energies

Article
Hosting Capacity of the Power Grid for Renewable
Electricity Production and New Large
Consumption Equipment
Math H. J. Bollen * ID
and Sarah K. Rönnberg *
Electric Power Engineering, Luleå University of Technology, 931 87 Skellefteå, Sweden
* Correspondence: math.bollen@ltu.se (M.H.J.B.); sarah.ronnberg@ltu.se (S.K.R.)

Academic Editor: Birgitte Bak-Jensen

Received: 27 July 2017; Accepted: 29 August 2017; Published: 2 September 2017

Abstract: After a brief historical introduction to the hosting-capacity approach, the hosting capacity
is presented in this paper as a tool for distribution-system planning under uncertainty. This tool
is illustrated by evaluating the readiness of two low-voltage networks for increasing amounts of
customers with PV panels or with EV chargers. Both undervoltage and overvoltage are considered
in the studies presented here. Probability distribution functions are calculated for the worst-case
overvoltage and undervoltage as a function of the number of customers with PV or EV chargers.
These distributions are used to obtain 90th percentile values that act as a performance index.
This index is compared with an overvoltage or undervoltage limit to get the hosting capacity.
General aspects of the hosting-capacity calculations (performance indices, limits, and calculation
methods) are discussed for a number of other phenomena: overcurrent; fast voltage magnitude
variations; voltage unbalance; harmonics and supraharmonics. The need for gathering data and
further development of models for existing demand is emphasised in the discussion and conclusions.

Keywords: hosting capacity; power quality; solar power integration; electric vehicle integration;
electricity distribution; distribution-system planning

1. Introduction
Changes in society are typically initiated and mainly take place outside of the power grid, however,
such changes might still affect the electric power grid. Three specific types of changes are currently
taking place at the same time, causing a range of serious challenges to the design, planning and
operation of the grid:

i) New types of electricity production. There is a shift from large production units connected to the
transmission grid to small units connected to the distribution grid, sometimes even connected
at low voltage on the customer side of the electricity meter. Driven by the need for a more
sustainable energy system, this new production is often of the renewable type and connected
through a power-electronics interface. This shift in production, including the expected future
developments, is rather well documented in papers, books, and government reports [1–4].
ii) Changes in electricity consumption. The electricity consumption is where societal changes often
have the first impact. There is since many years a general increase in the number of electric
devices used. The transition to a sustainable energy system is driving a shift towards more
energy-efficient equipment, equipment with a power-electronics interface, and the introduction
of new types of equipment. Examples of the latter are electric vehicles [5–7] and heat pumps
(as a replacement of either gas heating or as a replacement for resistive electric heating) [8].
The replacement of incandescent lamps by compact fluorescent and LED lamps should be

Energies 2017, 10, 1325; doi:10.3390/en10091325 www.mdpi.com/journal/energies

Energies 2017, 10, 1325 2 of 28

mentioned specifically [9]. In developing countries, an increase in wealth is strongly correlated to

a growth in electricity consumption.
iii) Changes in the grid. A combination of technical developments on the one hand and societal,
environmental and regulatory requirements on the other hand is leading to new types of solutions
being used as part of the power grid. The shift from overhead lines to underground cables is
one example, but also the slow but on-going introduction of a range of technology that comes
under the term “smart grids” [10–12]. This new technology is obviously intended to offer better
and/or more cost-effective solutions, but unintended consequences of the new technology may
still pose a challenge. An overview of some of the unintended consequences for power quality of
smart-grid technology is presented in [13].
All these changes create a range of challenges and a lot of research and practical studies have been
done and are ongoing to address those changes and the possible challenges. Many studies have been
done on the impact of local generation on the distribution grid, where overcurrent and overvoltage are
typically the risks being studied [2,14–18]. An overview of the power-quality related challenges for
some of the major changes is presented in [19,20]. Some of the specific conclusions from those studies
are:
i) The large-scale introduction of active power electronics, in production as well as consumption
equipment, results in additional phenomena becoming of importance: interharmonics; DC
components and low-frequency subharmonics (“quasi-DC”); and components above 2 kHz
(“supraharmonics” [21]).
ii) The amount of capacitance connected to the grid is expected to increase at all voltage levels.
This will result in a shift of resonances to lower frequencies. The increased emission at higher
frequencies may be (partly) compensated by the shift in resonance to lower frequencies. However,
at the same time, the transfer of disturbances will become less predictable.
An international working group [22] recently presented a number of recommendations, key
findings and open issues to be addressed because of the integration of solar power. Recommendations
were given for a number of power-quality phenomena, including harmonics, supraharmonics, fast
voltage variations (faster than 10-min time scale), slow voltage variations (slower than 10 min),
overvoltage, flicker, and voltage unbalance. The hosting capacity approach, as was proposed by an
international cooperation project in 2004 (see Section 2) is put forward in the report as an important
tool for quantifying the impact of solar power on the power system. Additional work is needed,
according to the report, for establishing suitable performance indices and corresponding limits.
This paper consists of three main parts. It starts in Section 2 with an overview, partly from a
historical insider perspective, of the hosting-capacity approach. This part also includes a discussion on
different kinds of uncertainly. A hosting-capacity-based planning approach is presented in Section 3,
applied in Section 4.1 through Section 4.6 and discussed in Section 4.7. The description and the
application are for overvoltage and undervoltage as these are the phenomena, with the possible
exception of overcurrent, for which the best calculation tools, performance indices and limits are
available. The third part of the paper contains a detailed discussion about including other phenomena
in hosting-capacity studies. For each phenomenon, performance indices, limits and calculation
methods are discussed.

2. Hosting Capacity
The term “hosting capacity” was coined in the context of distributed generation by André Even in
March 2004 during discussions within the integrated European EU-DEEP project [23,24]. An approach
for quantifying the hosting capacity was developed further by others within that same project [25].
The term “hosting capacity” was already in use before 2004, but in rather different context, for example
for internet servers [26], for watermarking of images [27] and for the settlement of refugees [28].
Hosting capacity is now widely used as a term and as a methodology by network operators, by
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energy regulators
capacity and by researchers. Many studiesnetworks
have been done where the hosting capacity was
capacity was
was calculated,
calculated, especially
especially forfor distribution
distribution networks and and especially
especially for
for new
new production,
production, for
for
calculated,
example especially for distribution networks and especially for new production, for example [29].
example [29].
[29]. The
The hosting
hosting capacity
capacity has has also
also been
been used
used toto quantify
quantify thethe impact
impact ofof electric
electric vehicle
vehicle
The hosting capacity
charging has also been usedThe to quantify the impact of electric vehicle charging on the
charging on on the
the grid,
grid, for
for example
example [30].[30]. The basic
basic hosting-capacity
hosting-capacity approach
approach waswas later
later extended,
extended,
grid,
among for example [30]. The basic hosting-capacity approach was later extended, among others to
among others
others to
to cover
cover solutions
solutions like
like curtailment
curtailment [24].
[24]. Studies
Studies towards
towards estimating
estimating hosting
hosting capacity
capacity
cover
are solutions like curtailment [24]. Studies towards estimating hosting capacity are common part of
are common
common partpart of
of studies
studies byby large
large network
network operators
operators as as part
part of
of their
their strategies
strategies towards
towards allowing
allowing
studies by largeofnetwork
the operators as part of their strategies towards allowing the integration of more
the integration
integration of more
more renewable
renewable electricity
electricity production
production intointo their
their electricity
electricity networks
networks [31–33].
[31–33].
renewable
An electricity production into their electricity networks [31–33].
An important
important recent
recent development
development is is the
the introduction
introduction of of aa stochastic
stochastic approach
approach to to hosting
hosting
An
capacity important recent development is the introduction of a stochastic approach to hosting
capacity [34–39].
[34–39]. The
The stochastic
stochastic element
element introduced
introduced concerns
concerns especially
especially the
the unknown
unknown location
location of
of
capacity
future PV [34–39]. The stochastic
installations in the element grid,
distribution introduced
but it concerns
can be especially
extended to the unknown
include other location of
uncertainties
future PV installations in the distribution grid, but it can be extended to include other uncertainties
future PV installations
(see in the distribution grid, but it can be extended to include other uncertainties
(see Section
Section 2.2).
2.2).
(see Section 2.2).
2.1.
2.1. Definition and Aim of Hosting Capacity
2.1. Definition
Definition and
and Aim
Aim ofof Hosting
Hosting Capacity
Capacity
The
The hosting-capacity approach, for distributed generation, has been introduced as aa transparent
The hosting-capacity approach, for
hosting-capacity approach, for distributed
distributed generation,
generation, has has been
been introduced
introduced as as a transparent
transparent
communication
communication tool between stakeholders concerning the connection of distributed generation to the
communication tool between stakeholders concerning the connection of distributed generation to
tool between stakeholders concerning the connection of distributed generation to the
the
grid.
grid. The hosting capacity is defined as the amount of new production or consumption that can be
grid. The hosting capacity is defined as the amount of new production or consumption that can be
The hosting capacity is defined as the amount of new production or consumption that can be
connected
connected to
to the
the grid
grid without
without endangering
endangering the
the reliability
reliability or
or voltage
voltage quality
quality for
for other
other customers
customers [2,25].
[2,25].
connected to the grid without endangering the reliability or voltage quality for other customers [2,25].
Essential
Essential to the approach are the selection of performance indices for the grid and acceptability limits
Essential toto the
the approach
approach are are the
the selection
selection of of performance
performance indices
indices for for the
the grid
grid andand acceptability
acceptability limitslimits
for
for those indices. The hosting capacity is the amount of new production or consumption where the
for those
those indices.
indices. The The hosting
hosting capacity
capacity is is the
the amount
amount of of new
new production
production or consumption where
or consumption where the the
first
first performance
performance index
index reaches
reaches its
its limit.
limit. This
This is
is illustrated
illustrated in
in Figures
Figures 11 and
and 2,
2, for
for two
two cases
cases involving
involving
first performance index reaches its limit. This is illustrated in Figures 1 and 2, for two cases involving
new
new production. For example, the risk of overvoltage already increases with very small amounts of
new production.
production. For For example,
example, the the risk
risk of
of overvoltage
overvoltage already
already increases
increases withwith veryvery small
small amounts
amounts of of
new
new production connected to aa part of the grid with only consumption (like in Figure 1); the risk of
new production connected to a part of the grid with only consumption (like in Figure 1); the
production connected to part of the grid with only consumption (like in Figure 1); the risk
risk ofof
overcurrent
overcurrent will
will initially
initially decrease
decrease (like(like
(like in
in Figure
Figure 2).2). In
In cases like in Figure 2, it sometimes makes sense
overcurrent will initially decrease in Figure 2). In cases
cases like
like in in Figure
Figure 2,2, it
it sometimes
sometimes makes makes sensesense
to
to introduce a second hosting capacity value (HC1) at which the performance is the same as for the
to introduce
introduce aa second
second hosting
hosting capacity
capacity valuevalue (HC1)
(HC1) at at which
which the the performance
performance is is the
the same
same as as for
for the
the
system
system without
without any
any new
new generation.
generation.
system without any new generation.
index
Performanceindex

Hosting
Hosting
capacity
capacity
Performance

Unacceptable deterioration
Unacceptable deterioration
Limit
Limit
Acceptable deterioration
Acceptable deterioration

Existing level
Existing level
Improvement
Improvement

Amount of generation
Amount of generation

Figure
Figure 1.1. Hosting
Hostingcapacity
Hosting capacityapproach,
capacity approach,where
approach, where the
where theperformance
the performance deteriorates
performance deteriorates already
deteriorates already with
with small
small amounts
amounts
amounts
of local generation.
of local generation.
index
Performanceindex

HC2
HC2
Performance

Unacceptable deterioration
Unacceptable deterioration
Limit
Limit
Acceptable deterioration
Acceptable deterioration
HC1
HC1
Existing level
Existing level

Improvement
Improvement
Amount of generation
Amount of generation

Figure
Figure 2.
Figure 2. Hosting
2. Hosting capacity
Hosting capacity approach
capacity approach where
approach where the
where the performance
the performance initially
performance initially improves
initially improves and
improves and only
and only deteriorates
only deteriorates
deteriorates
with
with larger amounts of local generation.
with larger amounts of local generation.

2.2.
2.2. Uncertainties
Uncertainties
Energies 2017, 10, 1325 4 of 28

2.2. Uncertainties
When determining the hosting capacity of the grid at a certain location or for a certain part of
the grid, several uncertainties play a role. The uncertainty that is most discussed and studied is the
variation of wind or solar power production with time. This is somewhat incorrectly referred to
as “intermittent” and regularly (but somewhat unwarranted) mentioned as the main concern with
integration of renewable electricity production. It is admittedly not possible to predict the solar or
wind-power production accurately, more than a few days ahead (for most countries). Even prediction a
few hours ahead is often difficult. This limits the usefulness of wind and solar power as a dispatchable
source of electricity.
It is however possible, with a reasonable accuracy, to obtain probability distributions for the
amount if solar or wind-power production at a certain location, from some basic information about the
size of the installation. Weather data, often obtained over several decades with high accuracy, is the
basis for the calculation of such distribution functions. Long-term trends are most likely present in
the weather, but their impact on the stochastic properties of wind and solar-power production is still
expected to be smaller than the impact of other uncertainties.
In a similar way, probability distributions and time series can be obtained for the consumption of
individual customers or for groups of customers (from the load of a single distribution transformer, up
to the consumption of a whole country). Time series over many years are rare, but the introduction
of smart metering makes that data for a few years becomes increasingly available. Consumption
patterns are prone to change, and likely faster than weather patterns, but not to the extent that the
measurements become useless.
Not all time variations in (renewable-electricity) production and consumption are uncertain.
The daily and seasonal variations in solar-power production are very predictable, as an example.
When studying solar-power integration for a limited part of the year (e.g., around noon during
Summer) the appropriate probability distribution function should be used.
Next to the above-mentioned uncertainties, there exists another level of uncertainty. That kind of
uncertainty cannot be obtained from past measurements. Some examples (all related to small-scale
solar power), are:

i) Which customers will have a PV installation and how big will these installations be?
ii) Will these installations be three-phase or single-phase connected?
iii) With single-phase connection: to which phase will it be connected?
iv) What will be the direction and tilt of the panels?
v) Will any of the panels follow the sun through single-axis or double-axis mounts?
vi) What type of inverter will the installation have? Will it be one large inverter or a number of
smaller inverters?
vii) Will the installation have on-site storage or not? When it has on-site storage, what will its size
be, which control algorithms will it use, and will the owner use the storage to participate in
day-ahead and balancing markets?
viii) Will the inverter be equipped with voltage and reactive power control?

The answers to all of these questions need to be known before an accurate hosting capacity can be
calculated. However, the answers will most likely not be known. Either an educated guess will have
to be made or a stochastic approach is needed. The latter is the approach that will be illustrated in
Section 4.

2.3. Impacts on the Hosting Capacity

The hosting capacity approach has been developed as a transparent approach aimed at enabling a
more open discussion between the different stakeholders. That does however not imply that there is a
unique value of the hosting capacity, as resulting from the calculations.
Energies 2017, 10, 1325 5 of 28

The before-mentioned uncertainties all have their impact on the results of the calculations.
In addition, the calculations themselves affect the results. Certain assumptions will have to be made
and certain parameter values are needed. The choice of these assumptions and parameter values
can have a big impact. Data, especially on the consumption patterns, is not always available when
the studies are made and assumptions can have a serious impact. A sensitivity analysis is needed to
evaluate if additional data collection and model development are needed. Alternatively, additional
stochastic variables can accommodate for the uncertainty.
What has an even bigger potential impact, and where no amount of data collection or
model development may help, is the choice of the performance index and the limit (as shown in
Figures 1 and 2). These choices depend strongly on the amount of risk that the stakeholders (especially
the network operators and their customers) are willing to take. The lower the risk the network
operators are willing to take, the lower the hosting capacity.

3. A Hosting-Capacity-Based Planning Approach

A range of hosting-capacity studies are presented in the literature and more are being used in
various studies without being published. The hosting-capacity-based planning approach proposed
here, consists of the following steps:

i) Estimate the no-load voltage variations in the low-voltage distribution network during those
hours of the year that the production from solar power may be high. These are the voltage
variations originating from the medium-voltage network.
ii) Estimate the range of the lowest consumption during those hours of the year that the production
from solar power may be high.
iii) Estimate the production per installation, during the 10-min period with the highest impact
from all installations together. This is not the same as the maximum production per panel, but
it can be referred to as an “after diversity maximum production”, next to an “after diversity
minimum consumption”.
iv) Add solar power installations in a random way and calculate the distribution of worst-case
voltage with increasing amount of solar power.
v) Define a performance index for the network, an appropriate limit for this index, and determine
the hosting capacity.

This approach for distribution-system planning can be seen as an adapted version of the classical
approach, where an “after diversity maximum consumption” is compared with the capacity of lines,
cables and transformers.
The difference between the planning approach used here, and the time-series approach often
used in other studies, is that the proposed planning approach immediately considers the worst-case
during a longer period, like several years. Distribution-network planning is largely about making
sure that the network can cope with for example the highest current through a transformer. It is this
worst case that matters. However, also the worst-case value can be treated as a random variable,
which is the base for the planning approach presented here. Probability distributions are used, for
example for the consumption. These are not the same as the probability distributions obtained from
time series. Instead, they are the range of values during those hours of the year that the worst-case
situation can occur.
The result of the calculations is thus not the probability distribution of the voltage magnitude,
but instead the probability distribution of the worst-case voltage magnitude. Alternatively, one may
consider this as the probability distribution obtained over a range of possible futures, all with a different
worst-case value. Important advantages of the approach proposed here and applied in Section 4, are:

i) The approach fits closely to existing planning approaches used by distribution companies.
ii) A limited amount of input data is needed.
Energies 2017, 10, 1325 6 of 28

iii) The results are such that they can be interpreted relatively easy by distribution companies.
iv) Different kinds of uncertainties can be added without changing the basic approach.
v) Any power-system analysis tool can be used to perform the actual calculations.

The limitation of the approach is that it requires certain assumptions, like in step (i) and (ii) above.
In practical planning studies, these assumptions might become more based on expert opinions than on
actual reproducible studies. Different persons may obtain different results. Such is however common
in practical planning studies for distribution grids. With the proposed approach, the assumptions
become clearly visible and might trigger further studies.

4. Overvoltage and Undervoltage

4.1. Two Swedish Low-Voltage Networks

To illustrate the calculation of the hosting capacity in a stochastic way for planning purposes, two
low-voltage networks in the North of Sweden have been used: a 6-customer rural network; and a
28-customer suburban network. Both networks were used in [39], where the details of the networks
can be found. Both networks contain only domestic customers and both networks are three-phase
down to the customer. The customer has the possibility of connecting three-phase equipment and of
spreading the equipment over the three phases. Note that this is not possible in distribution networks
with single-phase laterals, as are common in North America.

4.2. Risks Due to Single-Phase Equipment

In this section (Section 4), the risk of overvoltage and undervoltage due to single-phase equipment
will be quantified. Both new production (domestic PV installations) and new consumption (domestic
EV chargers) are included in the study. The connection of single-phase equipment is more severe for
the grid than the connection of three-phase equipment with the same power rating. Not only is the
voltage rise or drop higher for single-phase equipment (three times the current and about twice the
impedance), but the other phases are also impacted. Connection of a single-phase EV charger in one
phase results in a voltage drop in that phase and a voltage rise in the other phases.
Many hosting capacity studies consider detailed time series of both consumption and production
to find at which amount of production voltage or current limits are reached. At higher voltage levels,
the data is more likely available than at lower voltage levels. The additional time needed to obtain
the data (often several years of data collection are needed) will probably not result in a more accurate
result because of remaining uncertainties for example in the details of the installations. This holds
especially when the hosting-capacity study concerns the introduction of many devices or installations.
In this paper, the authors have therefore chosen for a probability distribution instead of time series.
Both methods should be further developed and compared. Some aspects of such comparison are
discussed in Section 4.7.3.

4.3. Single-Phase PV in a Rural Network—Overvoltage

The risk of overvoltage due to the introduction of single-phase-connected PV has been studied for
the six-customer rural network (see Section 4.1). The probability distribution for the highest voltage is
shown in Figure 3 for one through six customers with PV. The following input data has been used for
obtaining these distributions:

i) Each installation is connected single-phase and each installation produces 6 kW.

ii) The consumption per customer per phase, during the worst case, is uniformly distributed between
0 and 250 W. This range was obtained from measurements of 10-min values of two customers (one
in the rural network and one in the suburban network) and the study of hourly consumption from
other customers. The worst case, when considering the risk of overvoltage, is when consumption
is low and production is high. High production will likely last a period of one or two hours
Energies 2017, 10, 1325 7 of 28

around noon. The regulation in most European countries sets limits to 10-min values of rms
voltage. The lowest 10-min consumption values during one or two-hour periods were considered
to obtain the range from 0 to 250 W. Only measurement values around noon during the summer
months were used here.
Energies 2017, 10, 1325
iii) The no-load voltage in the low-voltage network, during the worst case, is uniformly7 distributed of 28

between iii) 238

TheVno-load
and 242voltage
V. Theinhighest 10-min network,
the low-voltage values during
during one or two-hour
the worst periods around
case, is uniformly
noon in thedistributed
summer between
months238 (asVobtained from the same measurements) were used to obtain
and 242 V. The highest 10-min values during one or two-hour
this distribution.
periods around noon in the summer months (as obtained from the same measurements)
were used to obtain this distribution.
All the random variables in the model are non-correlated. It is further assumed that the PV
All the random variables in the model are non-correlated. It is further assumed that the PV
installations are randomly distributed over the customers and over the phases. The network model
installations are randomly distributed over the customers and over the phases. The network model
used is used
a simple, linear linear
is a simple, one, consisting of the
one, consisting node-impedance
of the node-impedancematrix calculatedfrom
matrix calculated fromthethe positive and
positive
zero-sequence series impedance
and zero-sequence of the different
series impedance branches.
of the different Positive-sequence
branches. andand
Positive-sequence negative-sequence
negative-
sequence
impedances are impedances
considered are considered
equal. equal. Thebetween
The difference differencepositive
betweenandpositive and zero-sequence
zero-sequence impedance is
considered in the calculations. From the injected and consumed power for eachpower
impedance is considered in the calculations. From the injected and consumed for each
customer and phase,
customer and phase, a current vector is calculated. This vector is multiplied with the node-impedance
a current vector is calculated. This vector is multiplied with the node-impedance matrix to obtain the vector
matrix to obtain the vector with phase-to-neutral voltages for all customers and phases. All
with phase-to-neutral voltages for
calculations are performed all customers and phases. All calculations are performed in Matlab.
in Matlab.
A Monte-Carlo
A Monte-Carlo simulationused
simulation is totogenerate
is used generate aa large
largenumber
number of combinations
of combinations of customers
of customers and and
phases phases
with PV. withFor
PV.each combination,
For each combination,the thehighest phase-to-ground
highest phase-to-ground voltage
voltage is calculated
is calculated for eachfor each
customercustomer terminals.
terminals. The probability
The probability distribution
distribution forforthis
thisvoltage
voltage is
is shown
shown ininFigure
Figure3.3.InIn
this case,
this case, each
each distribution was obtained from 10,000 samples.
distribution was obtained from 10,000 samples.

Figure 3. Probability
Figure distribution
3. Probability (cumulative
distribution (cumulativedistribution
distributionfunction) forthe
function) for thehighest
highest voltage
voltage (worst-case
(worst-
voltage)case
for voltage)
increasing amount ofamount
for increasing single-phase connected
of single-phase solar solar
connected power in the
power in 6-customer
the 6-customerrural
ruralnetwork.
network.
The different The different
colours refer tocolours
the sixrefer to the six
different different customers.
customers. The red vertical
The red dashed dashed vertical
line isline
theisovervoltage
the
overvoltage limit at 110% of
limit at 110% of the nominal voltage. the nominal voltage.

The plots show how the distribution shifts towards higher voltage magnitudes with increasing
The plots show
amount of solarhow the The
power. distribution
probabilityshifts towards
that the higher
overvoltage voltage
limit (110%magnitudes with increasing
of nominal voltage) is
amountexceeded
of solarincreases
power.because of this. Already
The probability thatforthe
oneovervoltage
customer withlimit
PV, there
(110%is aof
small probability
nominal voltage) is
that the voltage with one of the customers exceeds the overvoltage limit.
exceeded increases because of this. Already for one customer with PV, there is a small probability that
An important advantage of the hosting-capacity approach is its transparency: a well-defined
the voltage with one of the customers exceeds the overvoltage limit.
performance index is compared with a well-defined limit. The same should hold when the hosting
Ancapacity
important advantage
is used of the
as a planning tool. hosting-capacity
In this example, the approach is its
90th percentile of transparency: a well-defined
the distribution shown in
performance
Figure index is compared
3 has been used as an with
indexaandwell-defined limit.voltage
110% of nominal The same should
as a limit. Thehold
indexwhen the hosting
value with
capacityincreasing
is used amount
as a planning tool. In
of solar power this example,
is shown in Figure the 90th each
4, where percentile
point isof
thethe distribution
result of 100,000 shown
simulations. The results are shows for each of the six customers. When one
in Figure 3 has been used as an index and 110% of nominal voltage as a limit. The index value of the 90th percentiles
exceeds the 110% limit for one of the customers, the hosting capacity has been exceeded. The hosting
with increasing amount of solar power is shown in Figure 4, where each point is the result of
capacity is in this case equal to only one customer with PV.
100,000 simulations. The results are shows for each of the six customers. When one of the 90th
Energies 2017, 10,
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percentiles exceeds the 110% limit for one of the customers, the hosting capacity has been exceeded.
The hosting
Energiescapacity is in this case equal to only one customer with PV.
2017, 10, 1325 8 of 28

Figure 4. 90th percentile of the worst-case overvoltage as a function of the number of customers with
Figure 4. 90th4.percentile
Figure of the
90th percentile worst-case
of the worst-caseovervoltage asa afunction
overvoltage as function of number
of the the number of customers
of customers with with
PV in the 6-customer rural network.
PV in the 6-customer rural
PV in the 6-customer rural network. network.

It has been
It has mentioned
been mentioned before (in(inSection
before Section 2.5) thatthe
2.5) that thehosting
hosting capacity
capacity is notisa not a unique
unique value. value.
It has been
Instead, it mentioned
depends strongly before
on (in
the Section
model and 2.3)
data that
used tothe hosting
Instead, it depends strongly on the model and data used to calculate the index, on the choice
calculate the capacity
index, on is
the not
choice a unique
of indexof value.
index
Instead,
and on the choice of limit. An example of the latter, with reference to Figure 4, is that the of
it
and depends
on the strongly
choice of on
limit. the
An model
example and
of thedata
latter,used
with to calculate
reference to the
Figureindex,
4, is on
thatthe
the choice
hosting index
hosting
and capacity
on the increases
choice to of twoto
limit. two customers
An example when 112% instead of 110% of nominal is used for the limit.
capacity increases customers whenof112% the latter,
instead with reference
of 110% to Figure
of nominal 4, is for
is used thatthe thelimit.
hosting
capacity Figure 5to
increases shows
two the performance
customers when index when
112% it is assumed
instead of 110%thatof
each PV installation
nominal is used injects
for the4 kW
limit.
Figure 5 shows the performance index when it is assumed that each PV installation injects 4 kW
instead of 6 kW during the worst case. The resulting hosting capacity is five customers. An example
Figure
instead 6 5kW
ofthe showsduringthe performance case.index when it ishostingassumed that each PV installation injects 4 kW
of impact of thethe worst
choice The resulting
of performance index is shown in Figure capacity is five
6, where thecustomers.
75th percentile An isexample
instead of 6 kW
of the impact
used ofduring
instead the90th
theofchoice
the worst case. The
ofpercentile.
performance Theresulting
index ishosting
production shown capacity
in Figure
per installation isisagain
6,five customers.
where assumedthe 75th Anpercentile
6 kW. example of
The is
the impact
used instead of
resulting the choice
ofhosting
the 90th of
capacity performance
percentile. index is
The production
is two customers shown
with PV. Inper in Figure 6,
the installation where
latter exampleis(Figure the 75th
again6),assumed percentile is used
6 kW. The
it is clear that
instead
resulting ofhosting
the the 90thcapacity
increase inpercentile.
hosting capacity Thecustomers
is two production
goes together perPV.
with
with installation
an increase
In the in is again
risk.
latter However,
example assumedeven
(Figure 6 kW.
for the The
6),example
it resulting
is clear that
hosting in Figure 5,isthe
capacity tworiskcustomers
of overvoltagewith increases,
PV. In as installations
the latter example may contribute
(Figure more
6), it isthan
clear 4 that
kW tothe theincrease
the increase in hosting capacity goes together with an increase in risk. However, even for the example
worst case. The choice of model, data, etc. with hosting-capacity calculations is strongly related to the
in
in hosting
Figure 5,capacity
the riskgoes together with
of overvoltage an increase
increases, in risk. However,
as installations even for the
may contribute more example
than 4inkW Figure 5,
to the
risks that the different stakeholders are willing to take. A brief discussion on this is part of Section
the risk
worst of overvoltage increases, as installations may contribute more than 4 kW to the worst case.
case.
4.7.7.The choice of model, data, etc. with hosting-capacity calculations is strongly related to the
The choice
risks that the of model,
different data, etc. with hosting-capacity
stakeholders are willing to take. calculations is stronglyonrelated
A brief discussion this isto theof
part risks that
Section
the different
4.7.7. stakeholders are willing to take. A brief discussion on this is part of Section 4.7.7.

Figure 5. 90th percentile of the worst-case overvoltage as a function of the number of customers with
PV in the 6-customer rural network; 4 kW production per PV installation.

Figure 5. 90th percentile of the worst-case overvoltage as a function of the number of customers with
network; 44 kW
PV in the 6-customer rural network; kW production
production per
per PV
PV installation.
installation.
Energies 2017, 10, 1325 9 of 28
Energies 2017, 10, 1325 9 of 28

Figure
Figure 6. 75th percentile
6. 75th percentile of
of the
the worst-case
worst-case overvoltage
overvoltage as
as aa function
function of
of the
the number
number of
of customers
customers with
with
PV in the 6-customer rural network.
PV in the 6-customer rural network.

4.4. Single-Phase PV
4.4. Single-Phase PV in
in aa Rural
Rural Network—Undervoltage
Network—Undervoltage
When consideringthe
When considering therisk
riskofofundervoltage,
undervoltage,other
other distributions
distributions have
have to considered
to be be considered for no-
for the the
no-load and no-PV voltages than when considering the risk of overvoltage (Section 4.3).
load and no-PV voltages than when considering the risk of overvoltage (Section 4.3). Undervoltage Undervoltage
occurs in the
occurs in the phases
phases without
without PVPV during periods with
during periods with high
high production
production andand at
at the
the same
same time
time high
high
consumption and low no-load voltages. The high production can occur, like before,
consumption and low no-load voltages. The high production can occur, like before, around noon around noon
during
during the
the summer
summer months. Instead of
months. Instead of the
the lowest
lowest consumption
consumption and and the
the highest
highest no-load
no-load voltage,
voltage, the
the
highest consumption and
highest consumption and the
the lowest
lowest no-load
no-load voltage
voltage should
should be
be used
used as input to
as input the calculation.
to the calculation. From
From
the same data
the same data as in the
as in the previous
previous section,
section, the
the following
following input data to
input data to the
the hosting-capacity
hosting-capacity calculation
calculation
has been used:
has been used:
i) Consumption:
i) 10001000
Consumption: W–2500
W–2500W per customer
W per perper
customer phase. Note
phase. again
Note againthat
thatthis
thisisisnot
not aa typical
consumption but an
consumption estimation
but of theofamount
an estimation of consumption
the amount that may
of consumption thatoccur duringduring
may occur a worsta
worst
case for case for undervoltage
undervoltage due to PV. due to PV.
ii) ii) No-load
No-load voltage:
voltage: 232 V–236
232 V–236 V. V.
Like before,
Like before, 66 kW
kW production
production per per PV
PV installation
installation hashas been
been assumed.
assumed. The The resulting
resulting probability
probability
distributions are shown in Figure 7. Compared to the previous figures, the lowest
distributions are shown in Figure 7. Compared to the previous figures, the lowest of of the
the three
three
voltages for
voltages foreach
eachcustomer
customer has
has been
been used
used as input
as input to thetoprobability
the probability distribution
distribution function
function (also
(also known
known as “cumulative distribution function” or CDF). The results in the figure
as “cumulative distribution function” or CDF). The results in the figure show that a voltage drop show that a voltage
drop occur
may may occur due
due to to solar
solar power,
power, but but values
values lessless than
than 95%95% ofof nominalduring
nominal duringsunny
sunnyhours
hours are
are very
very
unlikely. Undervoltage
unlikely. Undervoltage does does not
not set
set the
the hosting
hosting capacity
capacity in in this
this network.
network. However, when the
However, when the highest
highest
consumption occurs
consumption occurs during
during periods
periods with
with high
high solar
solar power
power production,
production, undervoltage
undervoltage maymay bebe aa bigger
bigger
concern than
concern than overvoltage.
overvoltage.
A further
A further look
look atat the
the results
results (not
(not presented
presented here),
here), including
including simulations
simulations with
with 1,000,000
1,000,000 samples,
samples,
showed that voltages as low as 92% of nominal are actually possible,
showed that voltages as low as 92% of nominal are actually possible, but with extremely but with extremely small
small
probabilities: of
probabilities: of the
the order
order ofof one
one per
per million.
million.ThisThisisisa agood
goodexample
exampleshowing
showingthat thatconsidering
considering a
stochastic approach is the way to go. Such low probabilities do not need
a stochastic approach is the way to go. Such low probabilities do not need to be considered in to be considered in
distribution-system planning.
distribution-system planning.
Energies 2017, 10, 1325 10 of 28
Energies
Energies 2017,
2017, 10,
10, 1325
1325 10
10 of
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28

Figure 7. Probability
Figure 7.
Figure 7. Probabilitydistribution
Probability distribution(cumulative
distribution (cumulative
(cumulative distribution
distributionfunction)
distribution forfor
function)
function) thethe
for lowest
the voltage
lowest
lowest (worst-case
voltage
voltage (worst-
(worst-
voltage)
case for increasing amount of single-phase connected solar power inpower
the 6-customer rural network.
case voltage) for increasing amount of single-phase connected solar power in the 6-customer rural
voltage) for increasing amount of single-phase connected solar in the 6-customer rural
The different different
network. colours refer to the six different customers. The black dashed vertical line is the
network. The
The different colours
colours refer
refer to
to the
the six
six different
different customers.
customers. The
The black
black dashed
dashed vertical
vertical line
line is
is
nominal
the voltage.
nominal voltage.
the nominal voltage.

4.5.
4.5. Single-Phase
Single-Phase PV
PV in
in aa Suburban
Suburban Network—Overvoltage
Network—Overvoltage
The
The calculations
calculations presented
presented in the previous
in the previous two
two sections have been
sections have been repeated
repeated forfor aa suburban
suburban
network
network with 28 customers (see Section 4.1). The distributions for no-load voltage and consumption
with 28 customers (see Section 4.1). The distributions for no-load voltage and consumption
are
are the
the same
same as
as used
used for
used for the
for the rural
the rural network.
rural network. The
network. The results
results are
are shown
shown in in Figures
Figures 888 and
and 9.
and 9. The
9. The hosting
hosting
capacity,
capacity, using
using the
the same
same values
values as
as before,
before, equals
equals three
three customers
customers (see
(seeFigure
Figure
capacity, using the same values as before, equals three customers (see Figure 9). 9).
9).

Figure
Figure 8.
8. Probability distribution (cumulative distribution function) for
for the highest voltage (worst-
Figure 8. Probability distribution
Probability (cumulative
distribution distribution
(cumulative function)
distribution function)thefor
highest voltage voltage
the highest (worst-
case
case voltage)
voltage) for
for increasing
increasing amount
amount of
of single-phase
single-phase connected
connected solar
solar power
power in
in the
the 28-customer
28-customer
(worst-case voltage) for increasing amount of single-phase connected solar power in the 28-customer
suburban network.
suburban network.
network.
suburban
Energies 2017, 10, 1325 11 of 28
Energies 2017, 10, 1325 11 of 28

Figure 9. 90th percentile of the worst-case overvoltage as a function of the number of customers with
PV in the 28-customer suburban network.

To illustrate how
To illustrate how different
different parameters
parameters affect
affect the
the outcome
outcome of of the
the calculation,
calculation, aa sensitivity
sensitivity analysis
analysis
has
has been done. The results of this are shown in Table 1. The hosting capacity turns out
been done. The results of this are shown in Table 1. The hosting capacity turns out to
to be
be most
most
sensitive
sensitive toto the
the percentile
percentile used
used andandto tothe
theproduced
producedpower
powerper perinstallation.
installation.The
Thepercentile
percentileusedused is is
a
matter
a matterofofhow
how much risk the
much risk thenetwork
networkoperator
operatoris is willing
willing or even
or even allowed
allowed to take
to take in theinplanning
the planning
stage.
stage. This remains largely an un-explored but very important area. The value
This remains largely an un-explored but very important area. The value of the produced power of the produced power
used
used
in thein the calculation
calculation depends depends
on the onsizethe
of size of the individual
the individual installations
installations andspread
and on the on theinspread in tilt
tilt direction
direction
and angle and anglethe
between between the installations.
installations. Some specific Some specific
studies, withstudies, with more
more detailed models detailed
includingmodels
this,
including this, are needed for a more accurate estimation of the hosting
are needed for a more accurate estimation of the hosting capacity. See Section 4.7.6. capacity. See Section 4.7.6.

Table 1. Sensitivity
Table 1. Sensitivity Analysis
Analysis of
of the
the Hosting
Hosting Capacity.
Capacity.
Case Parameter Default Value New Value Hosting capacity
0Case Parameter Default Value New Value Hosting Capacity
3 customers
10 Produced power per installation 6 kW 7 kW 23 customers
customers
1 Produced power per installation 6 kW 7 kW 2 customers
2 5 kW 6 customers
2 5 kW 6 customers
33 44kW
kW 11
11 customers
customers
44 Percentile
Percentile 90th
90th 95th
95th 11 customer
customer
55 85th
85th 55 customers
customers
66 75th
75th 8 customers
8 customers
7 load per customer per phase [0, 250 W] [0, 150 W] 3 customers
78 load per customer per phase [0, 250 W] [0, 150 W]
[0, 350 W]
33 customers
customers
89 No-load voltage [238 V, 242 V] [0, V,
[240 350
244W]
V] 32 customers
customers
910 No-load voltage [238 V, 242 V] [240 V,243
[239 V, 244V]V] 22 customers
customers
1011 [237 V,
[239 V,241
243V]V] 24 customers
customers
12 [236 V, 240 V] 6 customers
11 [237 V, 241 V] 4 customers
12 [236 V, 240 V] 6 customers
The hosting capacity turns out to be most sensitive to the percentile used and to the produced
The
power per hosting capacity
installation. turns
The out to be
percentile most
used is sensitive
a matter ofto the
howpercentile
much risk used
the and to theoperator
network produced is
power per
willing installation.
or even allowedThe percentile
to take used is astage.
in the planning matter of remains
This how much risk an
largely theun-explored
network operator
but veryis
willing
importantor even
area.allowed
The valueto take in the
of the planning
produced stage.used
power Thisinremains largely an
the calculation un-explored
depends on thebut very
size of
important area.installations
the individual The value ofand the on
produced power
the spread used
in tilt in the calculation
direction and angledepends
betweenon thethe size of the
installations.
individual
Some specificinstallations andmore
studies, with on the spread models
detailed in tilt direction
including and angle
these between the
parameters, areinstallations.
needed for a Some
more
specific studies, with more detailed models including
accurate estimation of the hosting capacity. See also Section 4.7.6.these parameters, are needed for a more
accurate estimation of the hosting capacity. See also Section 4.7.6.
Energies 2017, 10, 1325 12 of 28
Energies 2017, 10, 1325 12 of 28
4.6. Single-Phase Electric Vehicle Chargers in the Suburban Grid
The same methodology
4.6. Single-Phase Electric VehicleasChargers
before has been
in the used toGrid
Suburban study the risk of undervoltage due to large
numbers of single-phase EV chargers. Charging may take place any time of the day and any time of
The Therefore,
the year. same methodology as before
lower no-load has been
voltages used to
and higher study the risk
consumption of undervoltage
should be considereddue to when
than large
numbers of single-phase EV chargers. Charging may take place any time of the
studying the risk of undervoltage due to PV. The following values have been used for the day and any time of
the year. Therefore, lower no-load voltages and higher consumption should be considered than when
calculations:
studying the risk of undervoltage due to PV. The following values have been used for the calculations:
i) Active-power consumption: uniformly distributed between 1500 W and 3000 W.
i) Active-power consumption:
ii) No-load voltage: uniformly
uniformly distributed
distributed between
between 230 V 1500 W and
and 234 V. 3000 W.
ii) No-load voltage:
iii) Charging uniformly
power: 2300 W,distributed
3680 W, between 230 5750
4600 W and V andW234 V.
(corresponding to 10 A, 16 A, 20 A
and power:
iii) Charging 25 A). 2300 W, 3680 W, 4600 W and 5750 W (corresponding to 10 A, 16 A, 20 A and 25 A).
The resulting
The resulting performance
performance index
index is
is shown
shown inin Figure
Figure 1010 as
as function
function of
of the
the number
number of
of EV
EV chargers
chargers
that are
that are drawing
drawingcurrent
currentatatthe
thesame
sametime,
time,for
for 5760
5760 WW perper charger.
charger. TheThe hosting
hosting capacity
capacity equals
equals ninenine
EV
EV chargers. Assuming 4600 W per charger results in a hosting capacity of 14 chargers
chargers. Assuming 4600 W per charger results in a hosting capacity of 14 chargers (not shown here).(not shown
here).
For ForW3680
3680 and W and
2300 W 2300 W per charger,
per charger, 22 and 2822chargers,
and 28 chargers, respectively
respectively can be at
can be operating operating
the sameattime
the
same time
without thewithout the undervoltage
undervoltage limit being limit being exceeded.
exceeded.

Figure 10. 10th percentile of the lowest voltage (worst-case voltage)

Figure voltage) as
as a function of the number of EV
chargers in
in aa 28-customer
28-customer suburban
suburban network.
network. A consumption of 5750 W (25 A) per charger has been
used in
in the
the calculations.
calculations.

4.7. Discussion
The subsections below present some points of discussion,
discussion, including the need for further work
study. The discussion text refers only to the impact of new production,
resulting from the presented study.
discussion is
but a similar discussion is possible
possible for
for new
new consumption.
consumption.

4.7.1.
4.7.1. Reactive Power
In this
this study,
study,only
onlythe
the active
active power
power hashas
beenbeen included.
included. The reason
The reason for thisfor thisthe
is that is reactive-
that the
reactive-power consumption of modern domestic customers is small and that the X/R
power consumption of modern domestic customers is small and that the X/R ratio with the supply ratio with the
supply terminals
terminals in a low-voltage
in a low-voltage network
network is small.
is small. ForFor connection
connection ofofinstallations
installationstoto medium-voltage
networks, e.g., solar
solar parks
parks and
and wind
wind turbines,
turbines, the
the reactive
reactive power
power needs
needs toto be
be considered.
considered.

4.7.2.
4.7.2. Probability
Probability Distributions
Distributions
The
The study
studypresented herehere
presented usedused
uniform distributions
uniform for the no-load
distributions for thevoltage andvoltage
no-load the consumption
and the
during critical hours. More studies, based on measurements as well as on simulations, are needed
consumption during critical hours. More studies, based on measurements as well as on simulations,
Energies 2017, 10, 1325 13 of 28

to find out what are reasonable distributions for these input variables. More advanced stochastic
load models exist (for example [40]) and further development and application of those is important.
There is, however, a risk of over-sophistication here, where the other uncertainties dominate and make
that such advanced models have no higher accuracy than simplified models. With advanced models,
there is also the risk that the study loses generality. The development of appropriate load models is
an essential part of hosting-capacity studies, next to the development of appropriate models for new
production and consumption.
In the study, it was assumed that the no-load voltage was independent on the amount of customers
with PV. It requires further study to find out to which extent this no-load voltage is affected by solar
power elsewhere in the same medium-voltage network. Some positive correlation can be expected
here: when the number of customers with PV increases in a low-voltage network, it is also likely to
increase in neighbouring low-voltage networks supplied from the same medium-voltage feeder.

4.7.3. Time Series

The study presented here used probability distribution functions together with a fixed value of
the solar-power production. An alternative, commonly used in other studies, is to use time series
for both production and consumption. A discussion is needed on the advantages and disadvantages
of these two methods. In that discussion, the main comparison should be between time series
based on measurements and probability distributions or time series obtained from stochastic models.
With the former approach, all the time series should be obtained over the same or an equivalent
measurement period. The time series should be sufficiently long to cover all combinations (maximum
and minimum production, maximum and minimum consumption, but even medium values that
could combine towards a worst case). This requires data collection over several years, to include
year-to-year variations.
The main advantage of using measured time series is that these are closest to reality and therefore
include all phenomena and correlations as they occur in reality. An example is the relation between
solar power production and electric heating or cooling [41].
Comparison studies are needed, between measured time series, probability distributions, and
time series obtained from more advanced stochastic models. Differences between the results from the
different approaches do however not always imply that one method would be superior compared
to another.
The approach presented here can be combined with the use of (measured or generated) time
series. Instead of taking one value for consumption and no-load voltage for each spread of the PV
panels over the customers and phases, time series are used for each of such spreads. This will bypass
the discussion on when the production is expected to be highest (Section 4.7.6), but it will require
much more data and calculations.
The voltage-quality regulations in many countries set limits to the 95th percentile of the rms
voltage calculated over a 10-min window. This value shall not exceed the overvoltage limit, typically
at 110% of nominal voltage. During the planning, the distribution company may still decide to use the
highest voltage as a criterion. Alternatively, the 95th percentiles can be used for planning. The plots
in Figure 3 and similar would in that case have to show the distribution of the 95th percentile of the
voltage for random customers and phases with PV. The use of time series would be a possible choice;
but not necessarily, time series for the whole year would be needed. Those time series can be limited to
periods with high or low production and/or consumption; for example around noon during summer.
Alternatively, the estimated values (i, ii and iii) in Section 3 can be adjusted (see Section 4.7.2).

4.7.4. Need for Data Collection

Much of the work towards further developing the hosting-capacity approach requires measurement
data. The use of measured time series obviously requires large amounts of data. The choice of probability
Energies 2017, 10, 1325 14 of 28

distribution for the consumption and the development of more advanced load models is also not
possible without significant amounts of data available.
Such data might be available to the network operator, for example in the form of hourly metering.
However, the data is in most cases not available to universities or research institutes that work on
model development. There is no direct solution to this dilemma as this involves consumption patterns
from individual domestic customers with important privacy implications.
Data collection on consumption and consumption patterns for many domestic customers should
however still be pursuit. One way or the other, such data should become available for research and
education. The set of test feeders, some with load data, collected by [42] is an appropriate platform for
making such data available.

4.7.5. Generality of the Results and of the Method

The results of the study presented here are not valid beyond the specific two networks studied,
and even for those only under the assumptions presented. The example’s only aim is to illustrate the
method. Network operators should use data from their own networks to estimate the hosting capacity
as part of their distribution-system planning.
The calculations used here were performed using Matlab only, but any other power-system
analysis package can be used for this. In fact, several network operators are developing tools using
such packages to estimate the hosting capacity and to create hosting-capacity maps.
Although the specific results are only valid for the studied networks, the method itself has
a broader applicability. The method should be applied to different low and medium-voltage networks,
to find out how general the results are, but also to evaluate the broader applicability of the method.
The two example networks used here are typical Swedish low-voltage networks, dimensioned
to accommodate electric heating. This will result in a higher hosting capacity than for grids only
dimensioned for non-electric domestic consumption. The approach should be applied to networks in
countries without electric heating, like in the more southern parts of Europe. Both networks, like all
Swedish distribution grids, are three phase all the way down to the domestic customer. Two-phase
and three-phase equipment is common with domestic customers in Sweden. The approach should be
applied to networks dominated by single-phase laterals, like in North America.
The consumption of domestic customers in Sweden is rather constant, with mainly a small
downward trend due to increased energy efficiency. This allows the use of a “background consumption”
based on measurements with the new production or consumption added to this. This approach is not
possible for grids in developing countries where load growth could be significant.

4.7.6. Production per Installation during the Worst Case

In the study presented here, a fixed production per PV installation during the worst-case was
used. It was shown from a sensitivity analysis (Table 1) that this value has a big impact on the obtained
value for the hosting capacity.
Studies are needed to determine how to get a good model for the production per installation
during those hours of the year that the highest production can be expected. One of the questions that
has to be answered is, “what are the hours of the year during which the production from solar may be
high?” The answer to this question depends for example on the spread of roof top directions. When all
rooftops face south, the panels will produce the same amount and the period of peak production will
be relatively short. When there is a spread in rooftop direction, the period of expected peak production
will be longer but the peak will be smaller. Both measurements and simulations are needed to answer
this question.
Instead of a fixed value for the production during the worst case, a stochastic model could also be
considered here. The stochastic element is again not in the variation of production with time, but in
the uncertainty of the contribution of an individual panel to the worst-case situation.
Energies 2017, 10, 1325 15 of 28

4.7.7. Choice of Performance Indices and Limits

An essential discussion in hosting capacity studies concerns the choice of performance indices.
This discussion started soon after the introduction of the term for the integration of distributed
generation. A subject heavily discussed initially was the choice of the appropriate index to quantify
the performance of the supply, for example the highest 10-min rms voltage or the 95th percentile of the
3-s rms voltages. This is largely a regulatory issue. More recently, and during the study presented here,
the discussion is moving towards the choice of indices for planning under uncertainty. The sensitivity
study (Table 1) showed that the percentile value has a big impact on the obtained hosting capacity.
The choice of percentile value is strongly related to the amount of risk carried by the different
stakeholders. Important input to the choice of percentile values is who carries this risk and what the
possible consequences are. The smaller the consequences, the higher the risk that can be taken.
The selection of the percentile values (and risk management in general) is not a sole
power-engineering issue, but it is still very important. This is where economics, social aspects,
legal and regulatory aspects, politics and even psychological aspects have to be included in the studies.
A new line of interdisciplinary research is needed to address this.

5. Other Phenomena
Section 4 illustrates several aspects of the hosting-capacity approach, through overvoltage and
undervoltage. These are however not the only phenomena that can set the hosting capacity (i.e., can
set limits to the amount of new production or new consumption that can be connected). Several
other phenomena are discussed in the forthcoming sections. As of yet, there is no complete list of
phenomena and indices for hosting-capacity studies. An attempt at creating such a list is presented
in [43]. With reference to Figures 1 and 2, calculating the hosting capacity requires the following tools
and information:

i) A generally accepted performance index.

ii) A limit for the performance index that forms a border between “acceptable performance” and
“unacceptable performance”.
iii) A method for calculating the value of this index, either deterministically or in a stochastic way, as
a function of the amount of new production or consumption.

These three requirements will be used in the forthcoming sections to discuss the hosting-capacity
approach for different phenomena. In those sections, like in Section 4, the aim is to strike a balance
between the need for accuracy on one hand and the availability of data and models on the other hand.

5.1. Overcurrent

5.1.1. Performance Indices

Excessive currents (overcurrent) lead to excessive heating with too high temperatures as a result.
As this is a thermal issue, the rms current is the obvious choice as base for performance indices. As
voltage variations are normally small, the apparent power can be used instead. If reactive power is
small, active power can be used instead of apparent power.
Methods for calculating currents through the grid are very similar to methods for calculating
voltages. In fact, a load-flow calculation will result in both voltages and currents. When considering
them in hosting-capacity studies, some differences need to be considered. The first difference concerns
the importance of the phenomenon for the performance of the grid. In [2] and [44], a distinction is
made between primary and secondary aims of the power system. In the same way, a distinction
can be made between “primary performance indices” and “secondary performance indices” for the
hosting-capacity approach. Voltage magnitude would be a primary performance index: something
that matters directly to the network users. The current through for example a transformer is however
not of direct concern for the network users; it is a secondary performance index. The overloading of a
Energies 2017, 10, 1325 16 of 28

component will quickly result in an interruption for all network users downstream of the overloaded
component (either because that component fails or because the protection removes the component to
avoid its failure). Avoiding overloading is thus also in the interest of the network user. The probability
of an interruption due to transformer overloading would be a primary performance index.
The second difference is in the limit values to be used in the hosting capacity studies. The actual
values for current can be obtained in similar ways as before, through “after diversity maximum
production”, “after diversity minimum consumption”, etc. The challenge lies in the choice of
maximum-permitted-value of, for example, the current through the transformer. For voltage-magnitude
variations, the 10-min rms value is defined in standards and regulation, so that the choice becomes easy.
The window over which the value should be calculated depends on the thermal time constant of
the cable, line or transformer under study. Information on this can be obtained, for example, from the
increasing volume of works on dynamic rating [45]. Here it should be considered that much of the
work on thermal time constants is directed towards short circuits where adiabatic temperature rise can
be considered. For the lesser overloads that are part of hosting capacity studies, this assumption would
likely lead to an underestimation of the hosting capacity. From the literature [46–48], time constants
between minutes and hours were found. A 10-min value would be a good compromise, given the
above range of thermal time constants. Nevertheless, when only 1-hour values are available (e.g., from
hourly metering) those also seem to be reasonable.

5.1.2. Limits
In case apparent power or active power is used for the performance index, a margin is appropriate
to compensate for the incompleteness in the model. For example, a 10% reduction in limit could be
used to compensate for the possible 10% reduction in voltage when apparent power is used instead
of rms current. This reduction in limit corresponds mathematically to the assumption that voltage,
active power and reactive power are stochastically independent. A more complete model, supported
by more complete measurement data, will typically result in an increase in hosting capacity, as was
illustrated for a simple case in [49]. With many hosting capacity studies, the more data is available, the
less safety margins are needed, and the higher the hosting capacity.

5.1.3. Calculation Methods

The calculation of the currents through a cable, line or transformer, with increasing levels of new
production or consumption, is straightforward. The new current is added, in the complex plane, to
the existing current. Stochastic methods can be used in the same way as before: a fixed limit for the
maximum-permissible current has to be decided, corresponding to the 110% and 90% limits used for
the studies in Section 4. An example of such a study is given in Section 5.1.4. Alternatively, a detailed
thermal model of the line, cable or transformer can be used together with time series of production and
consumption. Many studies use such time series and compare the resulting currents with a maximum
current value, e.g., [50].

5.1.4. Planning Example

To illustrate the use of the hosting-capacity approach in distribution, assessing the risk
of transformer overload, a similar example as in Section 4 is presented here. This example
concerns a 500-kVA transformer supplying 83 customers. When all customers would have a
single-phase-connected PV installation (6 kW injected power), they would all together produce 500 kW.
When equally distributed over the three phases, this would exactly correspond to the transformer
rating. Note that reactive power has not been considered here, partly to simplify the calculations, but
also because its impact is limited and because reactive-power consumption from domestic customers
is small. For an actual planning study, it is recommended to consider the reactive power and even
its possible changes in the future. The results are shown in Figures 11 and 12. Figure 11 gives the
probability distribution of the highest single-phase current through the transformer. The consumption
Energies 2017, 10, 1325 17 of 28

per phase
Energies has again been assumed uniformly distributed between 0 and 250 W. The current17increases
Energies 2017,
2017, 10,
10, 1325
1325 17 of
of 28
28
when more customers install solar power. However, even when 40 (out of 83) customers have
solarcurrent
power,increases
current when
single-phase
increases more
more customers
when connected, install
install solar
the probability
customers power.
solarthat the However,
power. transformer
However, even
even when
will 40
40 (out
(out of
of 83)
be overloaded
when is still
83)
customers
small. have solar power, single-phase connected, the probability that the transformer will be
verycustomers have solar power, single-phase connected, the probability that the transformer will be
overloaded
overloaded is
is still
still very
very small.
small.

Figure 11. Probability distribution (cumulative distribution function) of the highest single-phase
Figure
Figure 11. 11. Probability
Probability distribution(cumulative
distribution (cumulative distribution
distributionfunction)
function)of of
thethe
highest single-phase
highest single-phase
current
current through
through the
the distribution
distribution transformer,
transformer, with
with increasing
increasing number
number of
of customers
customers with
with single-phase
single-phase
current through the distribution transformer, with increasing number of customers with single-phase
connected
connected PV.
connected PV.PV.

Figure 12. Four

Figure different percentiles (50th: red star; 75th: green
green circle;90th:
90th: blue plus; 95th: black
Figure 12.
12. Four
Four different
different percentiles
percentiles (50th:
(50th: red
red star; 75th:
75th: green circle;
circle; 90th: blue
blue plus;
plus; 95th:
95th: black
black
triangle)
triangle) for the current through the transformer, as a function of the number of customers (out of 83) 83)
for
triangle) the
for current
the through
current through the
thetransformer,
transformer, as a
a function
function of
of the
the number
number of of customers
customers (out(out
of of
83)
withwith
with single-phase
single-phase
single-phase connected
connected
connected PV.
PV.
PV.

For the
the application of the
the hosting-capacity approach, it
it is again
again necessary to define
define aa
For For application
the application of theofhosting-capacity
hosting-capacity approach,
approach, it is again isnecessary necessary
to definetoa performance
performance
performance index and a corresponding
index and a corresponding limit.
limit. For this
For this example,
example, four different
fourpercentile percentile
different percentile values (50th,
values75th,
(50th,90th
index and
75th,
a corresponding limit.used
For asthis example, four different values (50th,
75th, 90th and 95th) have been used as indices, with the (single-phase) transformer rating as a limit.
90th and 95th) have been indices, with the (single-phase) transformer rating as a limit.
and The
95th) haveisbeen used Figure
as indices,For with the (single-phase) transformerPV, rating current
as a limit. Theis result is
The result
result is shown
shown in in Figure 12.
12. For upup to
to about
about five
five customers
customers withwith PV, the the current index
index is notnot
shown in Figure
affected. 12. For up to about five customers with PV, the current index is not affected. For low
affected. For
For low
low amounts
amounts ofof PV,
PV, the
the highest
highest transformer
transformer loading
loading occurs
occurs for
for maximum
maximum load load and
and not
not
amounts
for of PV, the highest transformer loading occurs for maximum
for maximum production. Here it is important to realize that “maximum load” corresponds to
maximum production. Here it is important to realize that “maximum load
load” and not
correspondsfor maximum
to the
the
production.
period ofHere
period of the
the day it isand
day important
and year
year when to realize
when highestthat
highest “maximum
solar
solar productionload”
production can
can bebecorresponds
expected.
expected. This to the
This is period
is not
not in
in any
any ofway
the day
way
and related
related to
to the
year when highest
thehighest annual
highestsolar
annual consumption.
production
consumption. can be expected. This is not in any way related to the highest
annual consumption.
Energies 2017, 10, 1325 18 of 28

From Figure 12, the hosting capacity is shown to depend on the percentile value, i.e., on the
amount of risk that the network operator is willing and allowed to take. The hosting capacity ranges
from 63 (when using the 95th percentile) up to 76 (50th percentile). The impact of the percentile value
on the hosting capacity is less than for overvoltage (Table 1).

5.2. Fast Voltage Magnitude Variations

Fast voltage magnitude variations occur because of fast variations in production or consumption.

5.2.1. Performance Indices

Standard indices exist for the fastest voltage magnitude variations; at time scales less than one
minute. The short-term and long-term flicker severity (Pst and Plt, respectively) are defined in IEC
61000-4-15; IEC 61000-4-30 gives a definition of (individual) rapid voltage changes. Both definitions
are however strictly measurement based, which especially for flicker severity requires detailed models.
Incandescent lamps, which have been the base for the flicker-severity indices, are replaced by
other types of lamps in most countries. The flicker-severity indices can no longer be considered as
primary performance indices. Their future role as secondary performance indices (of importance to
the network operator but not of direct importance to the network user) remains unclear.
For the time scale between 1 s and 10 min (the lower limit for standards on slow voltage magnitude
variations in most countries) no standardized or generally accepted indices exist. An index referred to
as “very-short variations”, was proposed in 2005 [51,52], but received only limited following [53–59].
However, the need for performance indices in this range of time scale remains big: this is where the
main impact of fast variations in production with solar-power installations will be, as was quantified
among others by [60].

5.2.2. Limits
Limits exist for flicker severity and for the number of rapid voltage changes. No limits exist for
voltage magnitude variations in the time scale between 1 s and 10 min.

5.2.3. Calculation Methods

Three different phenomena were mentioned in Section 5.2.1, all of which require different methods
for calculation. Flicker severity requires either time series with very high time resolution (for example
20 ms) or the use of simplified aggregation rules for example as proposed in IEC/TR 61000-3-7.
For rapid voltage changes, simple voltage calculations (using only the source impedance at the
point of connection or at point of common coupling) are sufficient to obtain the step in voltage due to
a step in current. The latter can be the start of charging of an electric vehicle but also the unnecessary
tripping of a PV installation due to its anti-islanding protection.

5.3. Voltage Unbalance

Voltage unbalance occurs due to the connection of large single-phase devices; both
single-phase-connected PV and electric car chargers fall in this category.

5.3.1. Performance Indices

The ratio between negative-sequence and positive-sequence voltage is used as performance
index in both IEC and IEEE standards. As the magnitude of the positive-sequence voltage shows
limited variation, the negative-sequence voltage can also be used as an index. Next to that, IEEE
and NEMA define some additional indices including the difference between highest and lowest line
voltage. The different IEC, IEEE and NEMA definitions, all referred to as “unbalance”, are compared
in [61–63] where it for example is shown that different definitions can give rather different values for
the unbalance.
Energies 2017, 10, 1325 19 of 28

The negative-sequence voltage is a useful index to quantify the impact of unbalance on three-phase
rotating machines directly connected to the grid. The impact of unbalance on such devices is a thermal
issue, so that 10-min values are appropriate.
For machines connected through a three-phase rectifier, like adjustable-speed drives, and for
other equipment connected through a three-phase converter, the difference between the line voltages
is a better index. This difference results in current unbalance for three-phase converters that in
turn can result in unwanted tripping of the converter [64]. As shown in [62] this value is 87% to
101% of the absolute value of negative-sequence voltage, depending of the phase angle of the latter.
As this is a protection issue, a value over a much shorter time scale is needed, like a one-second or
three-second value.

5.3.2. Limits
For the negative-sequence unbalance (the IEC definition), a limit of 2% holds for low-voltage
networks in many countries. See [65] for an overview of regulatory limits in European countries.
Strictly speaking, the indictor is defined as the ratio between negative and positive-sequence voltage.
When the calculations give the negative-sequence voltage (or when nominal positive-sequence voltage
is assumed) a correction might have to be made for the limit. Assuming that the positive-sequence
voltage can be as low as 90% of nominal, and assuming that negative and positive-sequence voltage
are stochastically independent, the limit has to be reduced from 2% to 1.8%. There are no limits based
on the IEEE and NEMA definitions of unbalance. When 3-s values are used instead of 10-min values,
a higher limit than the IEC limit of 2% seems appropriate.

5.3.3. Calculation Methods

The negative-sequence transfer impedance matrix is used in [39] to calculate the increase in
negative-sequence voltage in a low-voltage network with increasing number of single-phase-connected
PV installations. The negative-sequence impedance of lines, cables and transformers is equal to their
positive-sequence value. That can also be generally assumed for the source impedance of public
medium-voltage networks. For industrial medium-voltage networks, large rotating machines might
result in a lower value for the negative-sequence than for the positive-sequence source impedance.
The presence of three-phase equipment in the low-voltage network may have to be considered as
well in the transfer-impedance matrix. The presence of three-phase equipment, like variable-speed heat
pumps (common in Sweden), results in a reduction of the negative-sequence transfer impedance and
thus in an increase of the hosting capacity. For a planning study, a value or range of values has to be
estimated for three-phase equipment that is connected during hours with high amount of production
from solar power. In [39] it was assumed that this could be a very small amount, so that its impact on
negative-sequence impedance could be neglected. This assumption may result in an underestimation
of the hosting capacity.
In [39] the same networks were used as in Section 4. That allows a comparison of the results.
The hosting capacity for unbalance, assuming a 1.5% limit for the negative-sequence voltage and
the 90th percentile as performance index, was estimated as 3 customers for the 6-customer network
and 26 customers for the 28-customer network. The results from the overvoltage studies were: two
customers for the 6-customer network (from Figure 4) and up to 22 customers for the 28-customer
network (from Table 1).
Important for a complete picture of the hosting capacity is to consider the background voltage
unbalance, i.e., the voltage unbalance without connection of any new production or consumption.
Here it is important to consider that negative-sequence voltage is a complex quantity, consisting
of magnitude and phase angle. During power-quality measurements, the phase angle of the
negative-sequence voltage is normally not recorded. This is partly because there is no measurement
definition of this angle available.
Energies 2017, 10, 1325 20 of 28

When the NEMA/IEEE definition of unbalance is used, the negative-sequence transfer impedance
is not sufficient for the calculations. Either the complex phase voltages should be used; or separate
impedances for positive, negative and zero-sequence components. The latter allows the incorporation
of the impact of three-phase-connected equipment on the unbalance. In addition, information on
background unbalance may be hard to obtain and require dedicated measurement campaigns.

5.4. Harmonic Voltage Distortion

Harmonic voltage distortion occurs because the current injected by the device is not sinusoidal.
The bigger the device, the bigger the impact is of even a small amount of waveform distortion.
Even when the relative emission (in percent of rated current) is small, the total impact on the grid
can still be significant. With the connection of multiple devices, both the transfer impedance and
aggregation rules should be considered.

5.4.1. Performance Indices

Standard indices are defined for each of the individual harmonics and interharmonics, and for
total harmonic distortion in IEEE 519, IEC 61000-4-7 and IEC 61000-4-30. Normally, only 10-min
values are considered as the impact of harmonics is considered a thermal phenomenon. However,
for power-electronic converters and for certain types of protection of other equipment, unwanted
protection operation can result from high harmonic or interharmonic distortion. Values obtained over
shorter periods, like 1 or 3 seconds, should be used to study such impacts.
In IEC 61000-4-7, both groups and subgroups are defined for harmonics up to order 40 (i.e., 2 kHz
in a 50 Hz system) and interharmonics. However, in IEC 61000-4-30 it is stated that the harmonic and
interharmonic subgroups should be used when quantifying power quality. Therefore, those are also
most appropriate for hosting-capacity studies.

5.4.2. Limits
The selection of limits for use in hosting-capacity studies is not obvious, despite the presence of
a range of limits (“objective values”) in national and international standards. Voltage characteristics
are given in EN 50160; compatibility levels in IEC 61000-2-2; planning levels can be selected by each
network operator themselves, but most of them follow the indicative planning levels from IEC/TR
61000-3-6. Especially the latter deviate a lot from the other ones and it is not obvious which limits
should be used.
One approach is to consider a hosting-capacity study as a planning study, in which the planning
levels would be appropriate. However, in more and more countries are the planning levels replaced by
the limits set in local regulations. These are in turn, at least in Europe, strongly based on the voltage
characteristics in EN 50160.
The final decision on the choice of limits, as many other choices in a hosting-capacity study, is part
of the risk management between the different stakeholders. A complete hosting capacity study should
therefore also consider a mapping of the risks as carried by the different stakeholders. Such a mapping
is beyond the scope of this paper.

5.4.3. Calculation Methods

The choice of performance indices and limits is relatively straightforward for harmonics. However,
the main barrier is the lack of appropriate calculation models, especially when considering low-voltage
and medium-voltage networks.
The basic approach used in the literature is the source impedance or the transfer impedance
matrix [66–70]; for harmonic frequencies instead of for the negative-sequence voltage as in the case
of unbalance [39] or the equivalent impedances for single-phase loads as in the case of overvoltage
due to single-phase PV. Once the injected harmonic currents and the impedance values are known,
the harmonic voltage distortion can be calculated as a function of the amount of new production
Energies 2017, 10, 1325 21 of 28

or consumption. Obtaining those values is however not easy and with the current state of the art
no generally accepted method is available. This was illustrated by several studies on the impact of
compact fluorescent lamps and LED lamps on the waveform distortion. Simulation studies concluded
that the voltage and current distortion would increase [71,72]; measurements showed however that
this was not the case and that the distortion was simply not impacted [73–76]. Acceptable harmonic
models exist for the components of the power system (cables, lines and transformers) but several
barriers remain before a complete model is available for use in hosting-capacity studies:

i) The emitted harmonic current is impacted by the voltage distortion at the terminals of the
equipment. This phenomenon has been observed early for diode rectifiers like the ones used in
televisions [77] and was explained and quantified by a model in [78]. That impact was shown to
be limited and the emission for a clean supply voltage was in most cases the worst case and the
one reasonably useable for harmonic studies. With modern power-electronic equipment, with
an actively controlled interface, there are observations showing the contrary, the emission for a
distorted supply voltage can be much higher than for a sinusoidal supply [79–82].
ii) No suitable models exist for the customers connected to a low-voltage network. Some recent
studies [83–85] show that the customer model is the main determining factor for the resonant
frequency and thus for the harmonic transfer impedance.
iii) The connecting of new production or consumption will change the impedance of the low-voltage
customer and therewith the harmonic transfer impedance. There exist no acceptable models
for new devices like PV inverters or EV chargers. Some measurements are presented in [86–89]
but there are big variations between manufacturers and for future equipment guesses have to
be made.
iv) The statistical aggregation between different sources of harmonics is not known. This holds for
the aggregation between different new devices (e.g., between different PV inverters) but also
for the aggregation between the new devices and the background distortion. The aggregation
between individual wind turbines has been studied by some authors [90–92] but it is not known
if similar conclusions hold for PV inverters, EV chargers or other large low-voltage equipment
like heat pumps [22,71,93].

5.5. Supraharmonics
Supraharmonics (waveform distortion in the frequency range between 2 kHz and 150 kHz) are
injected by an increasing amount of devices connected to the grid. Supraharmonics are mainly due to
active switching in the grid-interface of the devices. The transfer and aggregation of supraharmonics
is significantly different from the transfer and aggregation of harmonics. To do a complete hosting
capacity study of supraharmonics is to date not feasible, simply because there are no established limits
or indices for distortion in this frequency range. This section will instead give a general description of
supraharmonics, what levels can be expected and how they are transferred through the grid.
Supraharmonics commonly originate from two sources: power-electronic converters and
transmitters of power line communication [21], the former being the focus here. Magnitude, frequency
and duration of the emission vary between different devices but come in three general types: constant
in magnitude and/or frequency over one cycle of the power system frequency; varying in magnitude
and/or frequency over one cycle of the power system frequency or having a transient character [94].
For household devices the emission is in most cases of the varying type, two examples can be seen in
Figure 13, where the Short Time Fourier Transform of a fluorescent lamp and a heat pump is shown.
The emission from the fluorescent lamp varies in frequency and in magnitude during 20 ms whereas
the emission from the heat pump varies only in amplitude as it appears and disappears four times
per cycle.
Energies 2017, 10, 1325 22 of 28
Energies 2017, 10, 1325 22 of 28

Figure 13. Supraharmonics from a fluorescent lamp (left) and from a heat pump (right).
Figure 13. Supraharmonics from a fluorescent lamp (left) and from a heat pump (right).

In most cases, supraharmonics do not propagate over long distances. Damping in cables is one
In most cases,
of the causes of this.supraharmonics
More importantly, do not propagate
other devices over long distances.
connected to the lowDamping
voltageinnetwork
cables is offer
one of a
the
lowcauses
impedanceof this.pathMore forimportantly,
these currents other
sodevices
that they connected
tend to to flowthemainly
low voltagebetween network
devices offer[95,96].
a low
impedance
However, itpath for feasible
is still these currents so that they tendcan
that supraharmonics to flow mainly
transfer between
through the devices
grid. In[95,96].
[97] it is However,
shown,
it is still feasible that supraharmonics can transfer through the grid.
through both measurements and simulations, that a resonance between the distribution transformer In [97] it is shown, through both
measurements and simulations, that a resonance between the distribution
and an 800 m long cable amplified a 35 kHz voltage component on the low-voltage side of the transformer and an 800 m
long cable amplified a 35 kHz voltage component on the low-voltage
transformer five times. To predict how the emission from an installation or device will transfer side of the transformer five times.
To predict
through thehowgridthe is emission from anof
difficult because installation or device
the dominating impactwillfrom
transfer throughTo
connected. thecorrectly
grid is difficult
predict
because
what is connected at a certain grid at any given moment in time would not be possible. at a certain
of the dominating impact from connected. To correctly predict what is connected
grid at any given
Many modern moment
householdin time wouldemit
devices not supraharmonics
be possible. to some extent. In [94] it is concluded
that Many
more modern
than halfhousehold devices emit
of the household supraharmonics
devices on the market to somehaveextent. In [94] supraharmonic
identifiable it is concluded
that more than half of the household devices on the market have
emission. There is a large diversity in magnitude and frequency between different devices, identifiable supraharmonic emission.
even if
There is a large diversity in magnitude and frequency between different
they are of the same type. For instance, measurements of about 80% of the types of EV chargers devices, even if they areonof
the same type. For instance, measurements of about 80% of the
the German market show that the switching frequency is between 9 and 100 kHz with a magnitudetypes of EV chargers on the German
market
betweenshow 8 mAthat andthe 1.8switching
A [98]. frequency is between 9 and 100 kHz with a magnitude between 8 mA
and 1.8TheA emission
[98]. from a PV inverter and a heat pump are shown in Figure 14. The dominating
emission is seen at from
The emission 16 kHz a PVfrom inverter and aand
the inverter heatatpump
18 kHz are shown
from in Figure
the heat pump14. Thethat
(note dominating
these are
emission is seen at 16 kHz from the inverter and at 18 kHz from the
just two examples, other PV inverters and heat pumps on the market will typically show a completely heat pump (note that these are
just two examples,
different behavior).other For PVthe inverters
measurementsand heat
seenpumps
on the onleft
the inmarket
Figure will
14,typically
the devices showare a completely
connected
different behavior). For the measurements seen on the left in Figure 14,
alone at the test site. For the measurements seen on the right, other devices are connected nearby; the devices are connected alonea
at
TVthe testto
close site.
theForPVthe measurements
inverter seen on the
and an induction right,
stove other
close by devices
the heatare connected
pump. Whennearby; a TV close
other devices are
to the PV inverter and an induction stove close by the heat pump.
connected to the same phase, the emission at 16 kHz and 18 kHz originating from the inverter and When other devices are connected
to
thethe same
heat pump phase, the emission
is increased, twoatand16 five
kHztimes
and 18 kHz originating
respectively. This from the inverter
indicates a resonant andfrequency
the heat pump close
is increased, two and five times respectively. This indicates a resonant
to 16 kHz or 18 kHz. The impact of neighbouring equipment on the emission level of supraharmonics frequency close to 16 kHz or
18 kHz. The impact of neighbouring
from an EV charger is discussed in detail in [99]. equipment on the emission level of supraharmonics from an EV
charger is discussed in detail in [99].
Energies 2017, 10, 1325 23 of 28
Energies 2017, 10, 1325 23 of 28

Figure 14. Supraharmonics from a PV inverter connected alone (upper left), the same inverter while
Figure 14. Supraharmonics from a PV inverter connected alone (upper left), the same inverter while
neighbouring devices are connected (upper right). A heat pump connected alone (lower left), the
neighbouring devices are connected (upper right). A heat pump connected alone (lower left), the same
same heat pump while neighbouring devices are connected (lower right).
heat pump while neighbouring devices are connected (lower right).
6. Conclusions
6. Conclusions
The concept of hosting capacity has been introduced as a transparent tool allowing an open
The concept
discussion of hosting
between capacity
different has been introduced
stakeholders with the asintegration
a transparent oftool allowing an
distributed open discussion
generation. This
between different stakeholders with the integration of distributed generation. This
transparency remains an important characteristic of the hosting-capacity approach also when it is transparency remains
an important
used characteristic
as a planning tool for of thenew
both hosting-capacity
production and approach also when it isasused
new consumption, as a planning
illustrated in this tool for
paper.
both new
Any production and
hosting-capacity studynewrequires
consumption, as illustrated
(directly or indirectly)in this paper.
three Any
parts: a hosting-capacity
performance index; studya
requires (directly or indirectly) three parts: a performance index; a corresponding
corresponding limit; and a method to calculate the value of the performance index as a function of limit; and a method
to calculate
the amount of thenew
value of the performance
production or consumption.indexFurther
as a function
work is ofneeded
the amount
towardsof new
almostproduction or
all of these
consumption.
before complete Further work is needed
hosting-capacity studies towards
can be almost
done. all of these before complete hosting-capacity
studies can be done.
A hosting-capacity-based planning approach has been presented in this paper. The approach
A hosting-capacity-based
requires a network model, limited planning inputapproach
data andhas been presented in
a Monte-Carlo this paper.toThe
simulation approach
address the
requires a network model, limited input data and a Monte-Carlo simulation to
uncertainties. The approach has been applied to overvoltage and undervoltage due to increasing address the uncertainties.
The approach
amounts haspower
of solar been applied to overvoltage
and electric-vehicle and undervoltage
chargers in low-voltage due to increasing
networks. amountsanalysis
A sensitivity of solar
power and
shows that electric-vehicle
the size of thechargers in low-voltage
PV inverters networks. A sensitivity
and the performance index have analysis
the mainshows that the
impact on size
the
of the PV inverters
hosting capacity. and the performance index have the main impact on the hosting capacity.
It is
It is shown
shown that,
that, with
with single-phase
single-phase connection
connection ofof PV,
PV, not
not only
only overvoltage
overvoltage but but also
also undervoltage
undervoltage
limits may
limits may be be exceeded.
exceeded. The The hosting-capacity
hosting-capacity values
values obtained
obtained from
from the
the case
case studies
studies cannot
cannot be be
generalized and applied to other low-voltage
generalized and applied to other low-voltage networks. networks.
For the
For the main
main impacts
impacts of of new
new production
production and and consumption,
consumption, overvoltage, undervoltage and
overvoltage, undervoltage and
overcurrent, the
overcurrent, the calculation
calculation tools
tools are
are available.
available. However,
However, suitable
suitable models
models to to describe
describe thethe existing
existing
situation in terms of voltage and current are missing. Different approaches are discussed
situation in terms of voltage and current are missing. Different approaches are discussed in the paper, in the paper,
but as of yet no method is the dominating one. Data gathering is an important step in the
development of such models.
Energies 2017, 10, 1325 24 of 28

but as of yet no method is the dominating one. Data gathering is an important step in the development
of such models.
For harmonics and interharmonics, acceptable calculation models remain missing and further
work is needed towards those. Measurements are needed to develop component models so that
harmonics and supraharmonics can be sufficiently accurately predicted for future grids. Generally,
further work is needed towards selecting appropriate performance indices and the corresponding
limits. This requires an interdisciplinary research effort.

Acknowledgments: This studies presented in Section 3 of this paper have been funded by a number of Swedish
network operators through the smart-grid program of Energiforsk, by Skellefteå Kraft and by Umeå Energi.
Some of the simulations shown in Section 3 were performed by Cecilia Karlsson as part of her final-year
project. The measurements referred to in Section 3 were performed by Anders Larsson, Martin Lundmark
and Mikael Byström.
Author Contributions: Both authors contributed to this publication; Math H. J. Bollen has been involved in the
hosting-capacity approach since the term was first coined in 2004; Sarah K. Rönnberg has been a contributor to
introductory parts of the paper; a discussion partner for the simulations presented in Section 3 and the main
author for Sections 5.4 and 5.5.
Conflicts of Interest: The authors declare no conflict of interest.

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