phase, L-N or L-L, phasor average or
independent control loops, RMS or instantaneous, sampling rates.
3. Current Control Loop: independent phase control or 3 phase space
vector, saturated controls, different inverter bridge topologies.
4. Phase Lock Loop: αβ transform phase angle error.
5. Power Control: reactive power support, Volt/Var functions, power
There is an open debate whether defining the symmetrical component
impedances of an inverter has merit. But it is generally accepted that
a current source model is more accurate. However, this approach
has its limitations as well.
• Abnormal voltages producing imbalanced currents - non idealized
• Constant power regulation is more common than constant current.
Power is regulated in the steady state by an outer loop, typically with
slower dynamics than the inner loop which regulates current at high
bandwidth. Power regulation also will tend to have limits so that
excess current is not ordered during undervoltage conditions.
• New functions like LVRT change everything in a snap of the fingers.
100% real power to 100%, VARS in 10ms! How is that accounted
• Furthermore, most inverters do not inject zero sequence current.
Even if the switch controls permitted it, the unit is typically a 3 wire
connection without a neutral return.
Model validation is of course necessary
Proposed UL 1741 SLG TOV Test Setup
Keep in mind: There is more than one mechanism of TOV at play here.
Modeling can be a potential powerful tool for assessing the impact of
inverters on distribution systems. However, to date, most software
packages do not have an accurate model for the inverter.
Inverter manufacturers and simulations vendors need to define a library
of models that manufacturers can certify their products to. Otherwise
there is way too much variability for a generic model to be accurate.
Transformers and loads must be considered when simulating an inverter
and EPS. The dynamics are determined partly by Ohm’s Law,
because of the current-source inverter pushing current into the loads;
and partly by the controls of the inverter itself, because its ability to
source current does depend on its terminal voltage. In any case, it’s
all about the interaction between the inverter and the loads, and not
about an inherent GFO mechanism in the inverter, because it doesn’t
Thank you for your attention!
With Special Thanks to Michael Ropp, Northern Plains
Reigh Walling, Walling Energy Systems Consulting
1704/26/14 Effective Grounding
1. Protection for Unexpected Delta Sources
Ken Behrendt Schweitzer Engineering Laboratories, Inc. New Berlin, WI USA
2. A Review of System Grounding Methods and Zero Sequence Current Sources
Gerald Johnson (Basler Electric), Mark Schroeder (Dominion VA Power)
and Gerald Dalke (Power System Relay Services).
3. Advanced Grid Planning and Operations
Mark McGranaghan, Thomas Ortmeyer, David Crudele, Thomas Key, Jeff Smith, Phil
4. Alternate Energy Customer Interconnection Requirements
PECO Solar Conference. Barry Hornberger. June 1, 2011.
5. PECO Grey Book