Applicability of True Voltage Unbalance Approximation Formula for
Unbalance Monitoring in LV Networks with Single-phase Distributed
Generation
Ognjen Gagrica
1
, Tadeusz Uhl
1
, Phuong H. Nguyen
2
and J. F. G. Cobben
2
1
AGH University of Science and Technology, Krakow, Poland
2
Eindhoven University of Technology, Eindhoven, The Netherlands
Keywords: Voltage Unbalance, Power Quality, Photovoltaic, Distributed Generation, Smart Grid.
Abstract: In the hierarchy of power transmission and distribution systems, the three-phase LV distribution networks
are most susceptible to voltage unbalance (VU). The main causes are large presence of randomly distributed
single-phase loads and, following the latest trends, the increasing presence of single-phase distributed
generators. Most widely accepted VU calculation is based on percentile ratio of negative and positive
sequence voltage (voltage unbalance factor, VUF). Obtaining sequence voltages is a complex domain
calculation and requires simultaneous sampling of three-phase voltages and angles. This is why the existing
VU monitoring and mitigation solutions are dominantly three-phase. Without an additional three-phase
aggregation device, there is an inherent gap in VU monitoring for single-phase loads and generators. In this
paper, the data concentrators for a growing PV micro-inverter niche are identified as an infrastructure that
could be exploited to somewhat close this gap. Due to potential technical limitations of PV data
concentrators, a non-complex VUF approximation formula is tested as a "light" calculation alternative, by
comparing it against conventional VUF. The comparison results are obtained from Monte Carlo load flow
simulation for an unbalanced LV network.
1 INTRODUCTION
1.1 PV Penetration and Voltage
Unbalance Mitigation Problem
The voltages in a 3-phase distribution network are
considered unbalanced if differences in magnitudes
and/or angles between phases exist beyond specified
limits (Driesen and Craenenbroeck, 2002). At high
(HV) and medium voltage (MV) level loads are
mostly three-phase and balanced, but at low voltage
(LV) level many single-phase loads are encountered
and randomness of load profiles is greater. Despite
the best practices of LV network planning , some
increased unbalance is always experienced
compared to MV and HV level. The trends of
increasing single-phase distributed generation can
further promote the increase of unbalance at LV
levels. In most cases those are single-phase
photovoltaic (PV) systems, therefore studies were
performed on their impact on unbalance (Vegunta et
al. 2013; Shahnia et al. 2011a). The VU can cause a
decrease in the induction motor efficiency, sub-
optimal operation of power electronics and reduced
capacity in transformers, lines and cables, therefore
it is important to have mitigation solutions at
disposal.
Most basic and most limited solution is to
improve the planning practices. Further solutions
that can come from distribution operator side is the
application of specialized transformers and fast-
acting power electronics devices (Driesen and
Craenenbroeck, 2002). In (Shahnia et al. 2011b) VU
mitigation by distribution static compensators and
dynamic voltage restorers was analyzed. There are
also proposals for an active involvement of
distributed generation. In (Chua et al. 2012) a PV
with storage is used to mitigate unbalance. The new
control designs for PV inverters are integrating the
unbalance mitigation (Caldon et al. 2012; Wang et
al. 2008; Weckx et al. 2014).
286
Gagrica, O., Uhl, T., Nguyen, P. and Cobben, J.
Applicability of True Voltage Unbalance Approximation Formula for Unbalance Monitoring in LV Networks with Single-phase Distributed Generation.
In Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2016), pages 286-292
ISBN: 978-989-758-184-7
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
1.2 Voltage Unbalance Quantification
and Monitoring
Before reviewing the inverter-based solutions, the
calculation and quantification of VU needs to be
understood, because it impacts the technical
implementation of monitoring and control,
especially for single-phase devices. Whether only
magnitudes or both magnitudes and angles are
considered, the VU calculation depends on the
adopted VU definition (Pillay and Manyage, 2001).
Most widely accepted is the true voltage unbalance
definition that takes both magnitudes and angles into
account. Quantitatively it is expressed in percentages
as the voltage unbalance factor (VUF):

%

(1)
where V
-
and V
+
represent the magnitudes of
negative and positive sequence voltages. By
applying the method of symmetrical components,
positive and negative sequence voltages are
obtained:

1
3
111
1
1


(2)
These are complex domain calculations where
complex operator a is function of phase angle:
a=e(j2π/3). In order to calculate sequence voltages,
the instantaneous three-phase voltages and angles
must be obtained simultaneously (ed. Zobaa, 2013).
Technical implementation of monitoring therefore
requires a device directly connected to a 3-phase
supply. This is an inherently insurmountable
problem for single-phase devices unless an external
device acting as their coordinator is used.
1.3. Lack of Solutions for Single-phase
Inverters
In (Caldon et al. 2012) an external controller at
substation level coordinates single-phase and three-
phase inverters in order to mitigate unbalance.
Three-phase inverter control designs are proposed in
(Wang et al. 2008) and (Weckx et al. 2014). In
(Tangsunantham and Pirak, 2013) a three-phase
smart meter is used to monitor VU with high
accuracy and low cost. What is common for all
these referenced solutions is that they all use VUF
to assess VU. This is why these solutions are
dominantly three-phase. It is evident that without an
additional three-phase device, there is an inherent
gap in VUF monitoring and control for single-phase
inverters. Additional device also incurs additional
cost to the PV system, therefore it would be
worthwhile looking into single-phase devices whose
existing ICT infrastructure could be software-
retrofitted for purpose of enabling VUF monitoring
and control in LV networks.
In this paper, data concentrators used in PV
micro-inverters are addressed for their retrofit
potential in VU monitoring application. Due to
potential hardware limitations, a non-complex
approximation formula for VUF calculation (AVUF)
is tested as a light alternative to conventional VUF.
Modelling of VUF and AVUF is carried out in
Matlab/Simulink and presented in Section 2. To
account for randomness of PV generation a Monte
Carlo load flow is performed for an unbalanced 3-
phase 4-wire network model. Both Monte Carlo
scenario setup and network modelling are described
in Section 3. Comparison between VUF and AVUF
on the basis of Monte Carlo simulation results is
given in Section 4. The implication of results are
discussed in Section 5.
2 PROPOSED SOLUTION
2.1 Data Concentrators in LV
Networks
Data concentrators are the key components for
Advanced Metering Infrastructure (AMI). They
aggregate instantaneous data from numerous smart
meters and transmit it to the utility server. Without
their use as a mediator, the direct meter-to-server
communication would face many technical
difficulties. Other than application in AMI, the data
aggregation technology for PV generation is also
increasing its presence. It has become standard part
of the package for PV plants based on micro-inverter
and DC optimizer technology. The implementation
of power electronic converters at module-level
expanded the opportunity for monitoring operational
parameters from a single point to each
module/micro-inverter in the PV plant. This
generates a lot of data. In high PV penetration areas
there can be hundreds of panels and their data needs
to be aggregated and presented to the application or
the end-user in a meaningful way. Most of the
micro-inverters available on the market today are
sold in package with data concentrator devices, more
often called "gateways". They communicate to
micro-inverters via mesh radio or power line
communication while remote communication with
an application is done via internet (Enphase, 2015;
Applicability of True Voltage Unbalance Approximation Formula for Unbalance Monitoring in LV Networks with Single-phase Distributed
Generation
287
Figure 1: Simulink models of VUF (top) and AVUF (bottom).
ABB, 2014). One gateway can cover from several
tens to several hundreds of micro-inverters. PV
owners use them for monitoring and easy
troubleshooting, manufacturers for more
complicated troubleshooting and firmware updates.
In (Gagrica et al. 2015a; Gagrica et al. 2015b) it
was discussed how a gateway infrastructure could
be exploited by DSO for wide area feed-in
management of PV generation, only by software
retrofit without addition of external hardware.
However, trying software retrofit for the purpose of
obtaining VUF would likely face implementation
difficulties on the gateway hardware side. The
symmetrical components sequence analyzer requires
phase detection circuits and complex digital filtering
(ed. Zobaa, 2013). Such features are found in power
quality analyzers which are considerably more
expensive devices. The proposed alternative is to try
approximating the VUF with a less computationally
and technically demanding method.
2.2 VUF Approximation Formula and
Its Application
In (Pillay and Manyage, 2001) an overview of three
VU definitions and their respective calculations was
given: NEMA, IEEE, true definition (VUF). More
importantly a new formula was proposed. This is a
non-complex calculation formula that doesn't use
phase angles but nevertheless approximates VUF by
using only voltage magnitudes:

82






(3)
where V
ae
, V
be
and V
ce
are differences between
phase (a, b, c) voltages and the average phase
voltage. In (Pillay and Manyage, 2001) it was
provided in its final form without derivation steps.
The authors claimed that it can approximate to VUF
better than other definitions even under highly
unbalanced conditions, so it was selected as is for
this study. The modelling is performed in Simulink
for both VUF and AVUF. Models are presented in
Figure 1. For modelling VUF the default Simulink
three-phase sequence analyzer blocks are used, one
for positive and one for negative voltage sequence at
50Hz. Unlike VUF that uses instantaneous voltage at
input the voltages for AVUF had to be averaged to
RMS at fundamental frequency otherwise the output
will be sinusoidal and unsuitable for comparison
with VUF.
2.3 Application Limitations
The technical application would be to aggregate
micro-inverter output RMS voltages and execute
AVUF calculation by the existing gateway
microprocessor. Two limitations are currently
foreseen. The data concentrators often use wireless
communication (mesh radio) to aggregate data.
Compared to micro-inverters their sampling rate is
limited. For example in (ABB, 2014) the sampling
rate is limited to 1 minute. Providing AVUF in 1
min interval might be sufficient for a LV monitoring
application, but protection/control applications (like
fault clearing or dynamic unbalance control) would
be more demanding.
Secondly, the AVUF is only applicable in
scenarios where all three single-phase PV plants
connect to the same 3-phase supply point like in
Figure 2 (left). In reality PV plants will more likely
be scattered (Figure 2, right) due to randomness of
process of consumers becoming prosumers. If the
supply point where only Va is available is the AVUF
acquisition point, the other two phase voltages are
missing. The only available voltages are from the
neighbouring systems on different phases and supply
points (Vb' and Vc'').
SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems
288
Figure 2: The limitations of aggregating voltages from a
single supply point due to scattered single-phase PV.
In this case AVUF would have to be assisted with
some kind of state estimation method, which is out
of scope of this paper. Also the technical complexity
of acquiring voltages Vb' and Vc'' would increase as
they might be out of range of the data concentrator.
3 DISTRIBUTION NETWORK
MODELING AND SIMULATION
3.1 Distribution Network Model
A 3-phase 4-wire residential feeder is built in
Simulink (Figure 3). The feeder has 14 supply buses
extending radially from a 400kVA delta-star
transformer (400/230V, X/R ratio=3.2). The
transformer tap is set to 1.05pu to compensate for
voltage drop along the feeder. Each bus provides a
three-phase supply where each phase connects one
household. Total feeder length is 490m. There is a
common neutral going through each bus with star
grounding at transformer. The grounding, neutral
and lines are modelled as RL branches. One PV and
three load profiles with hourly resolution were
created based on profiles in (Shahnia et al. 2011a).
Peak values of three loads are 1, 1.8 and 4.6kW.
They are randomly distributed along the feeder. The
PV is modelled as a single-phase AC current with a
phase-locked loop.
The PV rating is in the 1-4kW range and varies in
accordance with Monte Carlo setup. Together, load
and generation form the net power flow subsystems
as shown in Figure 3 (Net flow 1, 2,...,14).
3.2 Monte Carlo Simulation
Monte Carlo is a convenient method for simulating
stochastic nature of PV generation. In particular it
was used in the unbalanced network analysis
(Shahnia et al. 2011a). Similarly, in this study
Monte Carlo is used to vary the PV ratings on all
three phases. The limitation of having PV present on
all three-phases simultaneously is taken into
account. The PV in 1-4kW range is varied following
a (0,1) uniform distribution. In Monte Carlo
applications in power system studies the coefficient
of variance is often used as a convergence criterion
or a stopping rule (Wenyuan, 2005). In this study
coefficient of variance

is used:


/
(4)
where Var(VUF)stands for variance. Simulink load
flow is carried out for each iteration until

)
reaches an acceptable convergence.
4 SIMULATION RESULTS
The AVUF and VUF results are retrieved for the
entire Monte Carlo set (1000 trials). Figure 4 shows
the outcome of applying two different calculation
methods. It can be seen that AVUF results are much
more dispersed with a higher density of extreme
values compared to VUF.
This is attributed to AVUF relying on voltage
magnitudes only. Also it can be observed that AVUF
almost always resolves in the same fashion being the
Figure 3: Simulink model of three-phase four-wire distribution network.
Applicability of True Voltage Unbalance Approximation Formula for Unbalance Monitoring in LV Networks with Single-phase Distributed
Generation
289
Figure 4: AVUF and VUF calculated in 1000 Monte Carlo trials.
highest at bus 14 and lowest at bus 1. Given how
the load and generation is distributed this should not
always be the case. The VUF at bus 7 will often
have a slightly higher unbalance than bus 14
especially during the more extreme unbalance cases
(over 2.5%), but around 2% the bus 14 will have a
higher VUF. Therefore in addition to inflated
magnitudes the AVUF will tend to give a voltage
magnitude-biased result when the whole feeder is
analyzed.
Three extreme VUF peaks and their
corresponding AVUF peaks are circled in Figure 4
at different simulation times (I,II,III). To better
understand when AVUF makes a good
approximation and when it diverges into extreme
peaks, the peaks are zoomed into and compared
against three-phase voltage snapshot at the
corresponding time (Figure 5). Daily three-phase
voltage profiles are taken from bus 1 for each of the
selected trials. It can be seen that the high AVUF
peaks correspond to situations when the load flow
resolves into simultaneous two-phase overvoltage.
VUF will also experience peaks at this time, but
AVUF, relying only on voltage magnitudes, is much
more sensitive to overvoltage than VUF.
In Figure 6 are presented the mean absolute
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290
Figure 5: Zoomed-in extreme VU cases I, II, III with voltage profiles.
error (MAE) and mean percentage error (MPE) for
buses 1-7-14 throughout the whole simulation. Also
the converging process of Monte Carlo is presented
in the bottom plot. While mean absolute error
(MAE) does not exceed 0.4% the mean percentage
error is much more sensitive to large peaks being
included in the error averaging process. From the
aspect of entire feeder both MAE and MPE increase
with impedance. The

converges between
0.46-0.48. after 500 trials. So 500 trials could have
been considered sufficient, although simulation was
run for 1000 trials.
Figure 6: MAE, MPE and η(VUF) at buses 1, 7 and 14.
5 DISCUSSION AND
CONCLUSION
The daily overvoltage occurrences due to excess PV
generation under unbalanced conditions have caused
at least two out of 24-hourly AVUF samples to give
false readings compared to VUF. That makes about
8.3% of recorded AVUF profile. In a power quality
analysis it would be possible to filter-out the false
AVUF peaks by using their corresponding
overvoltage events like it was presented in Figure 5,
however it is likely that such large peaks would not
have the chance to manifest in the first place. The
tips of the analyzed voltage peaks reach almost
400V. If it is a steady-state voltage change (the
subject of this study), its rise would be interrupted
much sooner due to inverter overvoltage protection
(at 253V) or even at a lower level if the inverter has
voltage control capability (curtailment, reactive
power). The AVUF preceding the trip or the
curtailment event would then be smaller.
Overvoltage could also occur in as a fast transient
due to a fault (i.e. floating neutral might cause phase
voltage to approach line voltage value), but again the
inverter protection would act. It was shown that
MAE and MPE increase with feeder impedance.
This suggests that, if AVUF is to be applied, a
calibration constant dependant on impedance would
have to be determined and the calibration itself
would have to be performed independently at each
point of connection by using a suitable standard
Applicability of True Voltage Unbalance Approximation Formula for Unbalance Monitoring in LV Networks with Single-phase Distributed
Generation
291
instrument (i.e. power analyzer).
Based on this study alone it is difficult to say
with certainty that AVUF formula can reliably
approximate VUF. But given the limitations that
distribution operators face at LV level: lack of
power quality monitoring capability, higher potential
for VU and big presence of single-phase loads, it
might be a worthwhile, intermediary monitoring
solution that can add more value to the already
deployed distributed generation. The proposed
concept does not have to be contained only within
the distributed generation context. Also home energy
management systems consisting of data
concentrators and smart single-phase
appliances/meters could be considered for the same
application.
ACKNOWLEDGEMENTS
This research is funded through Erasmus Mundus
Joint Doctoral Programme SELECT+, the support of
which is gratefully acknowledged.
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